How would you test for a difference in mean group differences between scenarios?

Question

Suppose I'm looking at gender differences across two scenarios (all respondents answered both scenarios) and I want to know whether the gap between men and women varies between scenarios. Suppose the "gap" (mean for men minus mean for women) in Scenario A is 5 and the gap in Scenario B is 3. What statistical test would I use to determine whether the gap in Scenario B is significantly smaller than the gap in Scenario A?

dbwilson · Answer

The classic approach to this problem is to use a split-plot ANOVA, that is, a 2 by 2 ANOVA with a between-subjects factor (sex) and a within-subjects factor (scenario). You get three F-tests from this, one for each main effect (sex and scenario) and one for the interaction (a difference-in-differences). Your interest is in the interaction. This is testing whether the effect of scenario differs between the sexes.

Answered by dbwilson on November 26, 2021

BertHobe · Answer

This depends on the underlying assumptions. Primarily distributional. Comparing means between groups could be done with analysis of variance which in the simplest case reduces to a T test. So you test your hypothesis that the effect difference is zero or not.
$H_0:mu_{scenario1}-mu_{scenario2}>=0$
$H_1:mu_{scenario1}-mu_{scenario2}<0$

How would you test for a difference in mean group differences between scenarios?

2 Answers

Add your own answers!

Ask a Question