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# non-inferioirty test for variances of two groups

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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## Re: non-inferioirty test for variances of two groups

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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## Re: non-inferioirty test for variances of two groups

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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## Re: non-inferioirty test for variances of two groups

[ Edited ]

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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Posts: 30