How to calculate a sample size for Equivalence tests & Variance comparison for 3 groups?

Alix

I whould like to determine the sample size per group to perform a variance comparison test and an equivalence test for 3 independent groups.

JMP 16.0 propose an option but only for 1 or 2 groups. There is a manner to "extrapolate"  the results to the 3rd group?

 

@Mark_Bailey , Florence Kussener gaves me your name, could you help me?

 

Thanks!!

calking

Hey @Alix!

 

@Mark_Bailey forwarded me your question. I'm the developer for the Sample Size Explorers in JMP. 

 

Regarding your question, the Fit Y by X platform does support testing of variances and/or equivalence for 3 groups, but the power calculations it provides are only for testing of means. That being said, it looks like it uses an all-ways comparison as the default for equivalence testing. In that case, you'd just be looking at any pair of groups anyways(1 vs. 2, 1 vs. 3, and 2 vs. 3). So you should be able to "extrapolate" results from the 2 group case, where you can consider different relationships between groups (equal vs. unequal size, equal vs. unequal variances). It does require a bit more juggling of different outcomes, but seems doable. 

 

Regarding power for testing variances, if your goal is to try and test for equal variances among the three groups prior to testing for equivalence, I would suggest you go ahead and act as if there are unequal variances among the groups. I know that is more difficult to plan for than assuming equal variances and so equal group sizes, but if you have good reason to suspect unequal variances, then you'd want to plan for that outcome. A good rule of thumb is that the ratio of samples needed in one group vs. the other is roughly on the order of the ratio of variances in the one group vs. the other.  So you may want to take that into consideration in your planning. 

 

Hope that helps!