The results of a two-factor ANOVA (J = 3, K = 2) show that both main effects are significant, but the interaction is not significant. We need to
A) conduct MCPs to examine the two main effects and the interaction
effect.
B) conduct MCPs to examine the interaction effect only.
C) conduct MCPs to examine the two main effects.
D) conduct MCPs to examine one main effect only.

Question

Quizplus · Accepted Answer

A two-factor ANOVA (Analysis of Variance) is used to evaluate the effects of two independent variables (factors) on a dependent variable. In this case, the two factors have J = 3 levels for the first factor and K = 2 levels for the second factor. When the results of a two-factor ANOVA indicate that both main effects are significant, it means that each factor independently has a statistically significant effect on the dependent variable. However, if the interaction effect is not significant, it suggests that the effect of one factor does not depend on the levels of the other factor.
Given these results, the appropriate course of action would be:
c. conduct MCPs (Multiple Comparison Procedures) to examine the two main effects.
Multiple Comparison Procedures are used after an ANOVA to determine exactly which means are different from each other. Since the main effects are significant, it is important to conduct MCPs to further investigate these effects and understand the differences between the levels of each factor. This could involve using post-hoc tests such as Tukey's HSD, Bonferroni, or Scheffé's method, among others.
On the other hand, since the interaction effect is not significant, there is no need to conduct MCPs for the interaction. The lack of a significant interaction suggests that the effect of one factor on the dependent variable is consistent across the levels of the other factor, and thus, there is no specific interaction to further investigate.
Therefore, the correct answer is:
c. conduct MCPs to examine the two main effects.

The Results of a Two-Factor ANOVA (J = 3, K