1. Chapter 12
Making Sense of
Advanced
Statistical
Procedures in
Research Articles

2. Measures of Association
Among Variables
• Hierarchical multiple regression
• Stepwise multiple regression
• Partial correlation
• Reliability measures
• Factor analysis
• Path analysis
• Structural equation modeling

3. A Brief Review of Multiple
Regression
• Predicting scores on a criterion variable
from two or more predictor variables
ˆ
Z Y = (β1 )( Z X 1 ) + (β 2 )( Z X 2 ) + (β3 )( Z X 3 )
• Overall accuracy of a prediction rule is
called the proportion of variance accounted
for, and is abbreviated as R2.

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

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

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

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 (α)
• Degree to which items “hang together” and assess a common
characteristic

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

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

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

11. Path Analysis
• Another example…

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

13. Structural Equation Modeling
• Another example…

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

15. Procedures that Compare
Groups
• Analysis of covariance
• Multivariate analysis of variance
• Multivariate analysis of covariance

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

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.

18. Overview of Statistical
Techniques

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!