Multivariate Statistics
Psychology 716 - Spring, 2014
Review Sheet, Test 1
I’ll let you know if I need to tweak this outline, as I work on the exam itself.
Information is from class notes, handouts, and/or readings
General comments –
 Be able to read output from SPSS or output in table form (eg from a published article)
 Bring a calculator
 You can create and use a ‘cheat sheet’ with equations (but only with equations)
Basic concepts / review
 The importance of variability and co-variability – why are these important in terms of research?
 In what way is experimental study a study of differences and co-variability?
 What is “multivariate” stats?
 Latent variables vs manifest variables
 What is a covariate?
 What does the textbook mean when it ways that variables have “fluid roles”?
 Effect sizes
o what are they?
o why are they important?
o Examples (e.g., r, d, etc)
 Inferential statistics
o Point estimates
o Confidence intervals
o Null hypothesis testing (df, sampling distributions, sample size, etc)
o Factors affecting power and statistical significance – what, how?
 Links to effect size and sample size
 Checking data
 Why do skew and kurtosis matter?
 What does a stem and leaf plot display? What about a box plot? A scatterplot? – read and interpret
 What are the options for dealing with missing data?
 Outliers –
o Causes
o What is a multivariate outlier?
o Detecting univariate and multivariate outliers
 Basic multivariate assumptions
Measurement
 Big picture on measurement:
o Reliability as precision?
o Validity as interpretation?
 Problems with ad hoc measures, single-item/observation measures, modified measures, using a measure for
a group other than that for which is was initially developed and evaluated?
 Reliability (Classical Test Theory perspective)
o Key assumptions
 O = T + E (what do these refer to, what is a “true score?”)
 Error is random (What are the implications of this assumption)
o Definition – in terms of:
 signal & noise,
 true-score variance and observed-score variance, be abel to compute, if given relevant
variances
 (Squared) correlation between true scores and observed scores
Interpretation – what are good vs poor levels of reliability?
Importance of reliability
 For applied decision-making
 For research: Connection between reliability, “true” effects, and observed effects
(attenuation)
 For research: Connection between reliability and inferential tests (via effect sizes)
o Estimating reliability via internal consistency (why must reliability be “estimated”, why can’t we
truly know a measure’s reliability?)
 (Cronbach’s) coefficient alpha (don’t worry about computations)
o What factors affect reliability, making it better or worse? Relatedly, how can you improve a
measure’s reliability?
 Interpreting item-level reliability information – item-total correlation, “alpha if deleted” etc
o Why is reliability relevant for any researcher, not just those who study questionnaires or “tests” and
even for those who do experimental research?
What are the types of evidence relevant to gauging validity?
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Covariance & Correlation
 Connections between correlation and causality. Correlation DOES imply causality? How’s that?
 Link (conceptual and statistical) between variance  covariance  correlation
o Mean differences and co-variation/association. Your book (p 291) addresses the link between mean
differences and covariation. What they say is true (i.e., that mean differences ≠ covariation), but in
some cases covariation can reveal mean difference – it depends on what you’re examining.
 Comparing the Mean of variable X to the Mean of variable Y - is NOT the same a looking
at the association between scores on X and Y (i.e, it’s not the same as seeing whether
variability on X corresponds with variability on Y)
 However, if you want know whether Males and Females differ on their mean levels of
variable Y, the Mean differences IS equivalent to covariation (between Gender and
Variable Y) . That is, the question of “do males and females have different means on Y?”
is the same as asking “Does variability on Gender correspond with variability on Y?”
 Covariance –
o interpretation (direction and magnitude?)
 Correlation –
o Interpretation (direction and magnitude, BESD, coefficient of determination, linearity, r-squared,
etc)
o Computation (you won’t have to compute from individual responses for the test)
o Subjective evaluation of the size of corrs (big, small, etc?)
o Factors affecting a correlation coefficient – what, how?
o Links to reliability (attenuation, etc)
o Scaling and correlations (eg corrs with nominal or ordinal variables – interpret, valid?)
o Inferential Issues
 Testing the null that ρ = 0. Computation, logic, interpretation (population!)
