Re: st: -ttest- does not report the pooled standard deviation

[Gary Longton <glongton@fhcrc.org>]

Paul Dickman wrote:

> Can anyone explain why -ttest- without the unequal option does not report
> the pooled standard deviation. In the output below, for example, it is
> possible one might erroneously conclude that the pooled standard deviation
> was 5.785503.

I suspect this was just a matter of judgment as to which estimates were the most 
relevant to display for 2-sample t-test results.  The pooled variance estimate 
may have been considered just an intermediate result on the way to calculating 
the se of the mean difference, which IS displayed.

It seemed reasonably clear to me that the mean and sd in the "combined" table 
entry referred to the mean and sd for the total sample (combined groups).

In any case, and at risk of pointing out what you may already know, the pooled 
variance estimate can be readily obtained, if desired, from the [2-sample, equal 
variance] -ttest- returned results either by working backward from the se of the 
mean difference:

.scalar s2_pool_a = (r(se)^2)/(1/r(N_1) + 1/r(N_2))

or alternatively (and to confirm), working forward to calculate directly from 
the group sample standard deviations:

.scalar s2_pool_b = ( (r(N_1)-1) * r(sd_1)^2 + (r(N_2)-1) * r(sd_2)^2 )/ r(df_t)

When calculated after -ttest mpg, by(foreign)-, these yield:

. di "   pooled sd, calculated from mean difference se: " sqrt(s2_pool_a)

   pooled sd, calculated from mean difference se: 5.3558197

. di "   pooled sd, calculated from group sample sd's:  " sqrt(s2_pool_b)

   pooled sd, calculated from group sample sd's:  5.3558197


- Gary

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