Question

how does a significant interaction affect our interpretation of the main effect?

Answer 1

Interaction Effect:-

Interaction effects occur when the effect of one variable depends on the value of another variable. Interaction effects are common in regression analysis, ANOVA, and designed experiments. In this blog post, I explain interaction effects, how to interpret them in statistical designs, and the problems you will face if you don’t include them in your model.

When you have statistically significant interaction effects, you can’t interpret the main effects without considering the interactions. Suppose we want to maximize satisfaction by choosing the best food and the best condiment. However, imagine that we forgot to include the interaction effect and assessed only the main effects. We’ll make our decision based on the main effects plots below.

Main effects plot for the taste test ANOVA design.

Based on these plots, we’d choose hot dogs with chocolate sauce because they each produce higher enjoyment. That’s not a good choice despite what the main effects show! When you have statistically significant interactions, you cannot interpret the main effect without considering the interaction effects.

Important Considerations for Interaction Effects

While the plots help you interpret the interaction effects, use a hypothesis test to determine whether the effect is statistically significant. Plots can display non-parallel lines that represent random sample error rather than an actual effect. P-values and hypothesis tests help you sort out the real effects from the noise.

The examples in two-way interactions because there are two independent variables in each term (Food*Condiment and Temperature*Pressure). It’s equally valid to interpret these effects in two ways. For example, the relationship between:

Satisfaction and Condiment depends on Food.

Satisfaction and Food depends on Condiment.

  Finally, when you have interaction effects that are statistically significant, do not attempt to interpret the main effects without considering the interaction effects. As the examples show, you will draw the wrong the conclusions!