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

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

3. 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 R2.
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

4. 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
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

5. 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
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

6. 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
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

7. 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
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

8. 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
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

9. 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
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

10. 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
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

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

12. 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
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

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

14. 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
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

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

16. 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
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

17. 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.
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

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

19. 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!
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall