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