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Alpha ( ) See Type I error; Probability of incorrectly rejecting the null hypothesis—in most cases, it means saying a difference or correlation exists when it actually does not. Also termed alpha, Typical levels are 5 or 1 per cent, termed the .05 or .01 level, respectively Beta (β) Type II error;Probability of incorrectly failing to reject the null hypothesis—in simple terms, the chance of not finding a correlation or mean difference when it does exist.Also termed beta (β), it is inversely related to Type I error. The value of 1 minus the Type II error (1 - β) is defined as power. Bivariate partial correlation Simple (two-variable) correlation between two sets of residuals (unexplained variances) that remain after the association of other independent variables is removed Bootstrapping "An approach to validating a multivariate model by drawing a large number of subsamples and estimating models for each subsample. Estimates from all the subsamples are then combined, providing not only the ""best"" estimated coefficients (e.g., means of each estimated coefficient across all the subsample models), but their expected variability and thus their likelihood of differing from zero; that is, are the estimated coefficients statistically different from zero or not? This approach does not rely on statistical assumptions about the population to assess statistical significance, but instead makes its assessment based solely on the sample data. <div><div><div><div><div><div><div>Bootstrapping is a way to check if a model we made using data is a good one. We do this by creating lots of different versions of the model using different subsets of the data. Then, we compare all of the different versions of the model to see how much they vary. If the results from the different models are very different from each other, then it might mean that the model is not a very good one. But if the results are similar, it might mean that the model is a good one and the results are likely to be true for the whole population.</div><div>For example, let's say we want to know if taller people tend to weigh more than shorter people. We could use bootstrapping to check if our model that tries to predict a person's weight based on their height is a good one. To do this, we would create many different versions of the model using different subsets of the data (like drawing subsamples from a hat). Then, we would compare the results from all of the different versions of the model to see how much they vary. If the results are very different from each other, it might mean that our model is not a very good one. But if the results are similar, it might mean that our model is a good one and that taller people do tend to weigh more than shorter people.</div></div></div></div><div></div></div></div></div> " Composite measure summated scales;Method of combining several variables that measure the same concept into a single variable in an attempt to increase the reliability of the measurement through multivariate measurement. In most instances, the separate variables are summed and then their total or average score is used in the analysis. Dependence technique Classification of statistical techniques distinguished by having a variable or set of variables identified as the dependent variable(s) and the remaining variables as an independent. The objective is the prediction of the dependent variable(s) by the independent variable(s). An example is regression analysis. Dependent variable Presumed effect of, or response to, a change in the independent variable(s). Dummy variable Nonmetrically measured variable transformed into a metric variable by assigning a 1 or a 0 to a subject, depending on whether it possesses a particular characteristic. Effect size Estimate of the degree to which the phenomenon being studied (e.g., correlation or difference in means) exists in the population Independent variable Presumed cause of any change in the dependent variable. Indicator Single variable used in conjunction with one or more other variables to form a composite measure. Interdependence technique Classification of statistical techniques in which the variables are not divided into dependent and independent sets; rather, all variables are analyzed as a single set (e.g., factor analysis). Measurement error "Inaccuracies of measuring the ""true"" variable values due to the fallibility of the measurement instrument (i.e., inappropriate response scales), data entry errors, or respondent errors. " Metric data "Also called quantitative data, interval data, or ratio data, these measurements identify or describe subjects (or objects) not only on the possession of an attribute but also by the amount or degree to which the subject may be characterized by the attribute. For example, a person's age and weight are metric data. " Multicollinearity Extent to which a variable can be explained by the other variables in the analysis. As multicollinearity increases, it complicates the interpretation of the variate because it is more difficult to ascertain the effect of any single variable, owing to their interrelationships. Multivariate analysis Analysis of multiple variables in a single relationship or set of relationships Multivariate measurement Use of two or more variables as indicators of a single composite measure. For example, a personality test may provide the answers to a series of individual questions (indicators), which are then combined to form a single score (summated scale) representing the personality trait. Nonmetric data Also called qualitative data, these are attributes, characteristics, or categorical properties that identify or describe a subject or object. They differ from metric data by indicating the presence of an attribute, but not the amount. Examples are occupation (physician, attorney, professor) or buyer status (buyer, nonbuyer). Also called nominal data or ordinal data. Power Probability of correctly rejecting the null hypothesis when it is false; that is, correctly finding a hypothesized relationship when it exists. Determined as a function of (1) the statistical significance level set by the researcher for a Type I error ( ), (2) the sample size used in the analysis, and (3) the effect size being examined. Practical significance Means of assessing multivariate analysis results based on their substantive findings rather than their statistical significance. Whereas statistical significance determines whether the result is attributable to chance, practical significance assesses whether the result is useful (i.e., substantial enough to warrant action) in achieving the research objectives. Reliability Extent to which a variable or set of variables is consistent in what it is intended to measure. If multiple measurements are taken, the reliable measures will all be consistent in their values. It differs from validity in that it relates not to what should be measured, but instead to how it is measured. Specification error Omitting a key variable from the analysis, thus affecting the estimated effects of included variables. Summated scales Method of combining several variables that measure the same concept into a single variable in an attempt to increase the reliability of the measurement through multivariate measurement. In most instances, the separate variables are summed and then their total or average score is used in the analysis Treatment Independent variable the researcher manipulates to see the effect (if any) on the dependent variable(s), such as in an experiment (e.g., testing the appeal of color versus black-andwhite advertisements). Type I error Probability of incorrectly rejecting the null hypothesis—in most cases, it means saying a difference or correlation exists when it actually does not. Also termed alpha ( ). Typical levels are 5 or 1 percent, termed the .05 or .01 level, respectively. Type II error Probability of incorrectly failing to reject the null hypothesis—in simple terms, the chance of not finding a correlation or mean difference when it does exist. Also termed beta (β), it is inversely related to Type I error. The value of 1 minus the Type II error (1 - β) is defined as power. Univariate analysis of variance (ANOVA) Statistical technique used to determine, on the basis of one dependent measure, whether samples are from populations with equal means Validity Extent to which a measure or set of measures correctly represents the concept of study— the degree to which it is free from any systematic or nonrandom error. Validity is concerned with how well the concept is defined by the measure(s), whereas reliability relates to the consistency of the measure(s). Variate Linear combination of variables formed in the multivariate technique by deriving empirical weights applied to a set of variables specified by the researcher. All-available approach Imputation method for missing data that compute values based on all-available valid observations, also known as the pairwise approach. Boxplot Method of representing the distribution of a variable. A box represents the major portion of the distribution, and the extensions—called whiskers—reach to the extreme points of the distribution. This method is useful in making comparisons of one or more variables across groups. Censored data Observations that are incomplete in a systematic and known way. One example occurs in the study of causes of death in a sample in which some individuals are still living. Censored data are an example of ignorable missing data  Comparison group reference category; The category of a nonmetric variable that is omitted when creating dummy variables and acts as a reference point in interpreting the dummy variables. In indicator coding, the reference category has values of zero (0) for all dummy variables. With effects coding, the reference category has values of minus one (-1) for all dummy variables. Complete case approach Approach for handling missing data that computes values based on data from complete cases, that is, cases with no missing data. Also known as the listwise approach. Data transformations A variable may have an undesirable characteristic, such as non-normality, that detracts from its use in a multivariate technique. A transformation, such as taking the logarithm or square root of the variable, creates a transformed variable that is more suited to portraying the relationship. Transformations may be applied to either the dependent or independent variables, or both. The need and specific type of transformation may be based on theoretical reasons (e.g., transforming a known nonlinear relationship), empirical reasons (e.g., problems identified through graphical or statistical means) or for interpretation purposes (e.g., standardization). Dummy variable Special metric variable used to represent a single category of a nonmetric variable. To account for L levels of a nonmetric variable, L - 1 dummy variables are needed. For example, gender is measured as male or female and could be represented by two dummy variables (X1 and X2). When the respondent is male, X1 = 1 and X2 = 0. Likewise, when the respondent is female, X1 = 0 and X2 = 1. However, when X1 = 1, we know that X2 must equal 0. Thus, we need only one variable, either X1 or X2, to represent the variable gender. If a nonmetric variable has three levels, only two dummy variables are needed. We always have one dummy variable less than the number of levels for the nonmetric variable. The omitted category is termed the reference category. Effects coding Method for specifying the reference category for a set of dummy variables where the reference category receives a value of minus one (-1) across the set of dummy variables. With this type of coding, the dummy variable coefficients represent group deviations from the mean of all groups, which is in contrast to indicator coding. Heteroscedasticity homoscedasticity;When the variance of the error terms (e) appears constant over a range of predictor variables, the data are said to be homoscedastic. The assumption of equal variance of the population error E (where E is estimated from e) is critical to the proper application of many multivariate techniques. When the error terms have increasing or modulating variance, the data are said to be heteroscedastic. Analysis of residuals best illustrates this point. <div><div><div><div><div><div><div>Heteroscedasticity occurs when the variance of the error terms is not constant. Homoscedasticity occurs when the variance of the error terms is constant. This is important in multivariate techniques because it affects the application of these techniques. Heteroscedasticity can be detected by analyzing residuals.</div></div></div></div><div></div></div></div></div><div><div><div><div><div><div><div>The variance of error (also known as the variance of the residuals) is a measure of the dispersion of the residuals around the mean. It is important to have a constant variance because many statistical techniques assume that the variance is constant. If the variance is not constant, then the results of the analysis may be biased or unreliable.</div></div></div></div><div></div></div></div></div> Histogram "Graphical display of the distribution of a single variable. By forming frequency counts in categories, the shape of the variable's distribution can be shown. Used to make a visual comparison to the normal distribution " Homoscedasticity When the variance of the error terms (e) appears constant over a range of predictor variables, the data are said to be homoscedastic. The assumption of equal variance of the population error E (where E is estimated from e) is critical to the proper application of many multivariate techniques. When the error terms have increasing or modulating variance, the data are said to be heteroscedastic. Analysis of residuals best illustrates this point. Ignorable missing data Missing data process that is explicitly identifiable and/or is under the control of the researcher. Ignorable missing data do not require a remedy because the missing data are explicitly handled in the technique used. Imputation "Process of estimating the missing data of an observation based on valid values of the other variables. The objective is to employ known relationships that can be identified in the valid values of the sample to assist in representing or even estimating the replacements for missing values. <div><div><div><div><div><div><div>To estimate missing data, we use known relationships between variables in our sample to fill in the missing values. This helps us better understand and represent the data even if we don't have all of it.</div></div></div></div><div></div></div></div></div> " Indicator coding Method for specifying the reference category for a set of dummy variables where the reference category receives a value of zero across the set of dummy variables. The dummy variable coefficients represent the category differences from the reference category. Also, see effects coding. Kurtosis Measure of the peakedness or flatness of a distribution when compared with a normal distribution. A positive value indicates a relatively peaked distribution, and a negative value indicates a relatively flat distribution. Linearity Used to express the concept that the model possesses the properties of additivity and homogeneity. In a simple sense, linear models predict values that fall in a straight line by having a constant unit change (slope) of the dependent variable for a constant unit change of the independent variable. In the population model Y = b0 + b1X1 + e, the effect of a change of 1 in X1 is to add b1 (a constant) units to Y. Missing at random (MAR) Classification of missing data applicable when missing values of Y depend on X, but not on Y. When missing data are MAR, observed data for Y are a random sample of the Y values, but the missing values of Y are related to some other observed variable (X) in the sample. For example, assume two groups based on gender have different levels of missing data between male and female. The data is MAR if the data is missing at random within each group, but the levels of missing data depend on the gender. Missing completely at random (MCAR) Classification of missing data applicable when missing values of Y are not dependent on X. When missing data are MCAR, observed values of Y are a truly random sample of all Y values, with no underlying process that lends bias to the observed data. Missing data Information not available for a subject (or case) about whom other information is available. Missing data often occur when a respondent fails to answer one or more questions in a survey. Missing data process Any systematic event external to the respondent (such as data entry errors or data collection problems) or any action on the part of the respondent (such as refusal to answer a question) that leads to missing data. Multivariate graphical display Method of presenting a multivariate profile of an observation on three or more variables. The methods include approaches such as glyphs, mathematical transformations, and even iconic representations (e.g., faces). Normal distribution Purely theoretical continuous probability distribution in which the horizontal axis represents all possible values of a variable and the vertical axis represents the probability of those values occurring. The scores on the variable are clustered around the mean in a symmetrical, unimodal pattern known as the bell-shaped, or normal, curve. Normal probability plot Graphical comparison of the form of the distribution to the normal distribution. In the normal probability plot, the normal distribution is represented by a straight line angled at 45 degrees. The actual distribution is plotted against this line so that any differences are shown as deviations from the straight line, making identification of differences quite apparent and interpretable. Normality Degree to which the distribution of the sample data corresponds to a normal distribution. Outlier An observation that is substantially different from the other observations (i.e., has an extreme value) on one or more characteristics (variables). At issue is its representativeness of the population. Reference category The category of a nonmetric variable that is omitted when creating dummy variables and acts as a reference point in interpreting the dummy variables. In indicator coding, the reference category has values of zero (0) for all dummy variables. With effects coding, the reference category has values of minus one (-1) for all dummy variables. Residual Portion of a dependent variable not explained by a multivariate technique. Associated with dependence methods that attempt to predict the dependent variable, the residual represents the unexplained portion of the dependent variable. Residuals can be used in diagnostic procedures to identify problems in the estimation technique or to identify unspecified relationships. Robustness The ability of a statistical technique to perform reasonably well even when the underlying statistical assumptions have been violated in some manner. Scatterplot Representation of the relationship between two metric variables portraying the joint values of each observation in a two-dimensional graph. Skewness Measure of the symmetry of a distribution; in most instances the comparison is made to a normal distribution. A positively skewed distribution has relatively few large values and tails off to the right, and a negatively skewed distribution has relatively few small values and tails off to the left. Skewness values falling outside the range of -1 to +1 indicate a substantially skewed distribution. Variate Linear combination of variables formed in the multivariate technique by deriving empirical weights applied to a set of variables specified by the researcher. Anti-image correlation matrix Matrix of partial correlations among variables after factor analysis, rep. - degree to which the factors explain each other in the results. The diagonal - measures of sampling adequacy of variable, and off-diagonal values - partial correlations of variables. Bartlett test of sphericity Statistical test - overall significance of all correlations in correlation matrix. Cluster analysis Multivariate technique - it groups respondents or cases with similar profiles on a particular characteristics. Similar to Q factor analysis. Common factor analysis considers only the common or shared variance, excluding unique and error variance. Communalities (instead of unities) are inserted in the diagonal. Thus, factors resulting from common factor analysis are based only on the common variance. Factor model in which the factors are based on a reduced correlation matrix. That is, communalities are inserted in the diagonal of the correlation matrix, and the extracted factors are based only on the common variance, with specific and error variance excluded. Common variance Variance shared with other variables in the factor analysis (i.e., shared variance represented by the squared correlation). Communality Total amount of variance an original variable shares with all other variables. commonality. Calculated as the sum of the squared loadings for a variable across the factors. Component analysis Component analysis, also known as principal components analysis - takes into account the total variance and derives factors containing small proportions of unique variance and error variance.unities (1s) used in the diagonal of the correlation matrix Composite measure summated scales;Method - combining several variables measuring one concept, into a single variable - to increase reliability of measurement. In most instances, the separate variables are summed and then their total or average score is used in the analysis Conceptual definition specifying the theoretical basis for a concept that is represented by a factor Content validity Assessing the compatibility between the items selected in the summated scale and its conceptual definition. Correlation matrix Table showing the intercorrelations among all variables. "Cronbach's alpha "Measure of reliability that ranges from 0 to 1, with values of .60 to .70 - lower limit of acceptability. .80 is good, lower than .60 isnt good Cross-loading When a variable is found to have more than one significant loading which makes interpreting the factors difficult. The difference between the highest factor loading and the highest but one < |.20|. Dummy variable Binary metric variable used to represent a single category of a nonmetric variable. Eigenvalue Column sum of squared loadings for a factor; also, latent root - rep. the amount of variance accounted for by a factor.Represents the amount of variance accounted for by a factor. Calculated as the column sum of squared loadings for a factor; also referred to as the latent root. EQUIMAX "One of the orthogonal factor rotation methods that is a ""compromise"" between the VARIMAX and QUARTIMAX approaches, but is not widely used. " Error variance Variance of a variable due to measurement error (e.g., errors in data collection or measurement). Face validity content validity;Assessment of compatibility between items selected in summated scale and its conceptual definition. Factor Linear combination (variate) of the original variables. Factors - rep. underlying dimensions (constructs) that summarize or account for the original set of observed variable. component Factor indeterminacy Characteristic - common factor analysis - different factor scores can be calculated for a respondent, each fitting the estimated factor model. It means the factor scores are not unique for each individual. Characteristic of common factor analysis such that several different factor scores can be calculated for a respondent, each fitting the estimated factor model. It means the factor scores are not unique for each individual. Factor loadings Correlation between the original variables and the factors, and used for understanding the nature of a factor. Squared ..... - what percentage of the variance in original variable can be explained by a factor. Factor matrix Table displaying factor loadings of all variables on each factor. Factor pattern matrix One of two factor matrices found in an oblique rotation that is most comparable to the factor matrix in an orthogonal rotation. Factor rotation Process of manipulation or adjusting the factor axes - to get simpler and pragmatically meaningful factor solution Factor score Composite measure created for each observation on each factor extracted in the factor analysis. The factor weights are used in conjunction with the original variable values to calculate each observation’s score. The factor score then can be used to represent the factor(s) in subsequent analyses. Factor scores are standardized to have a mean of 0 and a standard deviation of 1. Similar in nature to a summated scale. Factor structure matrix A factor matrix - in oblique rotation - rep. simple correlations between variables and factors, incorporating the unique variance and the correlations between factors. Most researchers prefer factor pattern matrix when interpreting an oblique solution Indicator Single variable used along with one or more variables to form a composite measure. Latent root eigenvalue; Column sum of squared loadings for a factor; It represents the amount of variance accounted for by a factor. Measure of sampling adequacy (MSA) Measure calculated for - entire correlation matrix and individual variable to evaluate appropriateness of applying factor analysis. Values above .50 - for entire matrix or individual variable indicate appropriateness. Measure calculated both for the entire correlation matrix and each individual variable. MSA values above .50 for either the entire matrix or an individual variable indicate appropriateness for performing factor analysis on the overall set of variables or specific variables respectively. Measurement error "Inaccuracies in measuring the ""true"" variable values due to the fallibility of the measurement instrument (i.e., inappropriate response scales), data entry errors, or respondent errors. One portion of unique variance. " Multicollinearity Extent to which a variable can be explained by the other variables in the analysis. Oblique factor rotation Factor rotation computed so that the extracted factors are correlated. Rather than arbitrarily constraining the factor rotation to an orthogonal solution, the oblique rotation identifies the extent to which each of the factors is correlated. Orthogonal Mathematical independence (no correlation) of factor axes to each other (i.e., at right angles, or 90 degrees). Orthogonal factor rotation Factor rotation - factors extracted for axes to maintain at 90 degrees.  