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

[Claus Mayer]

Which only shows that one should read these things properly before one 
replies. Very sorry about that!
I haven't come across that approach as a test for differences in 
variances yet, but I can see the idea now.  As the F-test has optimality 
properties for normal distributions I still would prefer it (possibly 
performed as a resampling test to make it more robust against deviations 
of non-normality).

Sorry again for misreading and misinterpreting the question

Claus

Naomi Altman wrote:
> Actually, since Benjamin took  abs(x-xbar) the means are not the same.  
> abs(x-sbar) should be centered roughly on SD(x).
> 
> --Naomi
> 
> At 04:15 AM 11/1/2006, Claus Mayer wrote:
>> Hello Benjamin!
>>
>> I think there is some misunderstanding here. The t-test is a test for
>> the differences between the means of two distributions. If you center
>> your data like you propose the difference is 0 so the t-statistic will
>> always behave very much like under the nullhypothesis (not exactly as
>> the distributions might differ in variances and other properties, but
>> the t-test is NOT meant to detect those).
>> The F-test on the other hand specifically tests for difference in
>> variances, so it is clearly the more appropriate test in your case (and
>> if you are worrried about non-normality you might determine p-values by
>> a resampling method like bootstrap).
>> I think what might have confused you is that there are TWO F-tests:
>> a) the one for testing differences between variances (lets call that F1)
>> b) the F-test that is being used in Analysis of Variance (ANOVA) (lets
>> call it F2)
>> Despite its name ANOVA is a method to compare MEANS not VARIANCES. With
>> two groups you have the trivial case of a one-way ANOVA and if you
>> calculate the F-statistic F2 for that it is just a transformation of the
>> usual t-statistic, i.e. the test will yield the same p-values.
>> So F1 and F2 are very different statistics for very different things,
>> but both have a F-distribution under normality assumptions so their
>> names are the same (there are plenty of chi-square tests out there as 
>> well!)
>>
>> Hope this helps
>>
>> Claus
>>
>> 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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>> >
>> >
>> >
>> >
>> >
>>
>> -- 
>> *********************************************************************************** 
>>
>>   Dr Claus-D. Mayer                    | http://www.bioss.ac.uk
>>   Biomathematics & Statistics Scotland | email: claus at bioss.ac.uk
>>   Rowett Research Institute            | Telephone: +44 (0) 1224 716652
>>   Aberdeen AB21 9SB, Scotland, UK.     | Fax: +44 (0) 1224 715349
>>
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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
> 
> 
> 
> 
> 
> 

-- 
***********************************************************************************
  Dr Claus-D. Mayer                    | http://www.bioss.ac.uk
  Biomathematics & Statistics Scotland | email: claus at bioss.ac.uk
  Rowett Research Institute            | Telephone: +44 (0) 1224 716652
  Aberdeen AB21 9SB, Scotland, UK.     | Fax: +44 (0) 1224 715349