1. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Chapter 12 Making Sense of Advanced Statistical Procedures in Research Articles

2. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Hierarchical multiple regression Stepwise multiple regression Partial correlation Reliability measures Factor analysis Path analysis Structural equation modeling Measures of Association Among Variables

3. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall A Brief Review of Multiple Regression Predicting scores on a criterion variable from two or more predictor variables Overall accuracy of a prediction rule is called the proportion of variance accounted for, and is abbreviated as R 2.

4. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Hierarchical and Stepwise Multiple Regression Hierarchical multiple regression –Predictor variables are entered into the regression sequentially Stepwise multiple regression –Computer selects predictor variable that accounts for most variance on the criterion variable, if significant –Process repeats by selecting variable that accounts for the most additional variance, if significant, and so on –Used as an exploratory technique; is controversial

5. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Hierarchical vs. Stepwise Multiple Regression Both involve adding variables sequentially and checking for significant improvement in the degree to which the model can predict scores on the criterion variable. –In hierarchical multiple regression, the order is determined in advance, by a theory or plan –In stepwise multiple regression, order is determined by a computer

6. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Partial Correlation Measures the degree of association between two variables, over and above the influence of one or more other variables. –Also called holding constant, partialing out, adjusting for, or controlling for one or more variables Often used by researchers to sort out alternative explanations for relations among variables

7. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Reliability Degree of stability or consistency of a measure –Test-retest reliability Correlation between two administrations of the same measure Problem: Taking some tests over can affect performance –Split-half reliability Correlation between two halves of the same measure –Internal consistency reliability Cronbach’s alpha (  ) Degree to which items “hang together” and assess a common characteristic

8. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Factor Analysis Technique for determining which variables tend to “clump together” –Which variables tend to be correlated with each other and not with other variables Clump of variables is called a factor Degree to which variable is correlated with a factor is called its factor loading

9. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Causal Modeling Set of techniques for testing whether a pattern of correlations among variables in a sample fits a theory of which variables are causing which Two methods of causal modeling –Path analysis –Structural equation modeling

10. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Path Analysis Variables connected to one another with arrows Each arrow has a path coefficient –Indicates the degree of association between the two variables –Holds constant any variables that have arrows pointing to the same variable

11. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Path Analysis Another example…

12. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Structural Equation Modeling Another type of causal modeling Differs from path analysis in two ways –Allows researcher to compute a fit index, a measure of the overall fit between the theory and the set of correlations –Depicts relations between latent variables, constructs that combine several measures, rather than measures themselves

13. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Structural Equation Modeling Another example…

14. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Independent vs. Dependent Variables Independent variables –Divide groups from each other –Often based on random assignment –Analogous to predictor variables in regression Dependent variables –Represent the effect of the experimental procedure –Analogous to criterion variables in regression

15. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Procedures that Compare Groups Analysis of covariance Multivariate analysis of variance Multivariate analysis of covariance

16. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Analysis of Covariance ANCOVA Like an analysis of variance in which one or more variables (called covariates) have been controlled for Analogous to a partial correlation

17. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Multivariate Analyses More than one dependent variable Multivariate analysis of variance –MANOVA –Like an analysis of variance with two or more dependent variables Multivariate analysis of covariance –MANCOVA –Like a multivariate analysis of variance in which one or more variables (covariates) have been controlled for.

18. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Overview of Statistical Techniques

19. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall How to Read Results Involving Unfamiliar Statistical Techniques Don’t panic! Look for a p level Look for indication of degree of association or size of a difference Reference an intermediate or advanced statistics text Take more statistics courses!