Each factor is independent of, or orthogonal to, all other factors (i.e., correlation between the factors is constrained to be zero). Q factor analysis Forms groups of respondents or cases based on their similarity on a set of characteristics. QUARTIMAX A type of orthogonal factor rotation method focusing on simplifying the columns of a factor matrix. Generally considered less effective than the VARIMAX rotation. R factor analysis Analyzes relationships among variables - to identify groups of variables forming latent dimensions (factors). Reliability Extent to which a variable or set of variables is consistent in what it is intended to measure. If multiple measurements are taken, reliable measures will all be consistent in their values. It differs from validity in that it does not relate to what should be measured, but instead to how it is measured. Reverse scoring Process of reversing the scores of a variable to retain distributional characteristics, to change the relationships (correlations) between two variables. Used in summated scale construction to avoid a cancelling out between variables with positive and negative factor loadings on the same factor. Specific variance Variance of each variable unique to that variable and not explained or associated with other variables in the factor analysis.One portion of unique variance. Summated scales Method of combining several variables that measure the same concept into a single variable in an attempt to increase the reliability of the measurement. In most instances, the separate variables are summed and then their total or average score is used in the analysis Surrogate variable Selection of a single proxy variable with the highest factor loading to represent a factor in the data reduction stage instead of using a summated scale or factor score Trace Rep. - total amount of variance on which the factor solution is based. It is equal to the number of variables, based on the assumption that the variance in each variable is equal to 1. Unique variance specific variance;Variance of each variable unique to that variable and not explained or associated with other variables in the factor analysis. Portion of a variable’s total variance that is not shared variance (i.e., not correlated with any other variables in the analysis. Has two portions—specific variance relating to the variance of the variable not related to any other variables and error variance attributable to the measurement errors in the variable’s value. Validity Extent to which a measure or set of measures correctly represents the concept of study—the degree to which it is free from any systematic or nonrandom error. Extent to which a single variable or set of variables (construct validity) correctly represents the concept of study—the degree to which it is free from any systematic or nonrandom error. Validity is concerned with how well the concept is defined by the variable(s), whereas reliability relates to the consistency of the variables(s). Variate Linear combination of variables by deriving empirical weights applied to a set of variables specified by the researcher. VARIMAX The most popular orthogonal factor rotation methods focusing on simplifying the columns in a factor matrix. Generally considered superior to other orthogonal factor rotation methods in achieving a simplified factor structure. Adjusted coefficient of determination (adjusted R2) Modified measure of the coefficient of determination that takes into account the number of independent variables included in the regression equation and the sample size. Although the addition of independent variables will always cause the coefficient of determination to rise, this may fall if the added independent variables have little explanatory power or if the degrees of freedom become too small. This statistic is quite useful for comparison between equations with different numbers of independent variables, differing sample sizes, or both. All-possible-subsets regression Method of selecting the variables for inclusion in the regression model that considers all possible combinations of the independent variables. For example, if the researcher specifies four potential independent variables, this technique would estimate all possible regression models with one, two, three, and four variables. The technique would then identify the model(s) with the best predictive accuracy. Backward elimination Method of selecting variables for inclusion in the regression model that starts by including all independent variables in the model and then eliminating those variables not making a significant contribution to prediction. Beta coefficient Standardized regression coefficient that allows for a direct comparison between coefficients as to their relative explanatory power of the dependent variable. this use standardized data and can be directly compared. Coefficient of determination (R2) Measure of the proportion of the variance of the dependent variable about its mean that is explained by the independent, or predictor, variables. The coefficient can vary between 0 and 1. If the regression model is properly applied and estimated, the researcher can assume that the higher the value of this, the greater the explanatory power of the regression equation, and therefore the better the prediction of the dependent variable. Collinearity Expression of the relationship between two or more independent variables. Two independent variables are said to exhibit complete -- if their correlation coefficient is 1, and complete lack of --- if their correlation coefficient is 0. ---- occurs when any single independent variable is highly correlated with a set of other independent variables. An extreme case of --- is singularity, in which an independent variable is perfectly predicted (i.e., correlation of 1.0) by another independent variable (or more than one). Correlation coefficient (r) Coefficient that indicates the strength of the association between any two metric variables. The sign (+ or -) indicates the direction of the relationship. The value can range from +1 to -1, with +1 indicating a perfect positive relationship, 0 indicating no relationship, and -1 indicating a perfect negative or reverse relationship (as one variable grows larger, the other variable grows smaller). Criterion variable (Y) Variable being predicted or explained by the set of independent variables;dependent variables Degrees of freedom (df) Value calculated from the total number of observations minus the number of estimated parameters. These parameter estimates are restrictions on the data because, once made, they define the population from which the data are assumed to have been drawn. For example, in estimating a regression model with a single independent variable, we estimate two parameters, the intercept (b0) and a regression coefficient for the independent variable (b1). it provides a measure of how restricted the data are to reach a certain level of prediction. If the number of ......is small, the resulting prediction may be less generalizable because all but a few observations were incorporated in the prediction. Conversely, a large ---- indicates the prediction is fairly robust with regard to being representative of the overall sample of respondents. Dependent variable (Y) Variable being predicted or explained by the set of independent variables. Dummy variable Independent variable used to account for the effect that different levels of a nonmetric variable have in predicting the dependent variable. To account for L levels of a nonmetric independent variable, L - 1 dummy variables are needed. For example, gender is measured as male or female and could be represented by two dummy variables, X1 and X2. When the respondent is male, X1 = 1 and X2 = 0. Likewise, when the respondent is female, X1 = 0 and X2 = 1. However, when X1 = 1, we know that X2 must equal 0. Thus, we need only one variable, either X1 or X2, to represent gender. We need not include both variables because one is perfectly predicted by the other (a singularity) and the regression coefficients cannot be estimated. If a variable has three levels, only two dummy variables are needed. Thus, the number of dummy variables is one less than the number of levels of the nonmetric variable. The two most common methods of determining the values of the dummy values are indicator coding and effects coding. Effects coding Method for specifying the reference category for a set of dummy variables in which the reference category receives a value of -1 across the set of dummy variables. In our example of dummy variable coding for gender, we coded the dummy variable as either 1 or 0. But with this the value of -1 is used instead of 0. With this type of coding, the coefficients for the dummy variables become group deviations on the dependent variable from the mean of the dependent variable across all groups. this coding contrasts with....., in which the reference category is given the value of zero across all dummy variables and the coefficients represent group deviations on the dependent variable from the reference group. Forward addition Method of selecting variables for inclusion in the regression model by starting with no variables in the model and then adding one variable at a time based on its contribution to prediction. Heteroscedasticity Description of data for which the variance of the error terms (e) appears constant over the range of values of an independent variable. The assumption of equal variance of the population error ε (where ε is estimated from the sample value e) is critical to the proper application of linear regression.  Independent variable Variable(s) selected as predictors and potential explanatory variables of the dependent variable. Indicator coding Method for specifying the reference category for a set of dummy variables where the reference category receives a value of 0 across the set of dummy variables. The regression coefficients represent the group differences in the dependent variable from the reference category. Indicator coding differs from effects coding, in which the reference category is given the value of -1 across all dummy variables and the regression coefficients represent group deviations on the dependent variable from the overall mean of the dependent variable. Influential observation An observation that has a disproportionate influence on one or more aspects of the regression estimates. This influence may be based on extreme values of the independent or dependent variables, or both. Influential observations can either be “good,” by reinforcing the pattern of the remaining data, or “bad,” when a single or small set of cases unduly affects the regression estimates. It is not necessary for the observation to be an outlier, although many times outliers can be classified as influential observations as well. Intercept (b0) Value on the Y axis (dependent variable axis) where the line defined by the regression equation Y = b0 + b1X1 crosses the axis. It is described by the constant term b0 in the regression equation. In addition to its role in prediction, this may have a managerial interpretation. If the complete absence of the independent variable has meaning, then the intercept represents that amount. For example, when estimating sales from past advertising expenditures, the intercept represents the level of sales expected if advertising is eliminated. But in many instances the constant has only predictive value because in no situation are all independent variables absent. An example is predicting product preference based on consumer attitudes. All individuals have some level of attitude, so the intercept has no managerial use, but it still aids in prediction. Least squares Estimation procedure used in simple and multiple regression whereby the regression coefficients are estimated so as to minimize the total sum of the squared residuals. Leverage points Type of influential observation defined by one aspect of influence. These observations are substantially different on one or more independent variables, so that they affect the estimation of one or more regression coefficients. Linearity Term used to express the concept that the model possesses the properties of additivity and homogeneity. In a simple sense, linear models predict values that fall in a straight line by having a constant unit change (slope) of the dependent variable for a constant unit change of the independent variable. In the population model Y = b0 + b1X1 + e, the effect of changing X1 by a value of 1.0 is to add b1 (a constant) units of Y. Measurement error Degree to which the data values do not truly measure the characteristic being represented by the variable. For example, when asking about total family income, many sources of measurement error (e.g., reluctance to answer full amount, error in estimating total income) make the data values imprecise. Moderator effect Effect in which a third independent variable (the moderator variable) causes the relationship between a dependent/independent variable pair to change, depending on the value of the moderator variable. It is also known as an interactive effect and is similar to the interaction effect seen in analysis of variance methods. Multicollinearity Expression of the relationship between two or more independent variables. Two independent variables are said to exhibit complete ...if their correlation coefficient is 1, and complete lack of ...if their correlation coefficient is 0. it occurs when any single independent variable is highly correlated with a set of other independent variables. An extreme case of ...is singularity, in which an independent variable is perfectly predicted (i.e., correlation of 1.0) by another independent variable (or more than one). Multiple regression Regression model with two or more independent variables. Normal probability plot Graphical comparison of the shape of the sample distribution to the normal distribution. In the graph, the normal distribution is represented by a straight line angled at 45 degrees. The actual distribution is plotted against this line, so any differences are shown as deviations from the straight line, making identification of differences quite simple Null plot Plot of residuals versus the predicted values that exhibits a random pattern. it is indicative of no identifiable violations of the assumptions underlying regression analysis. Outlier In strict terms, an observation that has a substantial difference between the actual value for the dependent variable and the predicted value. Cases that are substantially different with regard to either the dependent or independent variables are often termed --- as well. In all instances, the objective is to identify observations that are inappropriate representations of the population from which the sample is drawn, so that they may be discounted or even eliminated from the analysis as unrepresentative Parameter Quantity (measure) characteristic of the population. For example, μ and are the symbols used for the population ....mean (μ) and variance ( ). They are typically estimated from sample data in which the arithmetic average of the sample is used as a measure of the population average and the variance of the sample is used to estimate the variance of the population. Part correlation Value that measures the strength of the relationship between a dependent and a single independent variable when the predictive effects of the other independent variables in the regression model are removed. The objective is to portray the unique predictive effect due to a single independent variable among a set of independent variables. Partial correlation coefficient Value that measures the strength of the relationship between the criterion or dependent variable and a single independent variable when the effects of the other independent variables in the model are held constant. This value is used in sequential variable selection methods of regression model estimation (e.g., stepwise, forward addition, or backward elimination) to identify the independent variable with the greatest incremental predictive power beyond the independent variables already in the regression model. Partial F (or t) values The partial F-test is simply a statistical test for the additional contribution to prediction accuracy of a variable above that of the variables already in the equation.When a variable 1Xa 2 is added to a regression equation after other variables are already in the equation, its contribution may be small even though it has a high correlation with the dependent variable. The reason is that Xa is highly correlated with the variables already in the equation. The partial F value is calculated for all variables by simply pretending that each, in turn, is the last to enter the equation. It gives the additional contribution of each variable above all others in the equation. A low or insignificant partial F value for a variable not in the equation indicates its low or insignificant contribution to the model as already specified. A t value may be calculated instead of F values in all instances, with the t value being approximately the square root of the F value. Partial regression plot Graphical representation of the relationship between the dependent variable and a single independent variable. The scatterplot of points depicts the partial correlation between the two variables, with the effects of other independent variables held constant. This portrayal is particularly helpful in assessing the form of the relationship (linear versus nonlinear) and the identification of influential observations Polynomial Transformation of an independent variable to represent a curvilinear relationship with the dependent variable. By including a squared term (X2), a single inflection point is estimated. A cubic term estimates a second inflection point. Additional terms of a higher power can also be estimated. Power Probability that a significant relationship will be found if it actually exists. Complements the more widely used significance level alpha . Prediction error Difference between the actual and predicted values of the dependent variable for each observation in the sample. Predictor variable (Xn) Variable(s) selected as predictors and potential explanatory variables of the dependent variable.Independent variable PRESS statistic Validation measure obtained by eliminating each observation one at a time and predicting this dependent value with the regression model estimated from the remaining observations. Reference category The omitted level of a nonmetric variable when a dummy variable is formed from the nonmetric variable. Regression coefficient (bn) Numerical value of the parameter estimate directly associated with an independent variable; for example, in the model Y = b0 + b1X1 the value b1 is the regression coefficient for the variable X1. it represents the amount of change in the dependent variable for a one-unit change in the independent variable. In the multiple predictor model (e.g., Y = b0 + b1X1 + b2X2), the regression coefficients are partial coefficients because each takes into account not only the relationships between Y and X1 and between Y and X2, but also between X1 and X2. The coefficient is not limited in range, because it is based on both the degree of association and the scale units of the independent variable. For instance, two variables with the same association to Y would have different coefficients if one independent variable was measured on a 7-point scale and another was based on a 100-point scale. Regression variate Linear combination of weighted independent variables used collectively to predict the dependent variable. Residual (e or ε) Error in predicting our sample data. Seldom will our predictions be perfect. We assume that random error will occur, but we assume that this error is an estimate of the true random error in the population (ε), not just the error in prediction for our sample (e). We assume that the error in the population we are estimating is distributed with a mean of 0 and a constant (homoscedastic) variance. Sampling error The expected variation in any estimated parameter (intercept or regression coefficient) that is due to the use of a sample rather than the population. it is reduced as the sample size is increased and is used to statistically test whether the estimated parameter differs from zero. Significance level (alpha) Commonly referred to as the level of statistical significance, the significance level represents the probability the researcher is willing to accept that the estimated coefficient is classified as different from zero when it actually is not. This is also known as Type I error. The most widely used level of significance is .05, although researchers use levels ranging from .01 (more demanding) to .10 (less conservative and easier to find significance). Simple regression Regression model with a single independent variable, also known as bivariate regression. Singularity The extreme case of collinearity or multicollinearity in which an independent variable is perfectly predicted (a correlation of+or-1 by one or more independent variables. Regression models cannot be estimated when when a singularity exists. The researcher must omit one or more of the independent variables involved to remove the singularity. Specification error Error in predicting the dependent variable caused by excluding one or more relevant independent variables. This omission can bias the estimated coefficients of the included variables as well as decrease the overall predictive power of the regression model. Standard error Expected distribution of an estimated regression coefficient. it is similar to the standard deviation of any set of data values, but instead denotes the expected range of the coefficient across multiple samples of the data. It is useful in statistical tests of significance that test to see whether the coefficient is significantly different from zero (i.e., whether the expected range of the coefficient contains the value of zero at a given level of confidence). The t value of a regression coefficient is the coefficient divided by its standard error. Standard error of the estimate (SEE) Measure of the variation in the predicted values that can be used to develop confidence intervals around any predicted value. It is similar to the standard deviation of a variable around its mean, but instead is the expected distribution of predicted values that would occur if multiple samples of the data were taken. Standardization "Process whereby the original variable is transformed into a new variable with a mean of 0 and a standard deviation of 1. The typical procedure is to first subtract the variable mean from each observation's value and then divide by the standard deviation. When all the variables in a regression variate are standardized, the b0 term (the intercept) assumes a value of 0 and the regression coefficients are known as beta coefficients, which enable the researcher to compare directly the relative effect of each independent variable on the dependent variable " Statistical relationship Relationship based on the correlation of one or more independent variables with the dependent variable. Measures of association, typically correlations, represent the degree of relationship because there is more than one value of the dependent variable for each value of the independent variable. Stepwise estimation Method of selecting variables for inclusion in the regression model that starts by selecting the best predictor of the dependent variable. Additional independent variables are selected in terms of the incremental explanatory power they can add to the regression model. Independent variables are added as long as their partial correlation coefficients are statistically significant. Independent variables may also be dropped if their predictive power drops to a nonsignificant level when another independent variable is added to the model. Studentized residual The most commonly used form of standardized residual. It differs from other methods in how it calculates the standard deviation used in standardization. To minimize the effect of any observation on the standardization process, the standard deviation of the residual for observation is computed from regression estimates omitting the ith observation in the calculation of the regression estimates. Sum of squared errors (SSE) Sum of the squared prediction errors (residuals) across all observations. It is used to denote the variance in the dependent variable not yet accounted for by the regression model. If no independent variables are used for prediction, it becomes the squared errors using the mean as the predicted value and thus equals the total sum of squares. Sum of the squared prediction errors (residuals) across all observations. It is used to denote the variance in the dependent variable not yet accounted for by the regression model. If no independent variables are used for prediction, it becomes the squared errors using the mean as the predicted value and thus equals the total sum of squares. Sum of squares regression (SSR) Sum of the squared differences between the mean and predicted values of the dependent variable for all observations. It represents the amount of improvement in explanation of the dependent variable attributable to the independent variable(s). Suppression effect "The instance in which the expected relationships between independent and dependent variables are hidden or suppressed when viewed in a bivariate relationship. When additional independent variables are entered, the multicollinearity removes ""unwanted"" shared variance and reveals the ""true"" relationship. " Tolerance Commonly used measure of collinearity and multicollinearity. As this value grows smaller, the variable is more highly predicted by the other independent variables (collinearity).The tolerance of variable i( TOLi)  is 1 -R2*i, where R2*i is the coefficient of determination for the prediction of variable i by the other independent variables in the regression variate.  