dennis roberts wrote:
> now, we take (if this is really possible) a random sample of 100 ...
> .08 ... TEST A
>
> or, this test turned up a p value of .02 ... TEST B
>
> or, this test turned up a p value of .008 ... TEST C
>
> assume for a moment that we did things correctly in terms of sampling, run
> the right test, assumptions met, etc.
>
> are we able to accurately say ... that if we had the results as in TEST C
> ... that we are more convinced that the null of 100 is NOT true ... than
> for TEST B or TEST A?
>
> no ifs, ands, or buts or it depends on this or that ... just straight
> talking ... can we say this?
I'd prefer talking about samples of 100 from three different
populations taking the same test.
Suppose the SD of all tests is 10. Suppose A&B are such that
populations get scores normally distributed about their population's
mean, but C is such that scores are distributed about the sample
mean iff the mean is no more than 100. If the population mean is
greater than 100, scores are normally distributed about 150
regardless of the population mean. In that case, P=.008 (mean+-SEM
= 102.7+-1) from C would make me less likely to doubt the null than
P = 0.02 from B.
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