Chapter 12 Quantitative Approaches © 2017 Taylor & Francis Which Test to Use? You must identify: 1. The number of variables in the analysis 2. The level of measurement of the variables 3. Whether variables are independent or dependent 4. Whether the relationship is assumed to be linear © 2017 Taylor & Francis Hypothesis Testing Two basic elements: 1. The test is based on the ratio of percentage of explained variance to the percentage of unexplained variance • • Variance is the basis of all analysis The variance explained is the variance in the dependent variable (explained by the independent variable) 2. The relationship tested is generally a linear relationship © 2017 Taylor & Francis Two Basic Approaches to Analysis • Group Differences • Group differences use analysis of variance (ANOVA) • Variable Relationships • Within group variable relationships use correlation and regression © 2017 Taylor & Francis Translate the Measures Prepare the data set for a software program • A rectangular matrix presents variables in columns and subjects in rows • A column represents scores on a particular variable • A record may refer to a single line of data • A case (often the same as a record) is the set of data that represents a single subject © 2017 Taylor & Francis Group Difference Tests Generally, group differences have: • Independent variables with a nominal or ordinal level of measurement, and • A dependent variable measured at the interval or ratio level © 2017 Taylor & Francis Group Difference Tests • • • • T-test One way ANOVA ANOVA MANOVA © 2017 Taylor & Francis T-test • The simplest of differences of means tests • This difference of means test is an ANOVA (analysis of variance) with a single independent variable with only two levels and a single dependent variable; thus, there are only two groups to compare • T to test explained variance © 2017 Taylor & Francis One Way ANOVA • A one way ANOVA (analysis of variance) can be run wherever a difference of means t-test can be run • This difference of means test has a single independent variable with two or more levels and a single dependent variable; thus, it can compare two or more groups • F to test explained variance © 2017 Taylor & Francis ANOVA • The general form of ANOVA; any t-test or one way ANOVA can be run as a general ANOVA • This difference of means test can have more than one independent variable with two or more levels and a single dependent variable • F to test explained variance © 2017 Taylor & Francis MANOVA • Multivariate Analysis of Variance • An ANOVA that allows more than one dependent variable • Beyond the scope of this text © 2017 Taylor & Francis Variable Relationship Tests • Variables need to be interval or ratio level of measurement • • • • Correlation Simple correlation Multiple correlation/regression Canonical correlation © 2017 Taylor & Francis Correlation • The most common associative measure, the Pearson Product Moment Correlation, is a description of the linear relationship between two variables • No assumption that the two variables are independent or dependent © 2017 Taylor & Francis Simple Correlation/Regression • Correlation with two variables; one designated independent, the other dependent • b, β, a, 𝝰 © 2017 Taylor & Francis Multiple Correlation/Regression • Multiple regression is probably the most used statistical procedure in the world • More than one independent variable and a single dependent variable • R © 2017 Taylor & Francis Canonical Correlation • Analogous to MANOVA, canonical correlation is multiple regression with multiple independent variables and more than one dependent variables • Beyond the scope of this text © 2017 Taylor & Francis Descriptive Statistics Measures of central tendency: • Mean: the arithmetic average • Median: the middle score of the group (ordinal) • Mode: the most frequent score • The definition of a normal distribution: mean = median = mode © 2017 Taylor & Francis Descriptive Statistics Measures of dispersion: • Range: calculated by taking the difference between the highest number in the group and the lowest • Standard deviation: the average deviation a set of scores are from their mean © 2017 Taylor & Francis Statistical Difference • Do the means likely come from different groups? • Is there a real (statistical) difference between the groups being compared? • We need a hypothesis and a test © 2017 Taylor & Francis