Total sum of squares (SST) Total amount of variation that exists to be explained by the independent variables. This baseline value is calculated by summing the squared differences between the mean and actual values for the dependent variable across all observations. Total amount of variation that exists to be explained by the independent variables. This baseline value is calculated by summing the squared differences between the mean and actual values for the dependent variable across all observations. Transformation A variable may have an undesirable characteristic, such as nonnormality, that detracts from the ability of the correlation coefficient to represent the relationship between it and another variable. A ----, such as taking the logarithm or square root of the variable, creates a new variable and eliminates the undesirable characteristic, allowing for a better measure of the relationship. ----- maybe applied to either the dependent or independent variables, or both. The need and specific type of.... may be based on theoretical reasons (such as ...a known nonlinear relationship) or empirical reasons (identified through graphical or statistical means). Variance inflation factor (VIF) Indicator of the effect that the other independent variables have on the standard error of a regression coefficient. ----- is directly related to the tolerance value.Large ....values also indicate a high degree of collinearity or multicollinearity among the independent variables Analysis sample Group of cases used in estimating the logistic regression model. When constructing classification matrices, the original sample is divided randomly into two groups, one for model estimation (the analysis sample) and the other for validation (the holdout sample). Categorical variable nonmetric variable;Variable with values that serve merely as a label or means of identification, also referred to as a categorical, nominal, binary, qualitative, or taxonomic variable. The number on a football jersey is an example. Classification matrix Means of assessing the predictive ability of the logistic regression model. Created by cross-tabulating actual group membership with predicted group membership, this matrix consists of numbers on the diagonal representing correct classifications (True Positives and True Negatives) and off-diagonal numbers representing incorrect classifications (False Positives and False Negatives). <div>A classification matrix is a tool that is used to assess the predictive ability of a logistic regression model. It is created by cross-tabulating the actual group membership with the predicted group membership for a set of data.</div><div>The classification matrix consists of four cells: true positives (TP), true negatives (TN), false positives (FP), and false negatives (FN). These cells represent the number of correct and incorrect classifications made by the model.</div> Cross-validation Procedure of dividing the sample into two parts: the analysis sample used in estimation of the logistic regression model and the holdout sample used to validate the results. Cross-validation avoids the overfitting of the logistic regression by allowing its validation on a totally separate sample. Exponentiated logistic coefficient Antilog of the logistic coefficient, which is used for interpretation purposes in logistic regression. The exponentiated coefficient minus 1.0 equals the percentage change in the odds. For example, an exponentiated coefficient of .20 represents a negative 80 percent change in the odds (.20 - 1.0 = -.80) for each unit change in the independent variable (the same as if the odds were multiplied by .20). Thus, a value of 1.0 equates to no change in the odds and values above 1.0 represent increases in the predicted odds. <div>The exponentiated logistic coefficient, also known as the odds ratio, is a statistical measure used in logistic regression to interpret the relationship between an independent variable and the dependent variable. It represents the change in the odds of the dependent variable (e.g. the probability of an event occurring) for a one unit change in the independent variable.</div> Hit ratio Percentage of objects (individuals, respondents, firms, etc.) correctly classified by the logistic regression model. It is calculated as the number of objects in the diagonal of the classification matrix divided by the total number of objects. Also known as the percentage correctly classified or Accuracy Holdout sample Group of objects not used to compute the logistic regression model. This group is then used to validate the logistic regression model with a separate sample of respondents. Also called the validation sample. Likelihood value Measure used in logistic regression to represent the lack of predictive fit. Even though this method does not use the least squares procedure in model estimation, as is done in multiple regression, the likelihood value is similar to the sum of squared error in regression analysis. Logistic coefficient Coefficient in the logistic regression model that acts as the weighting factor for the independent variables in relation to their discriminatory power. Similar to a regression weight or discriminant coefficient. Logistic curve An S-shaped curve formed by the logit transformation that represents the probability of an event. The S-shaped form is nonlinear, because the probability of an event must approach 0 and 1, but never fall outside these limits. Thus, although the midrange involves a linear component, the probabilities as they approach the lower and upper bounds of probability (0 and 1) must flatten out and become asymptotic to these bounds. Logistic regression Special form of regression in which the dependent variable is a nonmetric, dichotomous (binary) variable. Although some differences exist, the general manner of interpretation is quite similar to linear regression. Logit analysis logistic regression;Special form of regression in which the dependent variable is a nonmetric, dichotomous (binary) variable. Although some differences exist, the general manner of interpretation is quite similar to linear regression Logit transformation Transformation of the values of the discrete binary dependent variable of logistic regression into an S-shaped curve (logistic curve) representing the probability of an event. This probability is then used to form the odds ratio, which acts as the dependent variable in logistic regression. Maximum chance criterion Measure of predictive accuracy in the classification matrix that is calculated as the percentage of respondents in the largest group. The rationale is that the best uninformed choice is to classify every observation into the largest group. Nonmetric variable Variable with values that serve merely as a label or means of identification, also referred to as a categorical, nominal, binary, qualitative, or taxonomic variable. The number on a football jersey is an example. Odds The ratio of the probability of an event occurring to the probability of the event not happening, which is used as a measure of the dependent variable in logistic regression. Percentage correctly classified hit ratio;Percentage of objects (individuals, respondents, firms, etc.) correctly classified by the logistic regression model. It is calculated as the number of objects in the diagonal of the classification matrix divided by the total number of objects. Also known as the percentage correctly classified. Proportional chance criterion Another criterion for assessing the hit ratio, in which the average probability of classification is calculated considering all group sizes. Pseudo R2 A value of overall model fit that can be calculated for logistic regression; comparable to the R2 measure used in multiple regression. Validation sample holdout sample;Group of objects not used to compute the logistic regression model. This group is then used to validate the logistic regression model with a separate sample of respondents. Also called the validation sample. Variate Linear combination that represents the weighted sum of two or more independent variables that comprise the discriminant function. Also called linear combination or linear compound. Wald statistic "Test used in logistic regression for the significance of the logistic coefficient. Its interpretation is like the F or t values used for the significance testing of regression coefficients. To simplify, the Wald statistic is a measure of how likely it is that the observed value of a logistic coefficient (a parameter in a logistic regression model) could have occurred by chance, if the true value of the coefficient were actually zero. If the Wald statistic is large and the p-value is small (below a certain threshold, usually 0.05), then we can conclude that the observed value of the coefficient is significantly different from zero and is therefore likely to be a meaningful predictor of the outcome variable.<div><div>In other words, the Wald statistic is used to test whether a given predictor variable is significantly associated with the outcome variable in a logistic regression model. If the Wald statistic is significant, it suggests that the predictor variable is important in explaining the variation in the outcome variable. If the Wald statistic is not significant, it suggests that the predictor variable is not a significant predictor of the outcome variable.</div></div><div><div><div><div><div><div><div><div>To simplify further, the Wald statistic is a statistical test used to determine whether a particular predictor variable is significantly associated with an outcome variable in a logistic regression model. It does this by comparing the observed value of the predictor variable's coefficient (a measure of the strength and direction of the association between the predictor and outcome variables) to what we would expect to see if there was no real association between the two variables. If the observed value is significantly different from what we would expect to see by chance, then we can conclude that the predictor variable is a meaningful predictor of the outcome variable. If the observed value is not significantly different from what we would expect to see by chance, then we can conclude that the predictor variable is not a meaningful predictor of the outcome variable.</div></div></div></div></div></div></div></div> " Average variance extracted (AVE) A summary measure of convergence among a set of items representing a latent construct. It is the average percentage of variation explained (variance extracted) among the items of a construct. Between-construct error covariance Covariance between two error terms of measured variables indicating different constructs. Communality Total amount of variance a measured variable has in common with the constructs upon which it loads. Good measurement practice suggests that each measured variable should load on only one construct. Thus, it can be thought of as the variance explained in a measured variable by the construct. Also referred to as a communality. Congeneric measurement model Measurement model consisting of several unidimensional constructs with all cross-loadings and between- and within-construct error covariances appropriately fixed at zero. Constraints Fixing a potential relationship in a SEM model to some specified value (even if fixed to zero) rather than allowing the value to be estimated (free). Construct reliability (CR) Measure of reliability and internal consistency of the measured variables representing a latent construct. Must be established before construct validity can be assessed. Construct validity Extent to which a set of measured variables actually represents the theoretical latent construct those variables are designed to measure Convergent validity Extent to which indicators of a specific construct converge or share a high proportion of variance in common. Discriminant validity Extent to which a construct is truly distinct from other constructs both in terms of how much it correlates with other constructs and how distinctly measured variables represent only this single construct Face validity "Extent to which the content of the items is consistent with the construct definition, based solely on the researcher's judgment. " Formative measurement theory Theory based on the assumptions that (1) the measured variables cause the construct and (2) the error in measurement is an inability to fully explain the construct. The construct is not latent in this case. See also reflective measurement theory. Heywood case Factor solution that produces an error variance estimate of less than zero (a negative error variance). SEM programs will usually generate an improper solution when a Heywood case(s) is present Identification Whether enough information exists to identify a solution for a set of structural equations. An identification problem leads to an inability of the proposed model to generate unique estimates and can prevent the SEM program from producing results. The three possible conditions of identification are overidentified, just-identified, and underidentified. Just-identified SEM model containing just enough degrees of freedom to estimate all free parameters. Just-identified models have perfect fit by definition, meaning that a fit assessment is not meaningful. Measurement model Specification of the measurement theory that shows how constructs are operationalized by sets of measured variables. The specification is similar to an EFA by factor analysis, but differs in that the number of factors and the items loading on each factor must be known and specified before the analysis can be conducted. Measurement theory Series of relationships that suggest how measured variables represent a construct not measured directly (latent). A measurement theory can be represented by a series of regression-like equations mathematically relating a factor (construct) to the measured variables.. Modification index Amount the overall model χ2 value would be reduced by freeing any single particular path that is not currently estimated Nomological validity Test of validity that examines whether the correlations between the constructs in the measurement theory make sense. The construct correlations can be useful in this assessment. Operationalization Manner in which a construct can be represented. With CFA, a set of measured variables is used to represent a construct Order condition Requirement that the degrees of freedom for a model be greater than zero; that is, the number of unique covariance and variance terms less the number of free parameter estimates must be positive. Overidentified model Model that has more unique covariance and variance terms than parameters to be estimated. It has positive degrees of freedom. This is the preferred type of identification for a SEM model. Parameter Numerical representation of some characteristic of a population. In SEM, relationships are the characteristic of interest for which the modeling procedures will generate estimates. Parameters are numerical characteristics of the SEM relationships, comparable to regression coefficients in multiple regression. Rank condition Requirement that each individual parameter estimated be uniquely, algebraically defined. If you think of a set of equations that could define any dependent variable, the rank condition is violated if any two equations are mathematical duplicates Reflective measurement theory Theory based on the assumptions that (1) latent constructs cause the measured variables and (2) the measurement error results in an inability to fully explain these measures. It is the typical representation for a latent construct. See also formative measurement theory. Residuals Individual differences between observed covariance terms and the estimated covariance terms. Specification search Empirical trial-and-error approach that may lead to sequential changes in the model based on key model diagnostics. Squared multiple correlations "Values representing the extent to which a measured variable's variance is explained by a latent factor. It is similar to the idea of communality from EFA. " Standardized residuals Residuals divided by the standard error of the residual. Used as a diagnostic measure of model fit. Tau-equivalence Assumption that a measurement model is congeneric and that all factor loadings are equal. Three-indicator rule Assumes a congeneric measurement model in which all constructs have at least three indicators; therefore the model is identified. Underidentified model Model with more parameters to be estimated than there are item variance and covariances. The term unidentified is used in the same way as underidentified. Unidentified model Model with more parameters to be estimated than there are item variance and covariances. The term unidentified is used in the same way as underidentified. Unidimensional measures Set of measured variables (indicators) with only one underlying latent construct. That is, the indicator variables load on only one construct. Variance extracted Total amount of variance a measured variable has in common with the constructs upon which it loads. Good measurement practice suggests that each measured variable should load on only one construct. Thus, it can be thought of as the variance explained in a measured variable by the construct Within-construct error covariance Covariance between two error terms of measured variables that are indicators of the same construct. Accuracy Percentage of objects (individuals, respondents, firms, etc.) correctly classified by the logistic regression model. It is calculated as the number of objects in the diagonal of the classification matrix divided by the total number of objects. Also known as the percentage correctly classified or the hit ratio. AUC (area under the curve) The area under the ROC curve which indicates the amount of discrimination for the estimated model. Higher values indicate better model discrimination and model fit, values of .5 indicate no discrimination and model fit no better than chance. AUC is a way to measure how well a model can predict something. It helps us see how accurate the model is at making predictions. A model with a higher AUC is better at making predictions than a model with a lower AUC. c/cBAR "An influence measure indicative of an observation’s impact on overall model fit, similar to Cook’s distance measure in multiple regression.  c/cBAR is a way to measure how much an individual observation affects the overall fit of a model. If an observation has a high c/cBAR value, it means it has a big impact on the model's results, and removing it from the dataset could change the model's predictions. If an observation has a low c/cBAR value, it means it has a small impact on the model's results, and removing it from the dataset is unlikely to change the model's predictions " chi-square difference "An influence measure that represents the amount the model chi-square value will decrease when the observation is omitted from the analysis. <div>Chi-square is a statistical test that is used to determine whether there is a significant difference between the observed values and the expected values in a dataset. In simpler terms, chi-square difference is a way to measure how much an individual observation is affecting the results of a statistical test. It tells us how much the test's results will change if we remove the observation from the analysis.</div>Chi-square difference is a way to measure how much an individual observation is affecting the results of a statistical test. It helps us see how much the test's results will change if we remove the observation from the analysis. " complete separation "Complete separation is a situation that occurs when an independent variable (a variable that is being used to predict an outcome) provides perfect prediction of the dependent measure (the outcome being predicted). This creates a situation in which the model cannot be estimated and the variable must be eliminated from the analysis. " Deviance difference An influence measure for an observation indicating the decrease in the model log likelihood value when that observation is omitted from the analysis. <div>Deviance difference is a statistical measure that is used to evaluate the impact of an individual observation on the overall fit of a model. It is calculated as the difference in the model log likelihood value when an observation is included in the analysis versus when it is omitted from the analysis.</div> Deviance residual "A residual of an observation indicating its contribution to the -2 log likelihood value of the estimated model. <div>A deviance residual is a measure that indicates the contribution of an individual observation to the overall fit of a statistical model. It is calculated as the difference between the observed value of the dependent variable and the predicted value of the dependent variable for that observation, scaled by the square root of the predicted value of the dependent variable. Deviance residuals are often used in statistical modeling to identify observations that may be influential or unusual, and to assess the robustness of the model. By analyzing deviance residuals, we can identify observations that may be affecting the model's ability to fit the data, and take steps to address these issues. This can help to improve the accuracy and reliability of the model, and make it more useful for making predictions and generalizations about the data.</div><div>In simpler terms, a deviance residual is a measure that tells us how much an observation is affecting the fit of a statistical model. By analyzing deviance residuals, we can identify observations that may be affecting the model's ability to fit the data, and take steps to improve the accuracy and reliability of the model.</div> " Dfbeta An influence measure indicating the change in each estimated parameter if that observation is omitted from the analysis. <div>Dfbeta is a statistical measure that tells us how much an individual observation is affecting the estimates of the parameters in a statistical model. It is calculated by comparing the parameter estimates when the observation is included in the analysis to the parameter estimates when the observation is omitted from the analysis.</div> False negative One of the four cells in the classification matrix that denotes the number of observations that were positive, but incorrectly predicted to be negative False positive One of the four cells of the classification matrix that denotes the number of observations that were negative, but incorrectly predicted to be positive. Hosmer and Lemeshow test A chi-square based test of overall model predictive accuracy where actual and predicted outcomes are compared and a statistical significance test performed. Nonsignificance indicates close correspondence between actual and predicted, thus indicating a good predictive model <div>The Hosmer and Lemeshow test is a statistical test used to assess the overall predictive accuracy of a model. It is often used in logistic regression, where the goal is to predict a binary outcome (e.g. whether or not an event will occur).</div><div>To perform the Hosmer and Lemeshow test, we first compare the actual outcomes (e.g. whether or not it rained) with the predicted outcomes (e.g. the probability of it raining predicted by the model). We then calculate a chi-square statistic based on the differences between the actual and predicted outcomes. If the chi-square statistic is not statistically significant, it indicates that there is a close correspondence between the actual and predicted outcomes, and the model is a good predictor of the outcome.</div> influence measure A measure of the impact of an individual observation either on the overall model fit or on any of the estimated model coefficients. <div>If an observation has a high influence, it means that it is having a significant impact on the estimated model coefficients.</div><div>In simpler terms, an influence measure is a way to understand how much a particular observation is affecting the results of a statistical analysis. It can help us identify observations that might be having a disproportionate influence on the results, and allow us to make more accurate and reliable conclusions.</div> information value "An overall measure of each independent variable’s ability to distinguish between the outcome categories based on weight of evidence for categories of the independent variable. It provides a method separate from the actual model estimates to assess the role of each independent variable to assist in both variable selection and relative comparison of independent variables in terms of their predictive impact. <div><div><div><div><div><div><div><div><div><div><div>Information value (IV) is a measure that is used to assess the ability of an independent variable (a predictor) to distinguish between different categories of a dependent variable (the outcome). It is based on the weight of evidence for each category of the independent variable, and is often used to help with variable selection and to compare the relative importance of different independent variables in a statistical model.