To answer this question, you first have to understand the basic concepts of a two-way ANOVA (Analysis of Variance).
A two-way ANOVA is a statistical procedure that involves evaluating the means of two or more variables (typically independent variables) to assess if they are significantly different from one another. In two-way ANOVA, these are known as factors, and the independent variables present in a study become the "main effects."
The options are:
A. Main effects.
The "main effects" in a two-way ANOVA are the individual effects of each independent variable on the dependent variable. While these are important, they do not encompass the full picture of what the ANOVA is evaluating.
B. ANOVA summary table.
This table is an output of the ANOVA test and contains a lot of useful information. However, while it is essential for interpreting the results, it is not the prime interpretation of a two-way ANOVA.
C. Interaction effect, if it is significant.
The interaction effect in a two-way ANOVA explores whether there is an interaction between the two independent variables that significantly affects the dependent variable. If the interaction effect is significant, this means that the effect of one factor depends on the level of the other factor.
D. Means for the main effects.
While the means of the main effects are also important in a two-way ANOVA, they are still not the primary interpretation, especially when an interaction effect is present.
Hence, among all these options, the primary interpretation of a two-way ANOVA lies in the 'Interaction effect, if it is significant'. This is because the interaction effect demonstrates how the two independent variables interact and work together to impact the dependent variable, which is the main focus of a two-way ANOVA.
Therefore, the correct answer is C. Interaction effect, if it is significant.