[Gretl-users] variance in mean test (again)

[Allin Cottrell]

On Wed, 7 Jun 2006, Sven Schreiber wrote:

> When testing the difference of two means (Utilities -> test statistic
> calculator), I cannot reproduce the standard deviation used in the
> denominator. For example, using
> mu1=1, sigma1=2, n1=25,
> mu2=1, sigma2=3, n2=36
>
> gretl's test statistic output is 0/0.687129. What's the formula for that
> value?

Having checked with DeGroot[*], I stand by this value.  It's what 
you get when you apply equation (5) on page 508.  DeGroot writes
the test statistic in this form:

U = \frac{\sqrt{(n_1 + n_2 - 2)} (\bar{X}_1 - \bar{X}_2)}
     {\sqrt{(1/n_1 + 1/n_2)} \sqrt{(S^2_1 + S^2_2)}}

where S^2_i is the sum of squared deviations from the mean for 
sample i.

[*] Morris H. DeGroot, Probability and Statistics, 2nd edition, 
Addison-Wesley, 1986 (Reprinted with corrections, 1989).

Allin