</div><div>For example, suppose we are using a logistic regression model to predict the likelihood of a customer churning (cancelling their service) based on their contract length, age, and payment history. We might use information value to understand which of these variables is the most important predictor of customer churn. If the contract length has a high information value, it means that it is a strong predictor of customer churn and is able to distinguish between different categories of the outcome (e.g. those who did and did not churn).</div><div>In simpler terms, information value is a measure that helps us understand how well an independent variable is able to predict the outcome in a statistical model. It can be used to identify the most important predictors and to compare the relative importance of different variables.</div></div></div></div><div></div></div></div></div><div><div><div><div></div></div><div><div><div>how to study 5 chapters in 11 days with anki</div></div><div></div></div></div></div><div><div><div><div></div></div><div><div><div><div><div>Here is a suggested study plan using Anki to cover 5 chapters in 11 days:</div><ol><li><div>Divide the chapters into manageable sections: Break each chapter down into smaller, more manageable sections that you can cover in a single study session. This will make it easier to review and retain the material.</div></li><li><div>Set aside dedicated study time: Plan specific blocks of time each day to study and review the material using Anki. It's important to be consistent with your study schedule to make the most of your time.</div></li><li><div>Create Anki cards for key concepts: As you study, create Anki cards for key concepts, definitions, formulas, and other important information. Be sure to include both the question and the answer on the card.</div></li><li><div>Review the cards regularly: Use Anki's spaced repetition algorithm to review the cards regularly. The more you review the cards, the more likely you are to retain the material.</div></li><li><div>Take breaks: Be sure to take breaks during your study sessions to rest and recharge. This can help you stay focused and avoid burnout.</div></li></ol><div>By following this plan and being consistent with your studying and reviewing, you should be able to cover the 5 chapters in 11 days and retain the material for the exam. It's also a good idea to review all the material just before the exam to refresh your memory.</div></div></div></div><div></div></div></div></div><div><div><div><div></div></div><div><div><div>give example</div></div><div></div></div></div></div><div><div><div><div></div></div><div><div><div><div><div>Here is an example study schedule using Anki to cover 5 chapters in 11 days:</div><div>Day 1:</div><ul><li>Study Chapter 1, sections 1-3</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 2:</div><ul><li>Study Chapter 1, sections 4-6</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 3:</div><ul><li>Study Chapter 2, sections 1-3</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 4:</div><ul><li>Study Chapter 2, sections 4-6</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 5:</div><ul><li>Review Chapter 1 material</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 6:</div><ul><li>Study Chapter 3, sections 1-3</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 7:</div><ul><li>Study Chapter 3, sections 4-6</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 8:</div><ul><li>Review Chapter 2 material</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 9:</div><ul><li>Study Chapter 4, sections 1-3</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 10:</div><ul><li>Study Chapter 4, sections 4-6</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 11:</div><ul><li>Review Chapter 3 material</li><li>Review Anki cards for 30 minutes</li><li>Review all material just before the exam</li></ul><div>This is just one example of how you might use Anki to cover 5 chapters in 11 days. You can adjust the schedule to fit your specific needs and study habits. It's important to be consistent with your studying and review sessions, and to take breaks as needed to rest and recharge.</div></div></div></div><div></div></div></div></div><div><div><div><div></div></div><div><div><div>i said chapter 5</div></div><div></div></div></div></div><div><div><div><div></div></div><div><div><div><div><div>Here is an updated example study schedule using Anki to cover 5 chapters in 11 days:</div><div>Day 1:</div><ul><li>Study Chapter 1, sections 1-3</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 2:</div><ul><li>Study Chapter 1, sections 4-6</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 3:</div><ul><li>Study Chapter 2, sections 1-3</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 4:</div><ul><li>Study Chapter 2, sections 4-6</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 5:</div><ul><li>Review Chapter 1 material</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 6:</div><ul><li>Study Chapter 3, sections 1-3</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 7:</div><ul><li>Study Chapter 3, sections 4-6</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 8:</div><ul><li>Review Chapter 2 material</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 9:</div><ul><li>Study Chapter 4, sections 1-3</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 10:</div><ul><li>Study Chapter 4, sections 4-6</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 11:</div><ul><li>Study Chapter 5, sections 1-3</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>This is just one example of how you might use Anki to cover 5 chapters in 11 days. You can adjust the schedule to fit your specific needs and study habits. It's important to be consistent with your studying and review sessions, and to take breaks as needed to rest and recharge. Don't forget to review all the material just before the exam to refresh your memory.</div></div></div></div><div></div></div></div></div><div><div><div><div></div><div></div></div><div><div><div>i have 11 days and 5 chapters with sums, slides and anki how should i divide my study</div></div><div></div></div></div></div><div><div><div><div></div></div><div><div><div><div><div>Here is an example study schedule that incorporates Anki, slides, and summaries to cover 5 chapters in 11 days:</div><div>Day 1:</div><ul><li>Review the slides for Chapter 1</li><li>Study Chapter 1, sections 1-3</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 2:</div><ul><li>Review the slides for Chapter 1</li><li>Study Chapter 1, sections 4-6</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 3:</div><ul><li>Review the slides for Chapter 2</li><li>Study Chapter 2, sections 1-3</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 4:</div><ul><li>Review the slides for Chapter 2</li><li>Study Chapter 2, sections 4-6</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 5:</div><ul><li>Review Chapter 1 material and slides</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 6:</div><ul><li>Review the slides for Chapter 3</li><li>Study Chapter 3, sections 1-3</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 7:</div><ul><li>Review the slides for Chapter 3</li><li>Study Chapter 3, sections 4-6</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 8:</div><ul><li>Review Chapter 2 material and slides</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 9:</div><ul><li>Review the slides for Chapter 4</li><li>Study Chapter 4, sections 1-3</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 10:</div><ul><li>Review the slides for Chapter 4</li><li>Study Chapter 4, sections 4-6</li><li>Create Anki cards for key concepts</li><li>Review Anki cards for 30 minutes</li></ul><div>Day 11:</div><ul><li>Review Chapter 3 material and slides</li><li>Review Anki cards for 30 minutes</li><li>Review all material and summaries just before the exam</li></ul><div>This is just one example of how you might divide your study time to cover 5 chapters in 11 days. You can adjust the schedule to fit your specific needs and study habits. It's important to be consistent with your studying and review sessions, and to take breaks as needed to rest and recharge. Don't forget to review all the material and summaries just before the exam to refresh your memory.</div></div></div></div><div></div></div></div></div><div></div></div></div></div></div><div><div><div>Regenerate response</div> </div></div> " Leverage An influence measure that depicts how “typical” an observation is based on the entire set of independent variables. High leverage observations are those that are most different from the centroid of the sample on the independent variables. Maximum likelihood procedure "A method for estimating the parameters of a statistical model based on parameter values that maximize the likelihood function. the maximum likelihood procedure is a way to find the values for the parameters in a statistical model that are most likely to have produced the data. It does this by looking for the values that would make the data most likely to occur, based on the assumptions of the model. This can be a useful way to estimate the parameters of a model, especially when the data follow certain patterns or distributions. " Misclassification cost "A method of portraying the differing costs of making an incorrect prediction (i.e., cost of a false positive or a false negative). Can be integrated into the classification matrix to reflect these differential impacts across all outcomes. <div><div><div><div><div><div><div>Misclassification cost is a way to show the different costs of making a mistake when predicting something. For example, if you are trying to predict if someone has a certain disease, making a mistake could have different costs. If you predict that someone has the disease when they actually don't (called a false positive), it could cost them money for unnecessary tests and treatments. On the other hand, if you predict that someone doesn't have the disease when they actually do (called a false negative), it could cost them their health.</div><div>Misclassification cost can be used to show these different costs in a classification matrix. A classification matrix is a table that shows how many predictions were correct and how many were wrong. Misclassification cost can be added to the classification matrix to show the different costs of making a mistake for each prediction. This can help people understand the different costs of making a mistake and make better decisions.</div></div></div></div><div></div></div></div></div><div><div><div><div> </div></div></div></div> " negative predictive value (nPV Represents the probability of making a correct negative prediction—the percentage of negative predictions that are actually true negative. <div>To calculate the nPV, you need to know the number of true negatives (when the test correctly predicts that someone does not have the disease) and the number of false negatives (when the test incorrectly predicts that someone does not have the disease). The nPV is calculated by dividing the number of true negatives by the total number of negative predictions (true negatives + false negatives).</div><div>So, the nPV is a way to measure how accurate a test is at predicting that something is not present (a negative result) by looking at the number of true and false negative predictions</div> original logistic coefficient Estimated parameter from the logistic model that reflects the change in the logged odds value (logit) for a one unit change in the independent variable. It is similar to a regression weight or discriminant coefficient. Pearson residual A residual for an observation that is the standardized difference between the actual outcome value (1 or 0) and the predicted probability. Percentage correctly classified Accuracy Positive predictive value (PPV) Represents the probability of making a correct positive prediction—the percentage of positive predictions that are actually true positive. Probit Alternative to the logistic function as the statistical model used in the estimation procedure. Generally provides results quite comparable to the logit transformation and while providing some advantages for instances of multi-category dependent measures, its estimated coefficients are somewhat more difficult to interpret. <div>The probit function is similar to the logistic function in that it is used to model the probability of a binary outcome (e.g., success or failure, yes or no). However, the probit function is based on the cumulative distribution function of the normal distribution, whereas the logistic function is based on the logistic curve.</div><div>One advantage of the probit function is that it can be used for multi-category dependent measures (e.g., more than two outcome categories). However, the estimated coefficients from the probit function may be somewhat more difficult to interpret than those from the logistic function, as they are not directly related to the odds of the outcome.</div> Quasi-complete separation A situation where at least one cell related to an independent variable has zero observations, causing problems in estimation of the parameter estimate associated with that independent variable. While the parameter estimate may be inaccurate, the model can still be estimated, which is not the case for complete separation Relative importance "A measure of contribution of each of the independent variable where the weights will sum to the coefficient of determination, R2. Relative importance is a way to measure how much each predictor in a statistical model contributes to the overall fit of the model. It is calculated by dividing the coefficient for each predictor by the sum of all the coefficients in the model " Roc curve "A receiver operating characteristic (ROC) curve is a graphical plot that shows the performance of a binary classification model at different classification thresholds. It is a visual representation of the trade-off between the true positive rate (sensitivity) and the false positive rate (1-specificity) of a model. A graphical means of portraying the trade-off between sensitivity (true positive rate) versus 1 – specificity (false positive rate) for all possible cutoff values between 0 and 1. <div>To make it easier to understand, you can think of an ROC curve as a plot that shows how well a binary classification model is able to distinguish between two classes (e.g., positive and negative). A good model will be able to correctly classify a large proportion of positive cases as positive and a large proportion of negative cases as negative. This will result in a curve that is close to the top left corner of the plot, which represents a high true positive rate and a low false positive rate.</div><div>The area under the curve (AUC) is a measure of how well the model performs. A model with an AUC of 1.0 is a perfect classifier, while a model with an AUC of 0.5 is a random classifier. You can use the AUC to compare the performance of different models and see which one is the best.</div><div><div><div><div><div><div><div><div>It is important to note that the ROC curve and AUC are most useful when you have a balanced dataset, where there are roughly equal numbers of positive and negative cases. If your dataset is heavily imbalanced, these metrics may not be as reliable.</div></div></div></div><div></div></div></div></div> </div> " Sensitivity Represents the true positive rate—percentage of actual positive outcomes that are predicted as positive. Specificity Represents the true negative rate—percentage of actual negative outcomes that are predicted as negative. true negative One of the four cells of the classification matrix that denotes the number of observations that were negative and were correctly predicted to be negative. true positive One of the four cells of the classification matrix that denotes the number of observations that were positive and were correctly predicted to be positive. Weight of evidence A measure of the impact of each category of a nonmetric independent variable in terms of distinguishing between the two outcome groups. When combined across all categories, it provides an overall measure termed information value. Youden index A measure of overall predictive accuracy that is calculated as the sum of sensitivity and specificity minus 1. Higher values indicate better model fit with a maximum value of 1 and a minimum value of -1 Atomistic fallacy Incorrect conclusions about group level behavior based on individual behavior. The reverse of ecological fallacy condition index Measure of the relative amount of variance associated with an eigenvalue. A large condition index indicates a high degree of collinearity. context Any external factor outside the unit of analysis that not only impacts the outcome of multiple individuals, but also creates differences between individuals in separate contexts and foster dependencies between the individuals in a single context. cook’s distance (Di) Summary measure of the influence of a single case (observation) based on the total changes in all other residuals when the case is deleted from the estimation process. Large values (usually greater than 1) indicate substantial influence by the case in affecting the estimated regression coefficients. COVRATIO Measure of the influence of a single observation on the entire set of estimated regression coefficients. A value close to 1 indicates little influence. If the COVRATIO value minus 1 is greater than +/-3p/n (where p is the number of independent variables + 1, and n is the sample size), the observation is deemed to be influential based on this measure. Deleted residual Process of calculating residuals in which the influence of each observation is removed when calculating its residual. This is accomplished by omitting the ith observation from the regression equation used to calculate its predicted value. DFBetA Measure of the change in a regression coefficient when an observation is omitted from the regression analysis. The value of DFBETA is in terms of the coefficient itself; a standardized form (SDFBETA) is also available. No threshold limit can be established for DFBETA, although the researcher can look for values substantially different from the remaining observations to assess potential influence. The SDFBETA values are scaled by their standard errors, thus supporting the rationale for cut-offs of 1 or 2, corresponding to confidence levels of .10 or .05, respectively.SDFBetA DFFit "Measure of an observation's impact on the overall model fit, which also has a standardized version (SDFFIT). The best rule of thumb is to classify as influential any standardized values (SDFFIT) that exceed 2 sq.p/n, where p is the number of independent variables + 1 and n is the sample size. There is no threshold value for the DFFIT measure. SDFFit " ecological fallacy Incorrectly drawing conclusions about individual behavior from relationships based on aggregated data. Fixed effect Default estimation of effects in regression where a point estimate with no variation is made for a parameter estimate (either an intercept or coefficient). Functional relationship Dependence relationship that has no error in prediction. Also see statistical relationship. Hat matrix Matrix that contains values for each observation on the diagonal, known as hat values, which represent the impact of the observed dependent variable on its predicted value. If all cases have equal influence, each would have a value of p/n, where p equals the number of independent variables + 1, and n is the number of cases. If a case has no influence, its value would be -1 / n, whereas total domination by a single case would result in a value of (n - 1) /n. Values exceeding 2p/n for larger samples, or 3p/n for smaller samples (n<=30 , are candidates for classification as influential observations. Hat value hat matrix. Hierarchical data structure Observations which have a natural nesting effect created by contexts. When the error terms have increasing or modulating variance, the data are said to be heteroscedastic. The discussion of residuals in this chapter further illustrates this point. intraclass correlation (icc) Measure of the degree of dependence among individuals within a higher-level grouping. Level-1 The lowest level in a hierarchical data structure, most often associated with individuals. Level-2 The first level of a hierarchical data structure where observations from Level-1 are grouped together because of a context present at Level-2. Common examples are students (Level-1) within classrooms (Level-2). Mahalanobis distance (D2) Measure of the uniqueness of a single observation based on differences between the observation’s values and the mean values for all other cases across all independent variables. The source of influence on regression results is for the case to be quite different on one or more predictor variables, thus causing a shift of the entire regression equation Mediation The effect of an independent variable “works through” an intervening or mediating variable. Multilevel model (MLM) Extension of regression analysis that allows for the incorporation of both individual (Level-1) and contextual (Level-2) effects with the appropriate statistical treatment Panel analysis panel models.Regression-based analytical technique designed to handle cross-sectional analyses of longitudinal or time-series data. Psychologistic fallacy  The failure to acknowledge the impact of contexts and group effects on relationships at the individual level. Random effect Makes an estimate of the variability or distribution of a parameters across a set of groups. Method of quantifying the variability of a parameter (intercept or coefficient) within a group by a form of pooling across groups. Regression coefficient variance–decomposition matrix Method of determining the relative contribution of each eigenvalue to each estimated coefficient. If two or more coefficients are highly associated with a single eigenvalue (condition index), an unacceptable level of multicollinearity is indicated. SDFBetA DFBETA Standardized residual Rescaling of the residual to a common basis by dividing each residual by the standard deviation of the residuals. Thus, standardized residuals have a mean of 0 and standard deviation of 1. Each standardized residual value can now be viewed in terms of standard errors in middle to large sample sizes. This provides a direct means of identifying outliers as those with values above 1 or 2 for confidence levels of .10 and .05, respectively. 1- R 2 ratio Diagnostic measure employed in variable clustering to assess whether variables are singularly represented by a cluster component or have a substantive cross-loading. A priori criterion A stopping rule for determining the number of factors. This rule is determined solely on the researcher’s judgment and experience. The researcher may know the desired structure, be testing a specific structure or other conceptually-based considerations so that the number of factors can be predetermined cluster component A principal component extracted in variable clustering which contains only a subset of the complete variable set. confirmatory approach An approach to factor analysis, typically associated with structural equation modeling, that assesses the extent to which a pre-defined structure fits the data. This approach contrasts with an exploratory approach, which is data driven and the analysis reveals the structure convergent validity The degree to which two measures (scales) of the same concept are correlated. One aspect of construct validity. construct validity Broad approach to ensure the validity of a set of items as representative of a conceptual definition. Includes specific sub-elements of convergent validity, discriminant validity and nomological validity Discriminant validity One element of construct validity focusing on the degree to which two concepts are distinct. Every scale in the analysis must be shown to have discriminant validity from all other scales. exploratory approach An approach to factor analysis in which the objective is to define the structure within a set of variables, with no pre-specification of number of factors or which variables are part of a factor. Contrasted to a confirmatory approach where the structure is pre-defined. item indicator Kaiser rule latent root criterion.One of the stopping rules to determine how many factors to retain in the analysis. In this rule, all factors with eigenvalues (latent roots) greater than 1.0 are retained optimal scaling  Process of transforming nonmetric data (i.e., nominal and ordinal) to a form suitable for use in principal component analysis. Parallel analysis  A stopping rule based on comparing the factor eigenvalues to a set of eigenvalues generated from random data. The basic premise is to retain factors that have eigenvalues exceeding those which would be generated by random data. Percentage of variance criterion  Percentage of variance criterion A stopping rule for the number of factors to retain which is based on the amount of total variance accounted for in a set of factors, or the communality of each of the variables. The threshold value is specified by the researcher based on the objectives of the research and judgments about the quality of the data being analyzed. Principal component analysis  Factor model in which the factors are based on the total variance. With principal component analysis, unities (1s) are used in the diagonal of the correlation matrix; this procedure computationally implies that all the variance is common or shared Scale development  A specific process, usually involving both exploratory and confirmatory factor analyses, that attempts to define a set of variables which represent a concept that cannot be adequately measured by a single variable.  