Re: data analysis bug

["Andreas J. Guelzow" <aguelzow math concordia ab ca>]

Andreas J. Guelzow wrote:

> I guess I should really file an official bug report but here is the 
> short form:
>
> The pooled variance calculated for the "T-test: Two Sample Assuming 
> Equal Variances" is not always correct:
>
> sample 1: 1,2,3
> sample 2: 1, 2.2, 3.4
>
> individual variances are 1 and 1.44. The pooled variance is a weighted 
> average of those two, ie. must be lying between 1 and 1.44 (in fact it 
> is 1.22), but gnumeric calculates 0.988
>
> This will normally also affect the t statistic etc. I didn't check 
> whether they were incorrect but since they should use the pooled 
> variance....
>
> This is today's CVS version of gnumeric. (But I observed the same  
> problem in an earlier version while using gnumeric in an introductory 
>   statistics class this May.) 


I didn't think I could find this in the code that fast (but the code 
very nicely written). In analysis-tools.c lines 1436ff
are:

  var = (set_one.sqrsum + set_two.sqrsum - (set_one.sum + set_two.sum) *
         (set_one.sum + set_two.sum)/ (set_one.n + set_two.n)) /
      (set_one.n + set_two.n - 1);  /* TODO: Correct??? */

this calculation is incorrect but should be:
 var = ((set_one.sqrsum - set_one.sum2 / set_one.n)+(set_two.sqrsum - 
set_two.sum2 / set_two.n))/
          (set_one.n + set_two.n - 2);

Interestingly enough in the following calculation for the t value this 
pooled variance isn't even used but the t-value under the assumption of 
unequal variances is calculated:

t = fabs (mean1 - mean2 - mean_diff) /
      sqrt (var1 / set_one.n + var2 / set_two.n);

should really be:

t = fabs (mean1 - mean2 - mean_diff) /
       sqrt (var / set_one.n + var / set_two.n);

Andreas


>

--
Prof. Dr. Andreas J. Guelzow                    
Assoc. Prof of Mathematics
Concordia University College of Alberta
http://www.math.concordia.ab.ca/aguelzow