# Paired samples-equality of variance and 95% CI around difference in variances

1. Aug 3, 2011

### wvguy8258

Hi,

Can a few of you please review the approach I plan to take for obvious errors?

I have 50 subjects and each have a measure taken on the same variable before and after treatment. So, this is standard paired t-test time, but what I am actually interested in is the variance of the treatment versus the control. I would like to test the equality of variance for these two groups of values (treatment and control) and also place a 95% confidence interval around the difference of these two variances. I would prefer randomization/resampling methods to be used for each as normality assumptions do not hold and I would like a robust result. I have not found any routines specifically like what I would want, so I think I may have to do the following in R. Any advice on an easier or better approach is welcome.

I know that equality of variance for paired data can be tested using the pitman-morgan statistic. I was planning on calculating this for the original data and then randomly switching the values within pairs the the pre-treatment and post-treatment measures in order to achieve randomization that respects the paired nature of the data. I could then extract p-values based upon the percent of randomizations with more extreme pitman-morgan statistic.

For the 95% CI interval around the differences, I thought I would resample pairs of values with replacement. So, I would select among the 50 subjects 50 times with replacement. I would then calculate the variance for the pre-treatment measures and for the post-treatment measures and I would then take the difference and store this value. I would do this many times and then determine the 95% confidence interval by ordering my resamples and simply taking the 2.5% and 97.5% percentiles.

Does this make sense at all?

NOTE: Since posting I have been advised elsewhere that a ratio of the variances would be better than the difference.

Thanks,
Seth

Last edited: Aug 3, 2011
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