[BioC] F-test vs.T-test-on-differences

[Naomi Altman]

Assuming that the data values are normally distributed within group, 
then the F-test has an F-distribution when there is no difference in variance.

Under the same assumption, abs(g1 - mean(g1)) will be very highly 
skewed, so that the t-test will not have a t-distribution, even if 
there is no difference in variance.  However, under the assumption of 
no difference in variance, the distributions should be the same, so 
nonparametric tests of differences between the samples should be 
valid - e.g. a Wilcoxon or Kolmogorov-Smirnov test might "work".

The F-test is known to be sensitive to non-normality.  The Wilcoxon 
and KS tests might have low power for this particular situation 
(although I could not say for sure).

Anyways, I think your idea is "on track" but implementing it using 
the t as the null distribution is not.

--Naomi

At 11:57 AM 10/31/2006, Benjamin Otto wrote:
>Dear community,
>
>
>
>That might be a stupid statistical question but I'm really not sure about
>the answer:
>
>
>
>Suppose I have two groups of numeric values x11-x19  and y11-y19. The
>conventional way to check for difference in variance here is performing an
>F-test with say
>
>
>
> > g1 <- c(x11:x19)
>
> > g2 <- c(y11:y19)
>
> > var.test( g1, g2)
>
>
>
>and looking at the resuting p.value. A second possibility is calculating
>some adjusted values first like
>
>
>
> > g1.adj <- abs(g1 - mean(g1))
>
> > g2.adj <- abs(g2 - mean(g2))
>
>
>
>And afterwards performing a T-test on those values. Should that give me the
>same result? I tried to solve it mathematically and the statistic doesn't
>seem to be the same. But then, why is the F-test calculated as it is AND is
>it really better for a comparison than the second version?
>
>
>
>Regards,
>
>
>
>benjamin
>
>
>
>--
>Benjamin Otto
>Universitaetsklinikum Eppendorf Hamburg
>Institut fuer Klinische Chemie
>Martinistrasse 52
>20246 Hamburg
>
>
>
>
>         [[alternative HTML version deleted]]
>
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Naomi S. Altman                                814-865-3791 (voice)
Associate Professor
Dept. of Statistics                              814-863-7114 (fax)
Penn State University                         814-865-1348 (Statistics)
University Park, PA 16802-2111