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- non-inferioirty test for variances of two groups

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10-13-2015 12:24 PM

Does anyone know the SAS code for non-inferiority test for VARIANCES of two group? I see lots on means and proportions but can't find help on variances. Thx!

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10-14-2015 08:28 AM

Not something done very often, so it isn't surprising that there is little available. In order to help, do you know what the measure of non-inferiority is for the variances, and how you might be thinking of attacking the problem? Is there literature available that can be worked from?

Steve Denham

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10-14-2015 08:44 AM

We can attack it as a difference between the two variances (using d=3), or as a ratio of the two variances (using d=0.5). I think I'll just build a confidence interval around the ratio and if d is outside then conclude non-inferior. Do you think that is sufficient?

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10-14-2015 08:50 AM - edited 10-14-2015 08:53 AM

I would definitely go with the ratio, as it has a known distribution (F distribution) and there are good methods for calculating confidence bounds. If d is outside the bound, then you are probably good to go--just be aware that the lower bound on the F distribution is a bit harder to calculate, and due to the skewness of the distribution, you may need (well, you WILL need) a much larger N to show non-inferiority for the variance, as compared to the mean.

Thinking on this just a bit more--that ratio may be a non-central F, with non-central chi square values needed for the confidence bound. It's been almost 40 years since math stat class, so I would need to dig through some old class notes to be sure.

Steve Denham

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10-14-2015 11:30 AM

Thanks so much for the helpful info Steve!