In a study with variables X and Y, is it possible that X has no main effect, Y has no main effect, yet the interaction of X and Y is significant?

Question

BlackTom AI · Accepted Answer

In a factorial analysis context, it is possible for the interaction between X and Y to be significant even when neither X nor Y shows a significant main effect.

Option True: This scenario can occur because the effect of one factor depends on the level of the other factor. A significant interaction means the combined effect cannot be explained by the sum of individual (main) effects alone, so X or Y might not show a main effect when averaged across the other factor’s levels, yet their joint influence is meaningful at specific level combinations.

Option False: If both main effects were truly absent, a statistically significant interaction would be surprising and would imply a more complex pattern or potential model misspecification. However, a significant interaction is not logically precluded by non-significant main effects; thus labeling this as impossible would be incorrect.

Additional nuance: It’s essential to look at interaction plots or simple effects to interpret the practical meaning of such an interaction, since the presence of a significant interaction changes how we understand the effect of X at each level of Y (and vice versa), independent of main effects.

PSY4230W01 2025- Final exam - Requires Respondus LockDown Browser

In a study with variables X and Y, is it possible that X has no main effect, Y has no main effect, yet the interaction of X and Y is significant?

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PSY*4230*W01 2025- Final exam - Requires Respondus LockDown Browser

In a study with variables X and Y, is it possible that X has no main effect, Y has no main effect, yet the interaction of X and Y is significant?

View Explanation

Log in for full answers

Similar Questions

What are all the interactions?

TRUE OR FALSE: Chang and Lauderdale statistically interact poverty income ratio with survey year in order to test whether relationships between income and cholesterol levels change over time.

An interaction term in a multiple regression model may be used when

Based on the output of summary() for the model from the previous question, interpret the interaction between nox and dis in the context of predicting medv. Choose the correct interpretation:

Based on the output of the summary() for the model from Question 1, is there evidence of an association between nox and medv? Choose the correct interpretation.

Parallel lines on a graph are a good indicator of an interaction.

More Practical Tools for Students Powered by AI Study Helper

Making Your Study Simpler

PSY4230W01 2025- Final exam - Requires Respondus LockDown Browser