If a two-factor analysis of variance produces a statistically significant interaction between the two factors A and B,then what can you conclude about the main effects for A and B?
A)Either the main effect for factor A or the main effect for factor B is also significant.
B)Both the main effect for factor A and the main effect for factor B are significant.
C)Neither the main effect for factor A nor the main effect for factor B is significant.
D)The significance of the main effects is not related to the significance of the interaction.

Question

If a two-factor analysis of variance produces a statistically significant interaction between the two factors A and B,then what can you conclude about the main effects for A and B?​
A)​Either the main effect for factor A or the main effect for factor B is also significant.
B)​Both the main effect for factor A and the main effect for factor B are significant.
C)​Neither the main effect for factor A nor the main effect for factor B is significant.
D)​The significance of the main effects is not related to the significance of the interaction.

Quizplus · Accepted Answer

The significance of the interaction effect in a two-factor ANOVA indicates how the effect of one factor varies across the levels of the other factor, but it does not directly inform about the significance of the main effects of either factor. Main effects can be significant or not, regardless of the interaction effect.

If a Two-Factor Analysis of Variance Produces a Statistically Significant