Question

When one uses an ANOVA, explain the difference between “main effects” and “interaction effects”. Give examples of each.

Answer 1

Ans.

When we use ANOVA:

Analysis of variance (ANOVA) is a statistical technique that is used to check if the means of two or more groups are significantly different from each other. ANOVA checks the impact of one or more factors by comparing the means of different samples.

We can use ANOVA to prove/disprove if all the medication treatments were equally effective or not.

Another measure to compare the samples is called a t-test. When we have only two samples, t-test and ANOVA give the same results. However, using a t-test would not be reliable in cases where there are more than 2 samples. If we conduct multiple t-tests for comparing more than two samples, it will have a compounded effect on the error rate of the result.

Main Effect:

A main effect (also called a simple effect) is the effect of one independent variable on the dependent variable. It ignores the effects of any other independent variables. In general, there is one main effect for each dependent variable. For example, let’s say you’re conducting a study to see how tutoring and extra homework help to improve math scores. As there are two independent variables (tutoring and extra homework), there are two main effects:

1. The effect tutoring has on math scores.
2. The effect extra homework has on math scores.

Interaction Effect:

An interaction effect happens when one explanatory variable interacts with another explanatory variable on a response variable.

The two independent variables can also work together on the dependent variable. In that case, the effects are called interaction effects.

Example:

Simultaneous effect of Tutoring and Extra Homework on math score.