Chapter 17
Making Sense of Advanced Statistical
Procedures in Research Articles
Brief Review of
Multiple Regression
 Predicting scores on a criterion variable
from two or more predictor variables
ZˆY  (1 )( Z X1 )  (2 )( Z X 2 )  (3 )( Z X 3 )
 Proportion of variance accounted for
(R2)
Hierarchical and Stepwise
Multiple Regression
 Hierarchical multiple regression
– Examine contribution to the prediction of each
variable added in a sequential fashion
 Stepwise Multiple regression
– Controversial exploratory procedure
– Predictor variable with best prediction located
– Find next predictor variable that gives highest
R2 with first predictor variable
– Repeat until best predictor variable does not
give significant improvement
Hierarchical and Stepwise
Multiple Regression
 Both involve adding variables a stage at
a time and checking for significant
improvement of prediction
 Theory/plan determines order of
variables in hierarchical regression
 No initial plan in stepwise regression
– Useful in exploratory and applied research
Partial Correlation
 Association between two variables, over
and above influence of one or more
other variables
 Holding constant, partialing out,
controlling for, adjusting for
 Partial correlation coefficient
Reliability
 Reliability
– Test-retest reliability
– Split-half reliability
– Cronbach’s alpha (α)
– Interrater reliability
Factor Analysis
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Measured large number of variables
Identifies variables that clump together
Factor
Factor loading
Several approaches to factor analysis
Naming the factors
Causal Modeling
 Measured large number of variables
 Does the pattern of correlations match
theory of which variables cause which?
 Path analysis
– Path
– Path coefficient
Causal Modeling
 Path analysis
Causal Modeling
 Structural equation modeling
– Elaboration of path analysis
– Fit index
• e.g., RMSEA
– Latent variable
– Measured variable
Causal Modeling
 Structural equation modeling
Causal Modeling
 Structural equation modeling
Causal Modeling
 Limitations
– Other patterns of causality possible
– Alternative theories
– Correlation and causality
– Linear relationships
– Restriction in range
Independent and Dependent
Variables
 Independent variable
– Predictor variable
 Dependent variable
– Criterion variable
Analysis of Covariance
(ANCOVA)
 ANOVA adjusting the dependent
variable for effect of additional variables
 Analogous to partial correlation
 Covariate
 Adjusted means
Multivariate Analysis of
Variance (MANOVA) and
Covariance (MANCOVA)
 Multivariate statistics
– More than one dependent variable
 Multivariate analysis of variance
(MANOVA)
– ANOVA with more than one dependent
variable
– Univariate ANOVA
Multivariate Analysis of
Variance (MANOVA) and
Covariance (MANCOVA)
 Multivariate analysis of covariance
(MANCOVA)
– ANCOVA with more than one dependent
variable
– MANOVA with covariates
Overview of Statistical
Techniques
Controversy: Should Statistics
be Controversial?
 Fisher
 Neyman
 Pearson
Reading Results Using
Unfamiliar Techniques
 Don’t panic!
 Look for a p level
 Look for pattern of results that is
considered significant
 Look for degree of association or size of
the difference
 Look up in statistics book
 Take more statistics courses!