This is true. I simulated the null distributions, those obtained when the null hypothesis is true, which is what the centered t-distribution represents. I didn't look at the sampling distributions for different effect sizes.
>Date: Sat, 17 Nov 2001 00:19:06 -0600 >From: jim clark <[EMAIL PROTECTED]> >Subject: Re: diff in proportions >Sender: [EMAIL PROTECTED] >X-Sender: [EMAIL PROTECTED] >To: [EMAIL PROTECTED] >Organization: The University of Winnipeg >X-Authentication-warning: dex.pathlink.com: news set sender to > [EMAIL PROTECTED] using -f >Original-recipient: rfc822;[EMAIL PROTECTED] > >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/ >================================================================= > ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