 Confidence intervals – interpretation, computation, link to sample size
Bivariate regression (one predictor)
 Interpretation of parameter estimates
o regression coefficients (intercept and slopes – unstandardized and standardized)
o R2 value
 Computation - as derived from more basic stats – zero-order correlations, variabilities, and means
 Interpretation of significance tests
o regression slopes and intercepts (t tests)
o R2 values (F tests)
 What does the “least squares” approach to regression mean?
 Link between Beta and correlation in a one-predictor model
 Why doesn’t the standardized equation have an intercept?
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In SPSS out, what are the sums of squares - the SS regression, SS residual, and SS total? –
Interpretations?
What is a “residual”?
R2 in relation to sums of squares
Multiple regression (more than one predictor)
 What are some purposes, uses of multiple regression ?
 Interpretation of parameter estimates
o regression coefficients (intercept and slopes – unstandardized and standardized)
o psychologically speaking, what does it mean to control, partial, or hold a variable constant?
o What are the different uses of the different slopes (standardized versus unstandardized)?
o R2 value
 Computation –
o As derived from more basic stats – zero-order correlations, variabilities, and means
o Note how computations reflect the conceptual meaning of the stats
 Slopes representing the unique predictive power of a variable
 R2 in terms of the total predictive power of both variables, accounting for their redundant
predictive power
 Interpretation of significance tests
o regression coefficients (t tests)
o R2 values (F tests)
 What is the “variate” in terms of a multivariate procedure such as multiple regression?
 What is the “multiple R”, in terms of a correlation. It is a correlation between what two things?
 What do the “ANOVA” values in regression mean? SSregression, etc?
 What is “Simlutaneous” or “Standard” regression?
 Adjusted R2 – what is it? What is a “cross-validation sample”, and why is adjusted R2 lower than regular
R2? “Shrinkage” and “Inflation”?
 Issues in comparing regression slopes to each other – b, beta, etc?
 What is collinearity/multicollinearity, and what are its effects? Tolerance and variance inflation factor?
 What are the effects of suppressor variables?
 Partial correlations and semipartial correlations
o How are (squared) semi-partials for predictors related to changes in R2 and R2 itself?
o What is a “residual” in regression/partialling?
o In terms of what’s being partialled from what?
o Why are semipartials generally lower than zero-order correlations and partial correlations?
 Forms of regression – simultaneous, stepwise, hierarchical
o Similarities and differences
o When might each be used?
o Procedures (roughly, how do they work?)
o Hierarchical regression
 Understand and explain the findings/logic related to changes in R2, changes in slopes,
ordering of variables (or sets of variables), etc in a hierarchical regression.
Moderated multiple regression
 Meaning (what is an interaction, in a regression context?) – explain and/or identify.
 What is a moderator variable?
 How is a moderator variable different from a mediator variable?
 Steps in the analysis (e.g., computation and interpretation of simple slopes),
 Read, interpret, and draw/evaluate inferences from a description
Nonlinear regression – polynomial/quadratic effects
 Meaning
 Steps in the analysis
 Relevant results and interpretation
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Don’t worry about “intrinsically nonlinear models”
Mediational Analysis
o Purpose, application?
o Be able to identify:
o A mediational hypothesis
o The predictor/IV, the mediator, and the outcome in a verbal description of a mediational hypothesis.
o Draw a mediational diagram, based on a verbal description of a mediational hypothesis
o Conduct a mediational analysis –
o know the steps (including the structure of the Sobel tests)
o be able to read, interpret, and use relevant SPSS output.
o Compute the relevant results
o What is the null hypothesis being evaluated?
o Explain the overall results of a mediational analysis – what do the results say about a given mediational
hypothesis (e.g., do they support a mediational hypothesis extremely well, partially well, not at all….?)
o What is a mediator variable?
o Read and interpret a descriptions of relevant output (eg, from a journal article/output/results)
The test will include interpretational/application questions, such as:
 Given a set of results, what are valid psychological conclusions, what are invalid conclusions, and why are
those conclusions valid/invalid?
 Given a certain research question/hypothesis and data set, what analyses would you run and what pattern of
results would support the hypothesis (or fail to support it) and why?