At 05:12 PM 11/16/01 +0000, you wrote:
>>On Thu, 15 Nov 2001, Jerry Dallal wrote:
>>> But, if the null hypothesis is that the means are the same, why
>>> isn't(aren't) the sample variance(s) calculated about a pooled
>>> estimate of the common mean?
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.
Rich Strauss
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