Scoring procedure Saves the scoring coefficients from the factor matrix and then allows them to be applied to new datasets to generate factor scores as a form of replication of the original results. Scree test  A stopping rule based on the pattern of eigenvalues of the extracted factors. A plot of the eigenvalues is examined to find an “elbow” in the pattern denoting subsequent factors that are not distinctive. Stopping rule  A criterion for determining the number of factors to retain in the final results, including the latent root criterion, a priori criterion, percentage of variance criterion, scree test and parallel analysis. Unidimensional  A characteristic of the set of variables forming a summated scale where these variables are only correlated with the hypothesized factor (i.e., have a high factor loading only on this factor). Variable clustering A variant of principal component analysis which estimates components with only subsets of the original variable set (cluster components). These cluster components are typically estimated in a hierarchical fashion by “splitting” a cluster component when two principal components can be extracted. This splitting process continues until some threshold is achieved. Binning Process of categorizing a metric variable into a small number of categories/bins and thus converting the variable into a nonmetric form. cardinality  The number of distinct data values for a variable. centering A variable transformation in which a specific value (e.g., the variable mean) is subtracted from each observation’s value, thus improving comparability among variables cold deck imputation Imputation method for missing data that derives the imputed value from an external source (e.g., prior studies, other samples). curse of dimensionality The problems associated with including a very large number of variables in the analysis. Among the notable problems are the distance measures becoming less useful along with higher potential for irrelevant variables and differing scales of measurement for the variables. <div>The curse of dimensionality is a problem that can happen when we have lots of different things to measure or consider in a situation. For example, if we are trying to predict how much someone will like a movie, we might consider things like the actors, the director, the genre, and the plot. These are all different dimensions or factors that we can use to describe the movie.</div> Data management All of the activities associated with assembling a dataset for analysis. With the arrival of the larger and diverse datasets from Big Data, researchers may now find they spend a vast majority of their time on this task rather than analysis. Data quality  Generally referring to the accuracy of the information in a dataset, recent efforts have identified eight dimensions that are much broader in scope and reflect the usefulness in many aspects of analysis and application: completeness, availability and accessibility, currency, accuracy, validity, usability and interpretability, reliability and credibility, and consistency. dcor  A newer measure of association that is distance-based and more sensitive to nonlinear patterns in the data. Dichotomization Dividing cases into two classes based on being above or below a specified value elasticity  Measure of the ratio of percentage change in Y for a percentage change in X. Obtained by using a log-log transformation of both dependent and independent variables. EM   Imputation method applicable when MAR missing data processes are encountered which employs maximum likelihood estimation in the calculation of imputed values. <div>EM, or Expectation-Maximization, is an iterative algorithm used to find the maximum likelihood estimate (MLE) of a set of parameters in a statistical model. It is often used when the MLE cannot be found directly, or when the data is incomplete or missing.</div> extreme groups approach  Transformation method where observations are sorted into groups (e.g., high, medium and low) and then the middle group discarded in the analysis Heat map  Form of scatterplot of nonmetric variables where frequency within each cell is color-coded to depict relationships. Hoeffding’s D "New measure of association/correlation that is based on distance measures between the variables and thus more likely to incorporate nonlinear components <div>Hoeffding's D is a way to compare two sets of numbers and see how different they are. It can help us tell if the differences between the sets of numbers are big enough to be important, or if they could have happened by chance.</div> " Hot deck imputation Imputation method in which the imputed value is taken from an existing observation deemed similar. ipsatizing  Method of transformation for a set of variables on the same scale similar to centering, except that the variable used for centering all of the variables is the mean value for the observation (e.g., person-centered). Mean substitution  Imputation method where the mean value of all valid values is used as the imputed value for missing data. Mic (mutual information correlation) New form of association/correlation that can represent any form of dependence (e.g., circular patterns) and not limited to just linear relationships Missingness   The absence or presence of missing data for a case or observation. Does not relate directly to how that missing data value might be imputed. Multiple imputation Imputation method applicable to MAR missing data processes in which several datasets are created with different sets of imputed data. The process eliminates not only bias in imputed values, but also provides more appropriate measures of standard errors. Regression imputation Imputation method that employs regression to estimate the imputed value based on valid values of other variables for each observation Response surface  A transformation method in which a form of polynomial regression is used to represent the distribution of an outcome variable in an empirical form that can be portrayed as a surface. Standardization  Transformation method where a variable is centered (i.e., variable’s mean value subtracted from each observation’s value) and then “standardized” by dividing the difference by the variable’s standard deviation. Provides a measure that is comparable across variables no matter what their original scale Algorithmic models  Models based on algorithms (e.g., neural networks, decision trees, support vector machine) that are widely used in many Big Data applications. Their emphasis is on predictive accuracy rather than statistical inference and explanation as seen in statistical/data models such as multiple regression.Data mining models Big Data  The explosion in secondary data typified by increases in the volume, variety and velocity of the data being made available from a myriad set of sources (e.g., social media, customer-level data, sensor data, etc.). causal inference Methods that move beyond statistical inference to the stronger statement of “cause and effect” in non-experimental situations. cross-validation  "Method of validation where the original sample is divided into a number of smaller sub-samples (validation samples) and that the validation fit is the “average” fit across all of the sub-samples. <div><div><div><div><div><div><div>Cross-validation is a method for evaluating the performance of a machine learning model. It involves dividing the data into smaller groups and using them to train and evaluate the model. This helps to get a more accurate idea of how well the model will perform on new data. It is useful because it allows the model to be tested on different data sets, which can provide a better estimate of its performance.</div></div></div></div></div></div></div><div><div><div></div></div></div><div><div><div><div></div></div><div><div><div><div><div>Cross-validation is like a test to see how well a machine learning model can predict things. We take our data and split it into smaller groups. Then we use those groups to train and test the model. This helps us understand how good the model is at predicting things it hasn't seen before. It's useful because it lets us test the model on different data and get a better idea of how it will do.</div></div></div></div></div></div></div> " Data mining models . Models based on algorithms (e.g., neural networks, decision trees, support vector machine) that are widely used in many Big Data applications. Their emphasis is on predictive accuracy rather than statistical inference and explanation as seen in statistical/data models such as multiple regression. Data models statistical models. The form of analysis where a specific model is proposed (e.g., dependent and independent variables to be analyzed by the general linear model), the model is then estimated and a statistical inference is made as to its generalizability to the population through statistical tests. Operates in opposite fashion from data mining models which generally have little model specification and no statistical inference. Dimensional reduction  The reduction of multicollinearity among variables by forming composite measures of multicollinear variables through such methods as exploratory factor analysis Directed acyclic graph (DAG) Graphical portrayal of causal relationships used in causal inference analysis to identify all “threats” to causal inference. Similar in some ways to path diagrams used in structural equation modeling. estimation sample  Portion of original sample used for model estimation in conjunction with validation sample General linear model (GLM)  Fundamental linear dependence model which can be used to estimate many model types (e.g., multiple regression, ANONA/MANOVA, discriminant analysis) with the assumption of a normally distributed dependent measure. Generalized linear model (GLZ or GLiM)  Similar in form to the general linear model, but able to accommodate non-normal dependent measures such as binary variables (logistic regression model). Uses maximum likelihood estimation rather than ordinary least squares. overfitting  "Estimation of model parameters that over-represent the characteristics of the sample at the expense of generalizability to the population at large <div><div><div><div><div><div><div><div>Overfitting is when a model is trained with too much data and it ends up learning the specific details and random noise in the data rather than just the important trends and patterns. This can make the model perform poorly when it is applied to new data. It is important to use techniques such as cross-validation or bootstrapping to prevent overfitting.</div></div></div></div><div></div></div></div></div><div><div> </div><div><div></div></div></div><div><div><div><div></div></div><div><div><div><div><div>Overfitting is a problem that occurs when a statistical model is too complex for the data it is trying to model. This can lead to the model fitting the data too closely, causing it to perform poorly when applied to new, unseen data. In other words, it is when a model is too specific to the data it was trained on and cannot generalize well to new data. To prevent overfitting, it is important to choose a model that is simple enough to avoid fitting the noise in the data, but complex enough to capture the underlying patterns.</div></div></div></div><div></div></div></div></div><div><div> </div><div><div></div></div></div><div><div><div><div></div></div><div><div><div><div><div>Overfitting is when we create a model that explains the data really well, but only for the specific data we have. It doesn't work as well for new data. It's like trying to fit a square peg into a round hole. We force the model to fit the data, but it doesn't fit other data very well.</div></div></div></div></div></div></div><div><div><div></div></div></div><div><div><div><div></div></div><div><div><div><div><div>An example of overfitting might be if you are trying to create a model to predict the weather in your city. You gather data on the temperature, humidity, and atmospheric pressure for the past year and use it to build your model. Your model might be very accurate when predicting the weather for the next few days, but if you try to use it to predict the weather a month in advance, it might not be as accurate because it is too specific to the characteristics of the data you used to build the model and doesn't generalize well to other weather patterns.</div></div></div></div></div></div></div></div><div>Overfitting occurs when we estimate the model parameters too closely to the characteristics of the sample, rather than trying to capture the true underlying relationship in the population. This can lead to poor predictions when the model is applied to new data. </div> " Statistical models   The form of analysis where a specific model is proposed (e.g., dependent and independent variables to be analyzed by the general linear model), the model is then estimated and a statistical inference is made as to its generalizability to the population through statistical tests. Operates in opposite fashion from data mining models which generally have little model specification and no statistical inference. treatment  Independent variable the researcher manipulates to see the effect (if any) on the dependent variable(s), such as in an experiment (e.g., testing the appeal of color versus black-and-white advertisements) Validation sample  Validation sample Portion of the sample “held out” from estimation and then used for an independent assessment of model fit on data that was not used in estimation. also known as Holdout sample. <div><div><div><div><div><div><div>Validation sample is a part of the data that is not used to build the model, but is used to test its accuracy. This is done to make sure that the model can accurately predict the outcome for new data, and is not just memorizing the training data.</div></div></div></div><div></div></div></div></div> Between-groups design another name for independent design. Between-subjects design another name for independent design. Bimodal a description of a distribution of observations that has two modes. Binary variable a categorical variable that has only two mutually exclusive categories (e.g., being dead or alive). Boredom effect refers to the possibility that performance in tasks may be influenced (the assumption is a negative influence) by boredom or lack of concentration if there are many tasks, or the task goes on for a long period of time. Central tendency a generic term describing the centre of a frequency distribution of observations as measured by the mean, mode and median. Concurrent validity a form of criterion validity where there is evidence that scores from an instrument correspond to concurrently recorded external measures conceptually related to the measured construct. Confounding variable "a variable (that we may or may not have measured) other than the predictor variables in which we're interested that potentially affects an outcome variable. I.e. a control variable gone wrong " Content validity evidence that the content of a test corresponds to the content of the construct it was designed to cover. Continuous variable a variable that can be measured to any level of precision. (Time is a continuous variable, because there is in principle no limit on how finely it could be measured.) Correlational research a form of research in which you observe what naturally goes on in the world without directly interfering with it. This term implies that data will be analysed so as to look at relationships between naturally occurring variables rather than making statements about cause and effect. Compare with cross-sectional research, longitudinal research and experimental research. Counterbalancing a process of systematically varying the order in which experimental conditions are conducted. In the simplest case of there being two conditions (A and B), counterbalancing simply implies that half of the participants complete condition A followed by condition B, whereas the remainder do condition B followed by condition A. The aim is to remove systematic bias caused by practice effects or boredom effects. Criterion validity evidence that scores from an instrument correspond with (concurrent validity) or predict (predictive validity) external measures conceptually related to the measured construct. Cross-sectional research a form of research in which you observe what naturally goes on in the world without directly interfering with it, by measuring several variables at a single time point. In psychology, this term usually implies that data come from people at different age points, with different people representing each age point. See also correlational research, longitudinal research. Dependent variable another name for outcome variable. This name is usually associated with experimental methodology (which is the only time it really makes sense) and is used because it is the variable that is not manipulated by the experimenter and so its value depends on the variables that have been manipulated. Deviance the difference between the observed value of a variable and the value of that variable predicted by a statistical model. Discrete variable a variable that can only take on certain values (usually whole numbers) on the scale. Ecological validity evidence that the results of a study, experiment or test can be applied, and allow inferences, to real-world conditions. Experimental research a form of research in which one or more variables are systematically manipulated to see their effect (alone or in combination) on an outcome variable. This term implies that data will be able to be used to make statements about cause and effect. Compare with cross-sectional research and correlational research. Falsification the act of disproving a hypothesis or theory. Frequency distribution a graph plotting values of observations on the horizontal axis, and the frequency with which each value occurs in the data set on the vertical axis (a.k.a. histogram). Histogram a frequency distribution. Hypothesis a prediction about the state of the world (see experimental hypothesis and null hypothesis). Independent design an experimental design in which different treatment conditions utilize different organisms (e.g., in psychology, this would mean using different people in different treatment conditions) and so the resulting data are independent (a.k.a. between-groups or between-subjects design). Independent variable another name for a predictor variable. This name is usually associated with experimental methodology (which is the only time it makes sense) and is used because it is the variable that is manipulated by the experimenter and so its value does not depend on any other variables (just on the experimenter). I just use the term predictor variable all the time because the meaning of the term is not constrained to a particular methodology. Interquartile range the limits within which the middle 50% of an ordered set of observations fall. It is the difference between the value of the upper quartile and lower quartile. Interval variable "data measured on a scale along the whole of which intervals are equal. For example, people's ratings of this book on Amazon.com can range from 1 to 5; for these data to be interval it should be true that the increase in appreciation for this book represented by a change from 3 to 4 along the scale should be the same as the change in appreciation represented by a change from 1 to 2, or 4 to 5. " Kurtosis this measures the degree to which scores cluster in the tails of a frequency distribution. There are different ways to estimate kurtosis and in SPSS no kurtosis is expressed as 0 (but be careful because outside of SPSS no kurtosis is sometimes a value of 3). A distribution with positive kurtosis (leptokurtic, kurtosis > 0) has too many scores in the tails and is too peaked, whereas a distribution with negative kurtosis (platykurtic, kurtosis < 0) has too few scores in the tails and is quite flat. Leptokurtic see Kurtosis. Levels of measurement the relationship between what is being measured and the numbers obtained on a scale. Longitudinal research a form of research in which you observe what naturally goes on in the world without directly interfering with it by measuring several variables at multiple time points. See also correlational research, cross-sectional research. Mean "a simple statistical model of the centre of a distribution of scores. A hypothetical estimate of the 'typical' score. " Measurement error "the discrepancy between the numbers used to represent the thing that we're measuring and the actual value of the thing we're measuring (i.e., the value we would get if we could measure it directly). " Median the middle score of a set of ordered observations. When there is an even number of observations the median is the average of the two scores that fall either side of what would be the middle value. Mode the most frequently occurring score in a set of data. Multimodal description of a distribution of observations that has more than two modes. Nominal variable "where numbers merely represent names. For example, the numbers on sports players' shirts: a player with the number 1 on her back is not necessarily worse than a player with a 2 on her back. The numbers have no meaning other than denoting the type of player (full back, centre forward, etc.). " Noniles a type of quantile; they are values that split the data into nine equal parts. They are commonly used in educational research. Normal distribution a probability distribution of a random variable that is known to have certain properties. It is perfectly symmetrical (has a skew of 0), and has a kurtosis of 0. Ordinal variable "data that tell us not only that things have occurred, but also the order in which they occurred. These data tell us nothing about the differences between values. For example, gold, silver and bronze medals are ordinal: they tell us that the gold medallist was better than the silver medallist, but they don't tell us how much better (was gold a lot better than silver, or were gold and silver very closely competed?). " Outcome variable a variable whose values we are trying to predict from one or more predictor variables. Percentiles a type of quantile; they are values that split the data into 100 equal parts. Platykurtic see Kurtosis. Positive skew see skew. Practice effect "refers to the possibility that participants' performance in a task may be influenced (positively or negatively) if they repeat the task because of familiarity with the experimental situation and/or the measures being used. " Predictive validity a form of criterion validity where there is evidence that scores from an instrument predict external measures (recorded at a different point in time) conceptually related to the measured construct. Predictor variable a variable that is used to try to predict values of another variable known as an outcome variable. Probability density function (PDF) the function that describes the probability of a random variable taking a certain value. It is the mathematical function that describes the probability distribution. Probability distribution a curve describing an idealized frequency distribution of a particular variable from which it is possible to ascertain the probability with which specific values of that variable will occur. For categorical variables it is simply a formula yielding the probability with which each category occurs. Qualitative methods extrapolating evidence for a theory from what people say or write (cf. quantitative methods). Quantiles values that split a data set into equal portions. Quartiles, for example, are a special case of quantiles that split the data into four equal parts. Similarly, percentiles are points that split the data into 100 equal parts and noniles are points that split the data into 9 equal parts (you get the general idea). Quartiles a generic term for the three values that cut an ordered data set into four equal parts. The three quartiles are known as the lower quartile, the second quartile (or median) and the upper quartile. Randomization the process of doing things in an unsystematic or random way. In the context of experimental research the word usually applies to the random assignment of participants to different treatment conditions. Range the range of scores is the value of the smallest score subtracted from the highest score. It is a measure of the dispersion of a set of scores. See also variance, standard deviation, and interquartile range. Ratio variable "an interval variable but with the additional property that ratios are meaningful. For example, people's ratings of this book on Amazon.com can range from 1 to 5; for these data to be ratio not only must they have the properties of interval variables, but in addition a rating of 4 should genuinely represent someone who who rated it as 2. Likewise, someone who rated it as 1 should be half enjoyed this book twice as much as someone as impressed as someone who rated it as 2. " Reliability the ability of a measure to produce consistent results when the same entities are measured under different conditions. Repeated-measures design an experimental design in which different treatment conditions utilize the same organisms (i.e., in psychology, this would mean the same people take part in all experimental conditions) and so the resulting data are related (a.k.a. related design or within-subject design). Skew a measure of the symmetry of a frequency distribution. Symmetrical distributions have a skew of 0. When the frequent scores are clustered at the lower end of the distribution and the tail points towards the higher or more positive scores, the value of skew is positive. Conversely, when the frequent scores are clustered at the higher end of the distribution and the tail points towards the lower more negative scores, the value of skew is negative. Standard deviation an estimate of the average variability (spread) of a set of data measured in the same units of measurement as the original data. It is the square root of the variance. Systematic variation "variation due to some genuine effect (be it the effect of an experimenter doing something to all of the participants in one sample but not in other samples, or natural variation between sets of variables). We can think of this as variation that can be explained by the model that we've fitted to the data. " Sum of squared errors another name for the sum of squares. Tertium