Hi On 16 Nov 2001, Rich Strauss wrote: > I've just done some quick simulations in Matlab, constructing randomized > null distributions of the t-statistic under both scenarious: (1) sample > variances based on sample means vs. (2) variances about the pooled mean. > Assuming I've done everything correctly, the result is that the null > distribution of the t-statistic in the second case consistently > approximates the theoretical t-distribution more closely that that of the > first case. This seems to be true regardless of sample sizes and of > whether the two sample sizes are identical or different. This result > implies that the t-statistic should indeed be calculated about a pooled > estimate of the common mean, as Jerry Dallal suggested. > > I could pass on the details of my simulation if anyone is interested, but > mostly I'd appreciate it if someone could repeat this simulation > independently of mine to see whether it holds up.
This simply cannot be generally true. It probably only applies when the null is in fact true, which may be the case for your simulations. To appreciate the illogical nature of this recommendation, consider creating a real difference of x between your population means, then 2x, then 3x, and so on. By the common mean approach, you are treating the variability between groups as though it were noise (i.e., a component in your estimate of sigma^2, the variance about the null-hypothesis of a common mean). It is critical to keep in mind that the null hypothesis is in fact just that, a hypothesis that may or may not be correct. Computing the within-group variance about the group means is the correct way to estimate sigma^2, however, irrespective of whether the Ho about the means is true or not. Best wishes Jim ============================================================================ James M. Clark (204) 786-9757 Department of Psychology (204) 774-4134 Fax University of Winnipeg 4L05D Winnipeg, Manitoba R3B 2E9 [EMAIL PROTECTED] CANADA http://www.uwinnipeg.ca/~clark ============================================================================ ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
