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

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

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

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

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

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

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

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

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

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

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

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

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