quid the possibility that an apparent relationship between two variables is actually caused by the effect of a third variable on them both (often called the third-variable problem). Test-retest reliability the ability of a measure to produce consistent results when the same entities are tested at two different points in time. Theory although it can be defined more formally, a theory is a hypothesized general principle or set of principles that explain known findings about a topic and from which new hypotheses can be generated. Unsystematic variation "this is variation that isn't due to the effect in which we're interested (so could be due to natural differences between people in different samples such as differences in intelligence or motivation). We can think of this as variation that can't be explained by whatever model we've fitted to the data. " Upper quartile the value that cuts off the highest 25% of ordered scores. If the scores are ordered and then divided into two halves at the median, then the upper quartile is the median of the top half of the scores. Validity evidence that a study allows correct inferences about the question it was aimed to answer or that a test measures what it set out to measure conceptually (see also Content validity, Criterion validity). Variance an estimate of average variability (spread) of a set of data. It is the sum of squares divided by the number of values on which the sum of squares is based minus 1. Within-subject design another name for a repeated-measures design. z-score the value of an observation expressed in standard deviation units. It is calculated by taking the observation, subtracting from it the mean of all observations, and dividing the result by the standard deviation of all observations. By converting a distribution of observations into z-scores a new distribution is created that has a mean of 0 and a standard deviation of 1. α-level the probability of making a Type I error (usually this value is .05). Alternative hypothesis the prediction that there will be an effect (i.e., that your experimental manipulation will have some effect or that certain variables will relate to each other). β-level the probability of making a Type II error (Cohen, 1992, suggests a maximum value of .2). Bonferroni correction a correction applied to the α-level to control the overall Type I error rate when multiple significance tests are carried out. Each test conducted should use a criterion of significance of the α-level (normally .05) divided by the number of tests conducted. This is a simple but effective correction, but tends to be too strict when lots of tests are performed. Central limit theorem this theorem states that when samples are large (above about 30) the sampling distribution will take the shape of a normal distribution regardless of the shape of the population from which the sample was drawn. For small samples the t-distribution better approximates the shape of the sampling distribution. We also know from this theorem that the standard deviation of the sampling distribution (i.e., the standard error of the sample mean) will be equal to the standard deviation of the sample(s) divided by the square root of the sample size (N). "Cohen's d ""An effect size that expressed the difference between two means in standard deviation units. In general it can be estimated using the formula above. <div><img src=""quizlet-C.h01M.DuqkV9S5OGtQF6w.png""></div> " Confidence interval for a given statistic calculated for a sample of observations (e.g., the mean), the confidence interval is a range of values around that statistic that are believed to contain, with a certain probability (e.g., 95%), the true value of that statistic (i.e., the population value). Degrees of freedom "an impossible thing to define in a few pages, let alone a few lines. Essentially it is the number of 'entities' that are free to vary when estimating some kind of statistical parameter. In a more practical sense, it has a bearing on significance tests for many commonly used test statistics (such as the F-ratio, t-test, chi-square statistic) and determines the exact form of the probability distribution for these test statistics. I.e. football players " Deviance the difference between the observed value of a variable and the value of that variable predicted by a statistical model. Effect size "an objective and (usually) standardized measure of the magnitude of an observed effect. Measures include Cohen's d, Glass's g and Pearson's correlations coefficient, r. " Experimental hypothesis synonym for alternative hypothesis. Experimentwise error rate the probability of making a Type I error in an experiment involving one or more statistical comparisons when the null hypothesis is true in each case. Familywise error rate "the probability of making a Type I error in any family of tests when the null hypothesis is true in each case. The 'family of tests' can be loosely defined as a set of tests conducted on the same data set and addressing the same empirical question. " Fit "how sexually attractive you find a statistical test. Alternatively, it's the degree to which a statistical model is an accurate representation of some observed data. (Incidentally, it's just plain wrong to find statistical tests sexually attractive.) " Linear model a model that is based upon a straight line. Meta-analysis this is a statistical procedure for assimilating research findings. It is based on the simple idea that we can take effect sizes from individual studies that research the same question, quantify the observed effect in a standard way (using effect sizes) and then combine these effects to get a more accurate idea of the true effect in the population. Method of least squares a method of estimating parameters (such as the mean, or a regression coefficient) that is based on minimizing the sum of squared errors. The parameter estimate will be the value, out of all of those possible, that has the smallest sum of squared errors. Null hypothesis "the reverse of the experimental hypothesis, it says that your prediction is wrong and the predicted effect doesn't exist. " One-tailed test "a test of a directional hypothesis. For example, the hypothesis 'the longer I write this glossary, the more I want to place my editor's genitals in a starved crocodile's mouth' requires a one-tailed test because I've stated the direction of the relationship (see also two-tailed test). " Parameter "a very difficult thing to describe. When you fit a statistical model to your data, that model will consist of variables and parameters: variables are measured constructs that vary across entities in the sample, whereas parameters describe the relations between those variables in the population. In other words, they are constants believed to represent some fundamental truth about the measured variables. We use sample data to estimate the likely value of parameters because we don't have direct access to the population. Of course it's not quite as simple as that. " Population in statistical terms this usually refers to the collection of units (be they people, plankton, plants, cities, suicidal authors, etc.) to which we want to generalize a set of findings or a statistical model. Power the ability of a test to detect an effect of a particular size (a value of .8 is a good level to aim for). Sample a smaller (but hopefully representative) collection of units from a population used to determine truths about that population (e.g., how a given population behaves in certain conditions). Sampling distribution the probability distribution of a statistic. We can think of this as follows: if we take a sample from a population and calculate some statistic (e.g., the mean), the value of this statistic will depend somewhat on the sample we took. As such the statistic will vary slightly from sample to sample. If, hypothetically, we took lots and lots of samples from the population and calculated the statistic of interest we could create a frequency distribution of the values we got. The resulting distribution is what the sampling distribution represents: the distribution of possible values of a given statistic that we could expect to get from a given population. Sampling variation the extent to which a statistic (the mean, median, t, F, etc.) varies in samples taken from the same population. Standard error the standard deviation of the sampling distribution of a statistic. For a given statistic (e.g., the mean) it tells us how much variability there is in this statistic across samples from the same population. Large values, therefore, indicate that a statistic from a given sample may not be an accurate reflection of the population from which the sample came. Standard error of the mean (SE) the standard error associated with the mean. Test statistic a statistic for which we know how frequently different values occur. The observed value of such a statistic is typically used to test hypotheses. = signal/noise = effect/error = variance explained by model/variance not explained by model Two-tailed test "a test of a non-directional hypothesis. For example, the hypothesis 'writing this glossary has some effect on what I want to do with my editor's genitals' requires a two-tailed test because it doesn't suggest the direction of the relationship. " Type I error "occurs when we believe that there is a genuine effect in our population, when in fact there isn't. " Type II error occurs when we believe that there is no effect in the population, when in fact there is. Bar chart a graph in which a summary statistic (usually the mean) is plotted on the y-axis against a categorical variable on the x-axis (this categorical variable could represent, for example, groups of people, different times or different experimental conditions). The value of the mean for each category is shown by a bar. Different-coloured bars may be used to represent levels of a second categorical variable. Boxplot (a.k.a. box-whisker diagram) a graphical representation of some important characteristics of a set of observations. At the centre of the plot is the median, which is surrounded by a box, the top and bottom of which are the limits within which the middle 50% of observations fall (the interquartile range). Sticking out of the top and bottom of the box are two whiskers which extend to the highest and lowest extreme scores, respectively. Chartjunk superfluous material that distracts from the data being displayed on a graph. Density plot similar to a histogram except that rather than having a summary bar representing the frequency of scores, it shows each individual score as a dot. They can be useful for looking at the shape of a distribution of scores Error bar chart a graphical representation of the mean of a set of observations that includes the 95% confidence interval of the mean. The mean is usually represented as a circle, square or rectangle at the value of the mean (or a bar extending to the value of the mean). The confidence interval is represented by a line protruding from the mean (upwards, downwards or both) to a short horizontal line representing the limits of the confidence interval. Error bars can be drawn using the standard error or standard deviation instead of the 95% confidence interval. Line chart a graph in which a summary statistic (usually the mean) is plotted on the y-axis against a categorical variable on the x-axis (this categorical variable could represent, for example, groups of people, different times or different experimental conditions). The value of the mean for each category is shown by a symbol, and means across categories are connected by a line. Different-coloured lines may be used to represent levels of a second categorical variable. Regression line a line on a scatterplot representing the regression model of the relationship between the two variables plotted. Scatterplot a graph that plots values of one variable against the corresponding value of another variable (and the corresponding value of a third variable can also be included on a 3-D scatterplot). Bootstrap a technique from which the sampling distribution of a statistic is estimated by taking repeated samples (with replacement) from the data set (in effect, treating the data as a population from which smaller samples are taken). The statistic of interest (e.g., the mean, or b coefficient) is calculated for each sample, from which the sampling distribution of the statistic is estimated. The standard error of the statistic is estimated as the standard deviation of the sampling distribution created from the bootstrap samples. From this, confidence intervals and significance tests can be computed. Contaminated normal distribution see mixed normal distribution. "Hartley's Fmax "also known as the variance ratio, this is the ratio of the variances between the group with the biggest variance and the group with the smallest variance. This ratio is compared to critical values in a table published by Hartley as a test of homogeneity of variance. Some general rules are that with sample sizes (n) of 10 per group, an Fmax less than 10 is more or less always going to be non-significant, with 15-20 per group the ratio needs to be less than about 5, and with samples of 30-60 the ratio should be below about 2 or 3. Heterogeneity of variance the opposite of homogeneity of variance. This term means that the variance of one variable varies (i.e., is different) across levels of another variable. Homogeneity of variance the assumption that the variance of one variable is stable (i.e., relatively similar) at all levels of another variable. Independence the assumption that one data point does not influence another. When data come from people, it basically means that the behaviour of one person does not influence the behaviour of another. Kolmogorov-Smirnov test a test of whether a distribution of scores is significantly different from a normal distribution. A significant value indicates a deviation from normality, but this test is notoriously affected by large samples in which small deviations from normality yield significant results. "Levene's test ""this tests the hypothesis that the variances in different groups are equal (i.e., the difference between the variances is zero). It basically does a one-way ANOVA on the deviations (i.e., the absolute value of the difference between each score and the mean of its group). A significant result indicates that the variances are significantly different - therefore, the assumption of homogeneity of variances has been violated. When samples sizes are large, small differences in group variances can produce a significant Levene's test. " M-estimator a robust measure of location. One example is the median. In some cases it is a measure of location computed after outliers have been removed: unlike a trimmed mean, the amount of trimming used to remove outliers is determined empirically. Mixed normal distribution a normal-looking distribution that is contaminated by a small proportion of scores from a different distribution. These distributions are not normal and have too many scores in the tails (i.e., at the extremes). The effect of these heavy tails is to inflate the estimate of the population variance. This, in turn, makes significance tests lack power. Outlier an observation or observations very different from most others. Outliers bias statistics (e.g., the mean) and their standard errors and confidence intervals. P-P plot Short for a probability-probability plot. A graph plotting the cumulative probability of a variable against the cumulative probability of a particular distribution (often a normal distribution). Like a Q-Q plot, if values fall on the diagonal of the plot then the variable shares the same distribution as the one specified. Deviations from the diagonal show deviations from the distribution of interest. Parametric test a test that requires data from one of the large catalogue of distributions that statisticians have described. Normally this term is used for parametric tests based on the normal distribution, which require four basic assumptions that must be met for the test to be accurate: a normally distributed sampling distribution (see normal distribution), homogeneity of variance, interval or ratio data, and independence. Q-Q plot short for a quantile-quantile plot. A graph plotting the quantiles of a variable against the quantiles of a particular distribution (often a normal distribution). Like a P-P plot, if values fall on the diagonal of the plot then the variable shares the same distribution as the one specified. Deviations from the diagonal show deviations from the distribution of interest. Robust test a term applied to a family of procedures to estimate statistics that are reliable even when the normal assumptions of the statistic are not met. Shapiro-Wilk test a test of whether a distribution of scores is significantly different from a normal distribution. A significant value indicates a deviation from normality, but this test is notoriously affected by large samples in which small deviations from normality yield significant results. Transformation the process of applying a mathematical function to all observations in a data set, usually to correct some distributional abnormality such as skew or kurtosis. Trimmed mean a statistic used in many robust tests. It is a mean calculated after a certain percentage of the distribution has been removed at the extremes. For example, a 20% trimmed mean is a mean calculated after the top and bottom 20% of ordered scores have been removed. Imagine we had 20 scores representing the annual income of students (in thousands, rounded to the nearest thousand: 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 35. The mean income is 5 (£5000). This value is biased by an outlier. A 10% trimmed mean will remove 10% of scores from the top and bottom of ordered scores before the mean is calculated. With 20 scores, removing 10% of scores involves removing the top and bottom 2 scores. This gives us: 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, the mean of which is 3.44. The mean depends on a symmetrical distribution to be accurate, but a trimmed mean produces accurate results even when the distribution is not symmetrical. There are more complex examples of robust methods such as the bootstrap. Variance ratio "see Hartley's Fmax. " Weighted least squares a method of regression in which the parameters of the model are estimated using the method of least squares but observations are weighted by some other variable. Often they are weighted by the inverse of their variance to combat heteroscedasticity. "Cochran's Q ""This test is an extension of McNemar's test and is basically a Friedman's ANOVA for dichotomous data. So imagine you asked 10 people whether they'd like to shoot Justin Timberlake, David Beckham and Simon Cowell and they could answer only 'yes' or 'no'. If we coded responses as 0 (no) and 1 (yes) we could do Cochran's test on these data. " "Friedman's ANOVA "a non-parametric test of whether more than two related groups differ. It is the non-parametric version of one-way repeated-measures ANOVA. Jonckheere-Terpstra test "this statistic tests for an ordered pattern of medians across independent groups. Essentially it does the same thing as the Kruskal-Wallis test (i.e., test for a difference between the medians of the groups) but it incorporates information about whether the order of the groups is meaningful. As such, you should use this test when you expect the groups you're comparing to produce a meaningful order of medians. " "Kendall's W ""this is much the same as Friedman's ANOVA but is used specifically for looking at the agreement between raters. So, if, for example, we asked 10 different women to rate the attractiveness of Justin Timberlake, David Beckham and Brad Pitt we could use this test to look at the extent to which they agree. Kendall's W ranges from 0 (no agreement between judges) to 1 (complete agreement between judges). " Kolmogorov-Smirnov Z not to be confused with the Kolmogorov-Smirnov test that tests whether a sample comes from a normally distributed population. This tests whether two groups have been drawn from the same population (regardless of what that population may be). It does much the same as the Mann-Whitney test and Wilcoxon rank-sum test! This test tends to have better power than the Mann-Whitney test when sample sizes are less than about 25 per group. Kruskal-Wallis test non-parametric test of whether more than two independent groups differ. It is the non-parametric version of one-way independent ANOVA. Mann-Whitney test "a non-parametric test that looks for differences between two independent samples. That is, it tests whether the populations from which two samples are drawn have the same location. It is functionally the same as Wilcoxon's rank-sum test, and both tests are non-parametric equivalents of the independent t-test. " "McNemar's test ""This tests differences between two related groups (see Wilcoxon signed-rank test and sign test), when nominal data have been used. It's typically used when we're looking for changes in people's scores and it compares the proportion of people who changed their response in one direction (i.e., scores increased) to those who changed in the opposite direction (scores decreased). So, this test needs to be used when we've got two related dichotomous variables. " Median test a non-parametric test of whether samples are drawn from a population with the same median. So, in effect, it does the same thing as the Kruskal-Wallis test. It works on the basis of producing a contingency table that is split for each group into the number of scores that fall above and below the observed median of the entire data set. If the groups are from the same population then these frequencies would be expected to be the same in all conditions (about 50% above and about 50% below). Monte Carlo method "a term applied to the process of using data simulations to solve statistical problems. Its name comes from the use of Monte Carlo roulette tables to generate 'random' numbers in the pre-computer age. Karl Pearson, for example, purchased copies of Le Monaco, a weekly Paris periodical that published data from the Monte Carlo casinos' roulette wheels. He used these data as pseudo-random numbers in his statistical research. " Moses extreme reactions "a non-parametric test that compares the variability of scores in two groups, so it's a bit like a non-parametric Levene's test. " Non-parametric tests a family of statistical procedures that do not rely on the restrictive assumptions of parametric tests. In particular, they do not assume that the sampling distribution is normally distributed. Pairwise comparisons comparisons of pairs of means. Ranking the process of transforming raw scores into numbers that represent their position in an ordered list of those scores. The raw scores are ordered from lowest to highest and the lowest score is assigned a rank of 1, the next highest score is assigned a rank of 2, and so on. Sign test Wald-Wolfowitz runs "another variant on the Mann-Whitney test. Scores are rank-ordered as in the Mann-Whitney test, but rather than analysing the ranks, this test looks for 'runs' of scores from the same group within the ranked order. Now, if there's no difference between groups then obviously ranks from the two groups should be randomly interspersed. However, if the groups are different then one should see more ranks from one group at the lower end, and more ranks from the other group at the higher end. By looking for clusters of scores in this way, the test can determine if the groups differ. " "Wilcoxon's rank-sum test "a non-parametric test that looks for differences between two independent samples. That is, it tests whether the populations from which two samples are drawn have the same location. It is functionally the same as the Mann-Whitney test, and both tests are non-parametric equivalents of the independent t-test. Wilcoxon signed-rank test a non-parametric test that looks for differences between two related samples. It is the non-parametric equivalent of the related t-test. Biserial correlation a standardized measure of the strength of relationship between two variables when one of the two variables is dichotomous. The biserial correlation coefficient is used when one variable is a continuous dichotomy (e.g., has an underlying continuum between the categories). Bivariate correlation a correlation between two variables. Coefficient of determination "the proportion of variance in one variable explained by a second variable. It is Pearson's correlation coefficient squared. " Covariance "a measure of the 'average' relationship between two variables. It is the average cross-product deviation (i.e., the cross-product divided by one less than the number of observations). " Cross-product deviations "a measure of the 'total' relationship between two variables. It is the deviation of one variable from its mean multiplied by the other variable's deviation from its mean. " "Kendall's tau ""a non-parametric correlation coefficient similar to Spearman's correlation coefficient, but should be used in preference for a small data set with a large number of tied ranks. " Partial correlation "a measure of the relationship between two variables while 'controlling' the effect of one or more additional variables on both. " "Pearson's correlation coefficient ""Pearson's product-moment correlation coefficient, to give it its full name, is a standardized measure of the strength of relationship between two variables. It can take any value from −1 (as one variable changes, the other changes in the opposite direction by the same amount), through 0 (as one variable changes the other doesn't change at all), to +1 (as one variable changes, the other changes in the same direction by the same amount). " Point-biserial correlation a standardized measure of the strength of relationship between two variables when one of the two variables is dichotomous. The point-biserial correlation coefficient is used