Re: Which type of variance?

In article <1123427174.655355.102710@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<jhartdc@xxxxxxxxx> wrote:
> Or, possibly better yet, how 'bout just doing an F-test to see if the
> STDEVs are significantly different in the 2 groups?

> John Hart

John, Here's a small example of the sort of thing you might get. It is
merely to show what happens if there's a doubt in your mind about the sizes
of the variances. The data were real test results from a school here, from
about 1988. The original values were grade scores, not the exam
percentages, so the grading convention has already discarded much possibly
useful information. If you have real numbers, use them if possible - NOT
the ones that have been generated by categorising them. The example was
done in my own software - which does not run on standard Windows PCs, I'm
afraid. I'm now going to drop some output into this email. The example is
a test for means, not paired samples, which would give a different result of
course.

***********************************************************

Univariate (Single Column) Statistics - Population Estimates.
Std Dev, etc are based on N-1 Degrees of Freedom.

Name Mean Std Dev Min Max N Std Err Total Coeff of Var


Math 3.28947 1.87311 0 7 38 0.303858 125 56.9
Lang 4.04878 1.22375 0 7 41 0.191117 166 30.2


Student's t test for Math against Lang

Difference = -0.759307

Assuming EQUAL variances, Std. Error of difference = 0.353459

't' = -2.148 with 77 DF. 2-sided probability of H0 (no difference) =
0.03484

95% Confidence interval for the difference = -1.46304 to -0.05557


Assuming UNEQUAL variances, Std Error of difference = 0.358965

't' = -2.115 with 62.952 DF. 2-sided probability of H0 = 0.03843

95% Confidence interval for the difference = -1.477 to -0.0421

F ratio for the variances = 2.343, probability 4.629E-3 (37 and 40 DF)

*********************************************************

The above output uses the (default) 6 sig. digits. I should have changed it
to 3 or 4 I suppose :-( However, the principle and the practical result
should be fairly clear. It seems to me to answer several of your questions.

Hope this helps!

Robin


.