[Gretl-devel] Some notes about the 2-means test in gretl's test statistic calculator

Hi, remember that back in June 2006 I semi-promised to write down something about a discussion we had? Well here it is: If the checkbox "assume equal variances" is checked, then gretl calculates the standard error of the difference in means as $se = \sqrt{ x / n_1 + x / n_2 }$, where \begin{equation} x = ((n_1 - 1) * s^2_1 + (n_2 - 1) * s^2_2) / (n_1 + n_2 - 2) \end{equation} which follows from equ. (5) in DeGroot (1986, p. 508). This is an exact test for any finite sample and thus the test statistic has a $t$ distribution. However, if the true variances are not equal (probably a realistic assumption in many applications) then finite-sample versions of the 2-means test are not available. Therefore if the checkbox "assume equal variances" is unchecked, gretl must use an asymptotic approximation even for small samples. If one of the two sample sizes is smaller than 30, gretl prints a warning but performs the test anyway. Morris H. DeGroot, Probability and Statistics, 2nd edition, Addison-Wesley, 1986 (Reprinted with corrections, 1989). ---- A further comment: It would be nice if "assuming equal variances" could be printed in the output. thanks, sven