when the dichotomy is a discrete, or true, dichotomy (i.e., one for which there is no underlying continuum between the categories). An example of this is pregnancy: you can be either pregnant or not, there is no in between. Semi-partial correlation "a measure of the relationship between two variables while 'controlling' the effect that one or more additional variables has on one of those variables. If we call our variables x and y, it gives us a measure of the variance in y that x alone shares. " "Spearman's correlation coefficient ""a standardized measure of the strength of relationship between two variables that does not rely on the assumptions of a parametric test. It is Pearson's correlation coefficient performed on data that have been converted into ranked scores. " Standardization the process of converting a variable into a standard unit of measurement. The unit of measurement typically used is standard deviation units (see also z-scores). Standardization allows us to compare data when different units of measurement have been used (we could compare weight measured in kilograms to height measured in inches). Adjusted predicted value a measure of the influence of a particular case of data. It is the predicted value of a case from a model estimated without that case included in the data. The value is calculated by re-estimating the model without the case in question, then using this new model to predict the value of the excluded case. If a case does not exert a large influence over the model then its predicted value should be similar regardless of whether the model was estimated including or excluding that case. The difference between the predicted value of a case from the model when that case was included and the predicted value from the model when it was excluded is the DFFit. Adjusted R² a measure of the loss of predictive power or shrinkage in regression. The adjusted R² tells us how much variance in the outcome would be accounted for if the model had been derived from the population from which the sample was taken. Autocorrelation when the residuals of two observations in a regression model are correlated. bi unstandardized regression coefficient. Indicates the strength of relationship between a given predictor, i, of many and an outcome in the units of measurement of the predictor. It is the change in the outcome associated with a unit change in the predictor. βi standardized regression coefficient. Indicates the strength of relationship between a given predictor, i, of many and an outcome in a standardized form. It is the change in the outcome (in standard deviations) associated with a one standard deviation change in the predictor. "Cook's distance "a measure of the overall influence of a case on a model. Cook and Weisberg (1982) have suggested that values greater than 1 may be cause for concern. Covariance ratio (CVR) "a measure of whether a case influences the variance of the parameters in a regression model. When this ratio is close to 1 the case has very little influence on the variances of the model parameters. Belsey et al. (1980) recommend the following: if the CVR of a case is greater than 1 + [3(k + 1)/n] then deleting that case will damage the precision of some of the model's parameters, but if it is less than 1 − [3(k + 1)/n] then deleting the case will improve the precision of some of the model's parameters (k is the number of predictors and n is the sample size). " Cross-validation assessing the accuracy of a model across different samples. This is an important step in generalization. In a regression model there are two main methods of cross-validation: adjusted R² or data splitting, in which the data are split randomly into two halves, and a regression model is estimated for each half and then compared. Deleted residual a measure of the influence of a particular case of data. It is the difference between the adjusted predicted value for a case and the original observed value for that case. DFBeta a measure of the influence of a case on the values of bi in a regression model. If we estimated a regression parameter bi and then deleted a particular case and re-estimated the same regression parameter bi, then the difference between these two estimates would be the DFBeta for the case that was deleted. By looking at the values of the DFBetas, it is possible to identify cases that have a large influence on the parameters of the regression model; however, the size of DFBeta will depend on the units of measurement of the regression parameter. DFFit a measure of the influence of a case. It is the difference between the adjusted predicted value and the original predicted value of a particular case. If a case is not influential then its DFFit should be zero - hence, we expect non-influential cases to have small DFFit values. However, we have the problem that this statistic depends on the units of measurement of the outcome and so a DFFit of 0.5 will be very small if the outcome ranges from 1 to 100, but very large if the outcome varies from 0 to 1. Dummy variables a way of recoding a categorical variable with more than two categories into a series of variables all of which are dichotomous and can take on values of only 0 or 1. There are seven basic steps to create such variables: (1) count the number of groups you want to recode and subtract 1; (2) create as many new variables as the value you calculated in step 1 (these are your dummy variables); (3) choose one of your groups as a baseline (i.e., a group against which all other groups should be compared, such as a control group); (4) assign that baseline group values of 0 for all of your dummy variables; (5) for your first dummy variable, assign the value 1 to the first group that you want to compare against the baseline group (assign all other groups 0 for this variable); (6) for the second dummy variable assign the value 1 to the second group that you want to compare against the baseline group (assign all other groups 0 for this variable); (7) repeat this process until you run out of dummy variables. Durbin-Watson test "a test for serial correlations between errors in regression models. Specifically, it tests whether adjacent residuals are correlated, which is useful in assessing the assumption of independent errors. The test statistic can vary between 0 and 4, with a value of 2 meaning that the residuals are uncorrelated. A value greater than 2 indicates a negative correlation between adjacent residuals, whereas a value below 2 indicates a positive correlation. The size of the Durbin-Watson statistic depends upon the number of predictors in the model and the number of observations. For accuracy, look up the exact acceptable values in Durbin and Watson's (1951) original paper. As a very conservative rule of thumb, values less than 1 or greater than 3 are definitely cause for concern; however, values closer to 2 may still be problematic depending on the sample and model. " F-ratio a test statistic with a known probability distribution (the F-distribution). It is the ratio of the average variability in the data that a given model can explain to the average variability unexplained by that same model. It is used to test the overall fit of the model in simple regression and multiple regression, and to test for overall differences between group means in experiments. Generalization the ability of a statistical model to say something beyond the set of observations that spawned it. If a model generalizes it is assumed that predictions from that model can be applied not just to the sample on which it is based, but to a wider population from which the sample came. Goodness of fit "an index of how well a model fits the data from which it was generated. It's usually based on how well the data predicted by the model correspond to the data that were actually collected. " Hat values another name for leverage. Heteroscedasticity the opposite of homoscedasticity. This occurs when the residuals at each level of the predictor variables(s) have unequal variances. Put another way, at each point along any predictor variable, the spread of residuals is different. Hierarchical regression a method of multiple regression in which the order in which predictors are entered into the regression model is determined by the researcher based on previous research: variables already known to be predictors are entered first, new variables are entered subsequently. Homoscedasticity an assumption in regression analysis that the residuals at each level of the predictor variable(s) have similar variances. Put another way, at each point along any predictor variable, the spread of residuals should be fairly constant. Independent errors for any two observations in regression the residuals should be uncorrelated (or independent). Leverage leverage statistics (or hat values) gauge the influence of the observed value of the outcome variable over the predicted values. The average leverage value is (k+1)/n in which k is the number of predictors in the model and n is the number of participants. Leverage values can lie between 0 (the case has no influence whatsoever) and 1 (the case has complete influence over prediction). If no cases exert undue influence over the model then we would expect all of the leverage values to be close to the average value. Hoaglin and Welsch (1978) recommend investigating cases with values greater than twice the average (2(k + 1)/n) and Stevens (2002) recommends using three times the average (3(k + 1)/n) as a cut-off point for identifying cases having undue influence. Mahalanobis distances "these measure the influence of a case by examining the distance of cases from the mean(s) of the predictor variable(s). One needs to look for the cases with the highest values. It is not easy to establish a cut-off point at which to worry, although Barnett and Lewis (1978) have produced a table of critical values dependent on the number of predictors and the sample size. From their work it is clear that even with large samples (N = 500) and five predictors, values above 25 are cause for concern. In smaller samples (N = 100) and with fewer predictors (namely three) values greater than 15 are problematic, and in very small samples (N = 30) with only two predictors values greater than 11 should be examined. However, for more specific advice, refer to Barnett and Lewis's (1978) table. " Mean squares a measure of average variability. For every sum of squares (which measure the total variability) it is possible to create mean squares by dividing by the number of things used to calculate the sum of squares (or some function of it). Model sum of squares a measure of the total amount of variability for which a model can account. It is the difference between the total sum of squares and the residual sum of squares. Multicollinearity a situation in which two or more variables are very closely linearly related. Multiple R the multiple correlation coefficient. It is the correlation between the observed values of an outcome and the values of the outcome predicted by a multiple regression model. Multiple regression "an extension of simple regression in which an outcome is predicted by a linear combination of two or more predictor variables. The form of the model is: (see above image) in which the outcome is denoted as Y, and each predictor is denoted as X. Each predictor has a regression coefficient b associated with it, and b0 is the value of the outcome when all predictors are zero. <div><img src=""quizlet-wLTgIHXQB81XobWw-TFC7A.png""></div> " Ordinary least squares (OLS) a method of regression in which the parameters of the model are estimated using the method of least squares. Outcome variable a variable whose values we are trying to predict from one or more predictor variables. Perfect collinearity exists when at least one predictor in a regression model is a perfect linear combination of the others (the simplest example being two predictors that are perfectly correlated - they have a correlation coefficient of 1). Predicted value the value of an outcome variable based on specific values of the predictor variable or variables being placed into a statistical model. Predictor variable a variable that is used to try to predict values of another variable known as an outcome variable. Residual The difference between the value a model predicts and the value observed in the data on which the model is based. Basically, an error. When the residual is calculated for each observation in a data set the resulting collection is referred to as the residuals. Residual sum of squares a measure of the variability that cannot be explained by the model fitted to the data. It is the total squared deviance between the observations, and the value of those observations predicted by whatever model is fitted to the data. Shrinkage the loss of predictive power of a regression model if the model had been derived from the population from which the sample was taken, rather than the sample itself. Simple regression "a linear model in which one variable or outcome is predicted from a single predictor variable. The model takes the form: (see above image) in which Y is the outcome variable, X is the predictor, b1 is the regression coefficient associated with the predictor and b0 is the value of the outcome when the predictor is zero. <div><img src=""quizlet-8djUia2K99xcFxSwu5wOIw.png""></div> " Standardized DFBeta a standardized version of DFBeta. These standardized values are easier to use than DFBeta because universal cut-off points can be applied. Stevens (2002) suggests looking at cases with absolute values greater than 2. Standardized DFFit a standardized version of DFFit. Standardized residuals the residuals of a model expressed in standard deviation units. Standardized residuals with an absolute value greater than 3.29 (actually, we usually just use 3) are cause for concern because in an average sample a value this high is unlikely to happen by chance; if more than 1% of our observations have standardized residuals with an absolute value greater than 2.58 (we usually just say 2.5) there is evidence that the level of error within our model is unacceptable (the model is a fairly poor fit of the sample data); and if more than 5% of observations have standardized residuals with an absolute value greater than 1.96 (or 2 for convenience) then there is also evidence that the model is a poor representation of the actual data. Stepwise regression a method of multiple regression in which variables are entered into the model based on a statistical criterion (the semi-partial correlation with the outcome variable). Once a new variable is entered into the model, all variables in the model are assessed to see whether they should be removed. Studentized deleted residual a measure of the influence of a particular case of data. This is a standardized version of the deleted residual. Studentized residuals a variation on standardized residuals. A Studentized residual is an unstandardized residual divided by an estimate of its standard deviation that varies point by point. These residuals have the same properties as the standardized residuals but usually provide a more precise estimate of the error variance of a specific case. Suppressor effects situation where a predictor has a significant effect, but only when another variable is held constant. t-statistic "Student's t is a test statistic with a known probability distribution (the t-distribution). In the context of regression it is used to test whether a regression coefficient b is significantly different from zero; in the context of experimental work it is used to test whether the differences between two means are significantly different from zero. See also paired-samples t-test and Independent t-test. " Tolerance tolerance statistics measure multicollinearity and are simply the reciprocal of the variance inflation factor (1/VIF). Values below 0.1 indicate serious problems, although Menard (1995) suggests that values below 0.2 are worthy of concern. Total sum of squares a measure of the total variability within a set of observations. It is the total squared deviance between each observation and the overall mean of all observations. Unstandardized residuals the residuals of a model expressed in the units in which the original outcome variable was measured. Variance inflation factor (VIF) "a measure of multicollinearity. The VIF indicates whether a predictor has a strong linear relationship with the other predictor(s). Myers (1990) suggests that a value of 10 is a good value at which to worry. Bowerman and O'Connell (1990) suggest that if the average VIF is greater than 1, then multicollinearity may be biasing the regression model. " Dependent t-test see paired-samples t-test Dummy variables a way of recoding a categorical variable with more than two categories into a series of variables all of which are dichotomous and can take on values of only 0 or 1. There are seven basic steps to create such variables: (1) count the number of groups you want to recode and subtract 1; (2) create as many new variables as the value you calculated in step 1 (these are your dummy variables); (3) choose one of your groups as a baseline (i.e., a group against which all other groups should be compared, such as a control group); (4) assign that baseline group values of 0 for all of your dummy variables; (5) for your first dummy variable, assign the value 1 to the first group that you want to compare against the baseline group (assign all other groups 0 for this variable); (6) for the second dummy variable assign the value 1 to the second group that you want to compare against the baseline group (assign all other groups 0 for this variable); (7) repeat this process until you run out of dummy variables. Grand mean the mean of an entire set of observations. Independent t-test a test using the t-statistic that establishes whether two means collected from independent samples differ significantly. Paired-samples t-test a test using the t-statistic that establishes whether two means collected from the same sample (or related observations) differ significantly. Standard error of differences if we were to take several pairs of samples from a population and calculate their means, then we could also calculate the difference between their means. If we plotted these differences between sample means as a frequency distribution, we would have the sampling distribution of differences. The standard deviation of this sampling distribution is the standard error of differences. As such it is a measure of the variability of differences between sample means. Variance sum law states that the variance of a difference between two independent variables is equal to the sum of their variances. Grand mean centring grand mean centring means the transformation of a variable by taking each score and subtracting the mean of all scores (for that variable) from it (cf. Group mean centring). Direct effect the effect of a predictor variable on an outcome variable when a mediator is present in the model (cf. indirect effect). Index of mediation a standardized measure of an indirect effect. In a mediation model, it is the indirect effect multiplied by the ratio of the standard deviation of the predictor variable to the standard deviation of the outcome variable. Indirect effect the effect of a predictor variable on an outcome variable through a mediator (cf. direct effect). Interaction effect the combined effect of two or more predictor variables on an outcome variable. It can be used to gauge moderation. Mediation perfect mediation occurs when the relationship between a predictor variable and an outcome variable can be completely explained by their relationships with a third variable. For example, taking a dog to work reduces work stress. This relationship is mediated by positive mood if (1) having a dog at work increases positive mood; (2) positive mood reduces work stress; and (3) the relationship between having a dog at work and work stress is reduced to zero (or at least weakened) when positive mood is included in the model. Mediator a variable that reduces the size and/or direction of the relationship between a predictor variable and an outcome variable (ideally to zero) and is associated statistically with both. Moderation Moderation occurs when the relationship between two variables changes as a function of a third variable. For example, the relationship between watching horror films (predictor) and feeling scared at bedtime (outcome) might increase as a function of how vivid an imagination a person has (moderator). Moderator a variable that changes the size and/or direction of the relationship between two other variables. Simple slopes analysis an analysis that looks at the relationship (i.e., the simple regression) between a predictor variable and an outcome variable at low, mean and high levels of a third (moderator) variable. Sobel test A significance test of mediation. It tests whether the relationship between a predictor variable and an outcome variable is significantly reduced when a mediator is included in the model. It tests the indirect effect of the predictor on the outcome Analysis of variance a statistical procedure that uses the F-ratio to test the overall fit of a linear model. In experimental research this linear model tends to be defined in terms of group means, and the resulting ANOVA is therefore an overall test of whether group means differ. Brown-Forsythe F a version of the F-ratio designed to be accurate when the assumption of homogeneity of variance has been violated. Cubic trend if you connected the means in ordered conditions with a line then a cubic trend is shown by two changes in the direction of this line. You must have at least four ordered conditions. Deviation contrast a non-orthogonal planned contrast that compares the mean of each group (except for the first or last, depending on how the contrast is specified) to the overall mean. Difference contrast a non-orthogonal planned contrast that compares the mean of each condition (except the first) to the overall mean of all previous conditions combined. Eta squared (η²) "an effect size measure that is the ratio of the model sum of squares to the total sum of squares. So, in essence, the coefficient of determination by another name. It doesn't have an awful lot going for it: not only is it biased, but it typically measures the overall effect of an ANOVA, and effect sizes are more easily interpreted when they reflect specific comparisons (e.g., the difference between two means). " Experimentwise error rate the probability of making a Type I error in an experiment involving one or more statistical comparisons when the null hypothesis is true in each case. Familywise error rate "the probability of making a Type I error in any family of tests when the null hypothesis is true in each case. The 'family of tests' can be loosely defined as a set of tests conducted on the same data set and addressing the same empirical question. " Grand variance the variance within an entire set of observations. Harmonic mean a weighted version of the mean that takes account of the relationship between variance and sample size. It is calculated by summing the reciprocal of all observations, then dividing by the number of observations. The reciprocal of the end product is the harmonic mean: Helmert contrast a non-orthogonal planned contrast that compares the mean of each condition (except the last) to the overall mean of all subsequent conditions combined. Independent ANOVA analysis of variance conducted on any design in which all independent variables or predictors have been manipulated using different participants (i.e., all data come from different entities). Omega squared "an effect size measure associated with ANOVA that is less biased than eta squared. It is a (sometimes hideous) function of the model sum of squares and the residual sum of squares and isn't actually much use because it measures the overall effect of the ANOVA and so can't be interpreted in a meaningful way. In all other respects it's great though. " Orthogonal means perpendicular (at right angles) to something. It tends to be equated to independence in statistics because of the connotation that perpendicular linear models in geometric space are completely independent (one is not influenced by the other). Pairwise comparisons comparisons of pairs of means. Planned contrasts a set of comparisons between group means that are constructed before any data are collected. These are theory-led comparisons and are based on the idea of partitioning the variance created by the overall effect of group differences into gradually smaller portions of variance. These tests have more power than post hoc tests. Polynomial contrast a contrast that tests for trends in the data. In its most basic form it looks for a linear trend (i.e., that the group means increase proportionately). Post hoc tests a set of comparisons between group means that were not thought of before data were collected. Typically these tests involve comparing the means of all combinations of pairs of groups. To compensate for the number of tests conducted, each test uses a strict criterion for significance. As such, they tend to have less power than planned contrasts. They are usually used for exploratory work for which no firm hypotheses were available on which to base planned contrasts. Quadratic trend if the means in ordered conditions are connected with a line then a quadratic trend is shown by one change in the direction of this line (e.g., the line is curved in one place); the line is, therefore, U-shaped. There must be at least three ordered conditions. Quartic trend if the means in ordered conditions are connected with a line then a quartic trend is shown by three changes in the direction of this line. There must be at least five ordered conditions. Repeated contrast a non-orthogonal planned contrast that compares the mean in each condition (except the first) to the mean of the preceding condition. Simple contrast a non-orthogonal planned contrast