Question

1. Explain what interaction means in two-factor analysis of variance. Your explanation needs to include how an interaction differs from main effect. In particular, how the interpretation of main effect differs when there is no interaction present and when there is an interaction present.

Answer 1

The Two Way ANOVA compares the mean differences between groups that have been split into 2 Factors. An interaction effect is defined as the simultaneous effect of two or more independent variables on at least one dependent variable in which their joint effect is significantly greater than or significantly less than the sum of the parts.The main effect is the effect of one of the independent variables on the dependent variable. Number of main effects is equal to the number of independent variables. An interaction effect occurs if there is an interaction between the independent variables that affect the dependent variable.

Example:

Two Factor ANOVA is conducted to study the effect of (i) tutoring and (ii) extra home work on the improvement of scores in a subject.

In this experiment, there are 2independent variables: (i) tutoring and (ii) extra home work

Dependent Variable: scores in a subject.

There are 2 Main Effects: (i) the effect of tutoring on the improvement of scores in a subject. (ii) the effect of extra home work on the improvement of scores in a subject.

If these 2 independent variables work together on the dependent variable, we have interaction effect.

If interaction effect is present, the impact of one factor depends on the level of the other factor.

If interaction effect is not present: Interpretation of main effects is valid and the results of study are reliable.

If interaction effect is present, the interpretaton of main effects is misleading and further analysis is needed.