14.1 Introduction to Mixed-Model Factorial ANOVA
In Chapters 9 and 10 we distinguished between two distinct applications of the t-test: the independent samples t-test and the correlated samples t-test. Similarly, in Chapters 11 and 12 we distinguished between independent and correlated samples one-way ANOVA's. Recall that when a between-subjects design is used, the appropriate statistical test to use assumes independent-samples, whereas within-subjects designs require statistical tests assuming correlated samples.
In Chapter 13 we introduced two-way factorial ANOVA involving independent samples designs for both independent variables. However, it is possible to have experimental designs involving two independent variables that are both within-subjects. So the same distinctions we made between the two types of t-tests and one-way ANOVA's can be applied to two-way factorial ANOVA.
The researcher must know his/her experimental design in order to run the appropriate statistical test. In this chapter we introduce a two-way ANOVA which combines one independent samples factor and one correlated groups factor. These types of designs are called mixed-model ANOVA's, since they involve a mixture of one between-groups factor and one within-subjects factor.
Recall from the past several chapters that we analyzed changes in leader performance, task skills, and social skills before and after attending a leadership training workshop. Since repeated measures were obtained from the sample participants on these variables, they are correlated samples (within-subjects) variables. We saw from these analyses that there were significant improvements from time 1 to time 2 on all of these variables.
Given the focus on gender and gender role stereotypes in this project, an interesting question that could be asked is whether or not the gains on these variables were the same for male employees compared to female employees. For example, it may be that men benefit more from training in social skills than do women, given that women are already relatively strong in this aspect of leadership given their socialization. Further, women may benefit more than men from training in task skills, given the socialization of task skills in men.
The answer to these questions can be obtained by conducting a mixed-model factorial ANOVA on the social skills and task skills of employees. The example in this chapter will examine the effects of the workshop on task skills in men and women, while the end-of-chapter exercise will ask you to do the same analysis for the effects of the workshop on social skill scores.