that compares the mean in each condition to the mean of either the first or last condition, depending on how the contrast is specified. Weight a number by which something (usually a variable in statistics) is multiplied. The weight assigned to a variable determines the influence that variable has within a mathematical equation: large weights give the variable a lot of influence. "Welch's F "a version of the F-ratio designed to be accurate when the assumption of homogeneity of variance has been violated. Not to be confused with the squelch test which is where you shake your head around after writing statistics books to see if you still have a brain. Adjusted mean in the context of analysis of covariance this is the value of the group mean adjusted for the effect of the covariate. Analysis of covariance a statistical procedure that uses the F-ratio to test the overall fit of a linear model, controlling for the effect that one or more covariates have on the outcome variable. In experimental research this linear model tends to be defined in terms of group means, and the resulting ANOVA is therefore an overall test of whether group means differ after the variance in the outcome variable explained by any covariates has been removed. Covariate "a variable that has a relationship with (in terms of covariance), or has the potential to be related to, the outcome variable we've measured. " Homogeneity of regression slopes "an assumption of analysis of covariance. This is the assumption that the relationship between the covariate and outcome variable is constant across different treatment levels. So, if we had three treatment conditions, if there's a positive relationship between the covariate and the outcome in one group, we assume that there is a similar-sized positive relationship between the covariate and outcome in the other two groups too. " Partial eta squared (partial η²) a version of eta squared that is the proportion of variance that a variable explains when excluding other variables in the analysis. Eta squared is the proportion of total variance explained by a variable, whereas partial eta squared is the proportion of variance that a variable explains that is not explained by other variables. Partial out to partial out the effect of a variable is to remove the variance that the variable shares with other variables in the analysis before looking at their relationships (see partial correlation). Šidák correction a slightly less conservative variant of a Bonferroni correction. Factorial ANOVA an analysis of variance involving two or more independent variables or predictors. Independent factorial design an experimental design incorporating two or more predictors (or independent variables) all of which have been manipulated using different participants (or whatever entities are being tested). Interaction graph a graph showing the means of two or more independent variables in which means of one variable are shown at different levels of the other variable. Unusually the means are connected with lines, or are displayed as bars. These graphs are used to help understand interaction effects. Mixed design "an experimental design incorporating two or more predictors (or independent variables) at least one of which has been manipulated using different participants (or whatever entities are being tested) and at least one of which has been manipulated using the same participants (or entities). Also known as a split-plot design because Fisher developed ANOVA for analysing agricultural data involving 'plots' of land containing crops. " Related factorial design an experimental design incorporating two or more predictors (or independent variables) all of which have been manipulated using the same participants (or whatever entities are being tested). Simple effects analysis this analysis looks at the effect of one independent variable (categorical predictor variable) at individual levels of another independent variable. Compound symmetry a condition that holds true when both the variances across conditions are equal (this is the same as the homogeneity of variance assumption) and the covariances between pairs of conditions are also equal. Greenhouse-Geisser estimate an estimate of the departure from sphericity. The maximum value is 1 (the data completely meet the assumption of sphericity) and minimum is the lower bound. Values below 1 indicate departures from sphericity and are used to correct the degrees of freedom associated with the corresponding F-ratios by multiplying them by the value of the estimate. Some say the Greenhouse-Geisser correction is too conservative (strict) and recommend the Huynh-Feldt correction instead. Huynh-Feldt estimate an estimate of the departure from sphericity. The maximum value is 1 (the data completely meet the assumption of sphericity). Values below this indicate departures from sphericity and are used to correct the degrees of freedom associated with the corresponding F-ratios by multiplying them by the value of the estimate. It is less conservative than the Greenhouse-Geisser estimate, but some say it is too liberal. Lower-bound estimate the name given to the lowest possible value of the Greenhouse-Geisser estimate of sphericity. Its value is 1/(k−1), in which k is the number of treatment conditions. "Mauchly's test "a test of the assumption of sphericity. If this test is significant then the assumption of sphericity has not been met and an appropriate correction must be applied to the degrees of freedom of the F-ratio in repeated-measures ANOVA. The test works by comparing the variance-covariance matrix of the data to an identity matrix; if the variance-covariance matrix is a scalar multiple of an identity matrix then sphericity is met. Repeated-measures ANOVA an analysis of variance conducted on any design in which the independent variable (predictor) or variables (predictors) have all been measured using the same participants in all conditions. Sphericity a less restrictive form of compound symmetry which assumes that the variances of the differences between data taken from the same participant (or other entity being tested) are equal. This assumption is most commonly found in repeated-measures ANOVA but applies only where there are more than two points of data from the same participant (see also Greenhouse-Geisser correction, Huynh-Feldt correction). Mixed ANOVA analysis of variance used for a mixed design. Mixed design "an experimental design incorporating two or more predictors (or independent variables) at least one of which has been manipulated using different participants (or whatever entities are being tested) and at least one of which has been manipulated using the same participants (or entities). Also known as a split-plot design because Fisher developed ANOVA for analysing agricultural data involving 'plots' of land containing crops. " "Bartlett's test of sphericity ""unsurprisingly, this is a test of the assumption of sphericity. This test examines whether a variance-covariance matrix is proportional to an identity matrix. Therefore, it effectively tests whether the diagonal elements of the variance-covariance matrix are equal (i.e., group variances are the same), and whether the off-diagonal elements are approximately zero (i.e., the dependent variables are not correlated). Jeremy Miles, who does a lot of multivariate stuff, claims he's never ever seen a matrix that reached non-significance using this test and, come to think of it, I've never seen one either (although I do less multivariate stuff), so you've got to wonder about its practical utility. " "Box's test ""a test of the assumption of homogeneity of covariance matrices. This test should be non-significant if the matrices are roughly the same. Box's test is very susceptible to deviations from multivariate normality, and so may be non-significant not because the variance-covariance matrices are similar across groups, but because the assumption of multivariate normality is not tenable. Hence, it is vital to have some idea of whether the data meet the multivariate normality assumption (which is extremely difficult) before interpreting the result of Box's test. " Discriminant function variate "a linear combination of variables created such that the differences between group means on the transformed variable are maximized. It takes the general form <div><img src=""quizlet-dRiKTosWOE5FuThmeQIDCA.png""></div> " Discriminant score "a score for an individual case on a particular discriminant function variate obtained by substituting that case's scores on the measured variables into the equation that defines the variate in question. " Error SSCP (E) the error sum of squares and cross-products matrix. This is a sum of squares and cross-products matrix for the error in a predictive linear model fitted to multivariate data. It represents the unsystematic variance and is the multivariate equivalent of the residual sum of squares. HE−¹ this is a matrix that is functionally equivalent to the hypothesis SSCP divided by the error SSCP in MANOVA. Conceptually it represents the ratio of systematic to unsystematic variance, so is a multivariate analogue of the F-ratio. Homogeneity of covariance matrices an assumption of some multivariate tests such as MANOVA. It is an extension of the homogeneity of variance assumption in univariate analyses. However, as well as assuming that variances for each dependent variable are the same across groups, it also assumes that relationships (covariances) between these dependent variables are roughly equal. It is tested by comparing the population variance-covariance matrices of the different groups in the analysis. Hypothesis SSCP (H) the hypothesis sum of squares and cross-products matrix. This is a sum of squares and cross-products matrix for a predictive linear model fitted to multivariate data. It represents the systematic variance and is the multivariate equivalent of the model sum of squares. Identity matrix "a square matrix (i.e., having the same number of rows and columns) in which the diagonal elements are equal to 1, and the off-diagonal elements are equal to 0. <div><img src=""quizlet-XB9KeCGaU6Igx8MYZCrnEQ.png""></div> " Matrix "a collection of numbers arranged in columns and rows. The values within a matrix are typically referred to as components or elements. Multivariate: means 'many variables' and is usually used when referring to analyses in which there is more than one outcome variable (MANOVA, principal component analysis, etc.). " Multivariate analysis of variance family of tests that extend the basic analysis of variance to situations in which more than one outcome variable has been measured. Multivariate normality "an extension of a normal distribution to multiple variables. It is a probability distribution of a set of variables (fig.1) given by: (fig.2) in which µ is the vector of means of the variables, and Σ is the variance-covariance matrix. If that made any sense to you then you're cleverer than I am. <div><img src=""quizlet-GbjPuDDXGAKEvPoV49T5.g.png""></div> " Square matrix a matrix that has an equal number of columns and rows. Sum of squares and cross-products matrix (SSCP matrix) a square matrix in which the diagonal elements represent the sum of squares for a particular variable, and the off-diagonal elements represent the cross-products between pairs of variables. The SSCP matrix is basically the same as the variance-covariance matrix, except that the SSCP matrix expresses variability and between-variable relationships as total values, whereas the variance-covariance matrix expresses them as average values. Total SSCP (T) the total sum of squares and cross-products matrix. This is a sum of squares and cross-products matrix for an entire set of observations. It is the multivariate equivalent of the total sum of squares. Univariate "means 'one variable' and is usually used to refer to situations in which only one outcome variable has been measured (ANOVA, t-tests, Mann-Whitney tests, etc.). " Variance-covariance matrix a square matrix (i.e., same number of columns and rows) representing the variables measured. The diagonals represent the variances within each variable, whereas the off-diagonals represent the covariances between pairs of variables. "Wilks's lambda () "a test statistic in MANOVA. It is the product of the unexplained variance on each of the discriminant function variates, so it represents the ratio of error variance to total variance (SSR/SST) for each variate. Alpha factoring a method of factor analysis. Anderson-Rubin method a way of calculating factor scores which produces scores that are uncorrelated and standardized with a mean of 0 and a standard deviation of 1. Common factor a factor that affects all measured variables and, therefore, explains the correlations between those variables. Common variance variance shared by two or more variables. Communality "the proportion of a variable's variance that is common variance. This term is used primarily in factor analysis. A variable that has no unique variance (or random variance) would have a communality of 1, whereas a variable that shares none of its variance with any other variable would have a communality of 0. " Component matrix general term for the structure matrix in principal component analysis. Confirmatory factor analysis (CFA) a version of factor analysis in which specific hypotheses about structure and relations between the latent variables that underlie the data are tested. "Cronbach's α ""a measure of the reliability of a scale defined (above image) <div><img src=""quizlet-Z6PWKwOscpkdTGd56pW8oA.png""></div> " Direct oblimin a method of oblique rotation. Extraction "a term used for the process of deciding whether a factor in factor analysis is statistically important enough to 'extract' from the data and interpret. The decision is based on the magnitude of the eigenvalue associated with the factor. See Kaiser's criterion, scree plot. " Factor analysis a multivariate technique for identifying whether the correlations between a set of observed variables stem from their relationship to one or more latent variables in the data, each of which takes the form of a linear model. Factor loading the regression coefficient of a variable for the linear model that describes a latent variable or factor in factor analysis. Factor matrix general term for the structure matrix in factor analysis. Factor score "a single score from an individual entity representing their performance on some latent variable. The score can be crudely conceptualized as follows: take an entity's score on each of the variables that make up the factor and multiply it by the corresponding factor loading for the variable, then add these values up (or average them). " Factor transformation matrix, ∧ "a matrix used in factor analysis. It can be thought of as containing the angles through which factors are rotated in factor rotation. Intraclass correlation (ICC): a correlation coefficient that assesses the consistency between measures of the same class, that is, measures of the same thing (cf. Pearson's correlation coefficient which measures the relationship between variables of a different class.) Two common uses are in comparing paired data (such as twins) on the same measure, and assessing the consistency between judges' ratings of a set of objects. The calculation of these correlations depends on whether a measure of consistency (in which the order of scores from a source is considered but not the actual value around which the scores are anchored) or absolute agreement (in which both the order of scores and the relative values are considered), and whether the scores represent averages of many measures or just a single measure is required. This measure is also used in multilevel linear models to measure the dependency in data within the same context. " "Kaiser's criterion "a method of extraction in factor analysis based on the idea of retaining factors with associated eigenvalues greater than 1. This method appears to be accurate when the number of variables in the analysis is less than 30 and the resulting communalities (after extraction) are all greater than 0.7, or when the sample size exceeds 250 and the average communality is greater than or equal to 0.6. Latent variable a variable that cannot be directly measured, but is assumed to be related to several variables that can be measured. Kaiser-Meyer-Olkin measure of sampling adequacy (KMO) the KMO can be calculated for individual and multiple variables and represents the ratio of the squared correlation between variables to the squared partial correlation between variables. It varies between 0 and 1: a value of 0 means that the sum of partial correlations is large relative to the sum of correlations, indicating diffusion in the pattern of correlations (hence, factor analysis is likely to be inappropriate); a value close to 1 indicates that patterns of correlation are relatively compact and so factor analysis should yield distinct and reliable factors. Values between .5 and .7 are mediocre, values between .7 and .8 are good, values between .8 and .9 are great and values above .9 are superb (see Hutcheson and Sofroniou, 1999). Oblique rotation a method of rotation in factor analysis that allows the underlying factors to be correlated. Orthogonal rotation a method of rotation in factor analysis that keeps the underlying factors independent (i.e., not correlated). Pattern matrix a matrix in factor analysis containing the regression coefficients for each variable on each factor in the data. See also Structure matrix. Principal component analysis (PCA) a multivariate technique for identifying the linear components of a set of variables. Random variance variance that is unique to a particular variable but not reliably so. Rotation a process in factor analysis for improving the interpretability of factors. In essence, an attempt is made to transform the factors that emerge from the analysis in such a way as to maximize factor loadings that are already large, and minimize factor loadings that are already small. There are two general approaches: orthogonal rotation and oblique rotation. Singularity a term used to describe variables that are perfectly correlated (i.e., the correlation coefficient is 1 or −1). Split-half reliability "a measure of reliability obtained by splitting items on a measure into two halves (in some random fashion) and obtaining a score from each half of the scale. The correlation between the two scores, corrected to take account of the fact the correlations are based on only half of the items, is used as a measure of reliability. There are two popular ways to do this. Spearman (1910) and Brown (1910) developed a formula that takes no account of the standard deviation of items (fig.1) in which r¹² is the correlation between the two halves of the scale. Flanagan (1937) and Rulon (1939), however, proposed a measure that does account for item variance (fig.2) in which S¹ and S² are the standard deviations of each half of the scale, and S²T is the variance of the whole test. See Cortina (1993) for more details. <div><img src=""quizlet-VX0GqG8K300wLJFf1DbpMQ.png""></div> " Structure matrix a matrix in factor analysis containing the correlation coefficients for each variable on each factor in the data. When orthogonal rotations used this is the same as the pattern matrix, but when oblique rotation is used these matrices are different. Unique factor a factor that affects only one of many measured variables and, therefore, cannot explain the correlations between those variables. Unique variance "variance that is specific to a particular variable (i.e., is not shared with other variables). We tend to use the term 'unique variance' to refer to variance that can be reliably attributed to only one measure, otherwise it is called random variance. " Varimax a method of orthogonal rotation. It attempts to maximize the dispersion of factor loadings within factors. Therefore, it tries to load a smaller number of variables highly onto each factor, resulting in more interpretable clusters of factors. Chi-square distribution a probability distribution of the sum of squares of several normally distributed variables. It tends to be used to test hypotheses about categorical data, and to test the fit of models to the observed data. Chi-square test "although this term can apply to any test statistic having a chi-square distribution, it generally refers to Pearson's chi-square test of the independence of two categorical variables. Essentially it tests whether two categorical variables forming a contingency table are associated. " Contingency table a table representing the cross-classification of two or more categorical variables. The levels of each variable are arranged in a grid, and the number of observations falling into each category is noted in the cells of the table. For example, if we took the categorical variables of glossary (with two categories: whether an author was made to write a glossary or not), and mental state (with three categories: normal, sobbing uncontrollably and utterly psychotic), we could construct a table as in the textbook. This instantly tells us that 127 authors who were made to write a glossary ended up as utterly psychotic, compared to only 2 who did not write a glossary. "Cramér's V "a measure of the strength of association between two categorical variables used when one of these variables has more than two categories. It is a variant of phi used because when one or both of the categorical variables contain more than two categories, phi fails to reach its minimum value of 0 (indicating no association). "Fisher's exact test ""Fisher's exact test (Fisher, 1922) is not so much a test as a way of computing the exact probability of a statistic. It was designed originally to overcome the problem that with small samples the sampling distribution of the chi-square statistic deviates substantially from a chi-square distribution. It should be used with small samples. " "Goodman and Kruskal's λ "measures the proportional reduction in error that is achieved when membership of a category of one variable is used to predict category membership of the other variable. A value of 1 means that one variable perfectly predicts the other, whereas a value of 0 indicates that one variable in no way predicts the other. Loglinear analysis a procedure used as an extension of the chi-square test to analyse situations in which we have more than two categorical variables and we want to test for relationships between these variables. Essentially, a linear model is fitted to the data that predicts expected frequencies (i.e., the number of cases expected in a given category). In this respect it is much the same as analysis of variance but for entirely categorical data. Odds ratio "the ratio of the odds of an event occurring in one group compared to another. So, for example, if the odds of dying after writing a glossary are 4, and the odds of dying after not writing a glossary are 0.25, then the odds ratio is 4/0.25 = 16. This means that the odds of dying if you write a glossary are 16 times higher than if you don't. An odds ratio of 1 would indicate that the odds of a particular outcome are equal in both groups. " Phi "a measure of the strength of association between two categorical variables. Phi is used with 2 x 2 contingency tables (tables which have two categorical variables and each variable has only two categories). Phi is a variant of the chi square test, X², (above image) in which n is the total number of observations. <div><img src=""quizlet-rkkrl2HKNZbS19D3saawRw.png""></div> " Saturated model a model that perfectly fits the data and, therefore, has no error. It contains all possible main effects and interactions between variables. "Yates's continuity correction "an adjustment made to the chi-square test when the contingency table is 2 rows by 2 columns (i.e., there are two categorical variables both of which consist of only two categories). In large samples the adjustment makes little difference and is slightly dubious anyway (see Howell, 2012). The research method model The Research Method 1. Theory 2. Hypothesis 3. Research Design 4. Measurement of Concepts 5. Select Research Sites 6. Select Respondents 7. Collect Data 8. Process Data 9. Analyze Data 10. Finding/Conclusions David Hume on cause and effect To infer cause and effect 1. Cause and effect must occur at same time (contiguity) 2. The cause must occur before an effect does 3. The effect should never occur without the presence of the cause What do the variance and standard deviation tell us about the distribution of scores? If the mean represents the data well then most of the scores will cluster close to the mean and the resulting standard deviation Sum of squared errors (SS) = ∑(outcome-model)² Mean squared error = SS/df Hypothesis testing Jerzy Neyman and Egon Pearson P-values Ronald Fisher Glass, Peckham, and Sanders (1972) Transforming data is never really worth it Belsey et. al. (1980) Diagnostic statistics should not be used to justify omitting cases so as to support evidence Weighting It assigns an adjustment weight to each survey respondent. Persons in under-represented get a weight larger than 1, and those in over-represented groups get a weight smaller than 1. In the computation of means, totals and percentages, not just the values of the variables are used, but the weighted values. National statistician "The National Statistician's role is to safeguard the production and publication of high quality official statistics by all departments, agencies and institutions within the UK. The current National Statistician is John Pullinger who took up post in July 2014 " NUTS NUTS is a geographical nomenclature subdividing the territory of the European Union (EU) into regions at three different levels (NUTS 1, 2 and 3, respectively, moving from larger to smaller territorial units) Social class schema Script to construct an indicator of social class in the ESS by Daniel Oesch

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