Re: [Gretl-users] variance in mean test
On Wed, 7 Jun 2006, Sven Schreiber wrote:
Well, as you can see from my recent posts I have been using the
test statistic calculator for the last couple of days. Here's
another question about it:
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? I would use \sqrt(4/25 + 9/36) = 0.6403... in
the denominator instead, and I couldn't get gretl's ouput by
some variations.
In this case, since at least one of the sample sizes is less than
30, gretl is calculating the standard error of the difference in
means as follows (in TeX notation):
x = ((n_1 - 1) * s^2_1 + (n_2 - 1) * s^2_2) / (n_1 + n_2 - 2)
se = \sqrt{ x / n_1 + x / n_2 }
I can't recall right now on what authority I have this formula.
I will check with my "bible" on such matters, DeGroot's
Probability and Statistics, 2e.
Allin.