DATA ANALYSIS PSYC 610

Multiple Regression with multiple predictors (and no interactions)

Situation 1 – Additional explanatory power: There is a variable (or a set of variables) for which it has been established in the literature that it has an effect on the DV. We have identified a new variable of which we think that it further explains the phenomenon under consideration. We run a multiple regression analysis to show that the new variable has an effect over and above the effect of the other variable. The goal is to show that the new variable adds explanatory power and that it is worthwhile to study the new variable!

Situation 2 – Statistical power: There is a variable (or a set of variables) for which it has been established in the literature that it has an effect on the DV. We have identified a new variable of which we think that it also has an effect on the DV but that this effect is rather small. We run a multiple regression analysis to remove the part of the variance that is explained by the other variable prior to testing the effect of our "new" variable. The goal is to increase statistical power!

Situation 3 – Mediation: There is a variable that has been shown to have an effect on the DV, either in the study at hand or in the literature. We have identified a new variable of which we think that it mediates the effect of the other variable on the DV. We run a multiple regression analysis to examine whether the effect of the other variable disappears (or becomes much smaller) when we add the new variable to the regression model. The goal is to test for mediation!

Additional explanatory power

/

Statistical power

/ Mediation
Expected bivariate relationship between the "new" variable and the DV: / Significant / Non significant (not enough statistical power). / Significant (the mediator is related to the dependant variable)
Expected relationship between the "new" variable and the other predictor(s): / No particular assumption (but in most cases they will be somewhat correlated). / Rather uncorrelated. / Rather correlated (the independent variable is related to the mediator).
What happens to the other pre-dictor(s) when the "new" variable is added to the regression model? / The other predictor probably remains significant. / The other predictor probably remains significant. / The other predictor becomes non significant (or its effect becomes considerably smaller).
Effect of the "new" variable in the multiple regression model: / Significant / Significant / Significant