dennis roberts wrote:
> when we do a 2 sample t test ... where we are estimating the
> population variances ... in the context of comparing means ... the
> test statistic ...
>
> diff in means / standard error of differences ... is not exactly like
> a t distribution with n1-1 + n2-1 degrees of freedom (without using
> the term non central t)
>
> would it be fair to tell students, as a thumb rule ... that in the
> case where:
>
> ns are quite different ... AND, smaller variance associated with
> larger n, and reverse ... is the situation where the test statistic
> above is when we are LEAST comfortable saying that it follows (close
> to) a t distribution with n1-1 + n2-1 degrees of freedom?
>
> that is ... i want to set up the "red flag" condition for them ...
>
> what are guidelines (if any) any of you have used in this situation?
G. E. P. Box says, (a) if n(1) = n(2), treat them as if s(1) = s(2).
(b) if s(1)/s(2) (selecting 1 & 2 so ratio is >1) is less than about 3,
treat them as if s(1) = s(2). This is approx. equal to running an F
test for diff in vars. And I think this is where he gets this from.
(c) if n(1) is within 'about' 10% of n(2), go for option (a) above. I
have a paper I can't find for (a) and (b), but (c) was a verbal.
When you speak of getting 'LEAST comfortable' I think you are saying,
how much deviation can you stand. A lot depends on the consequences of
deviation - decision 'theory' etc. If you take a non-dichotomous view
of 't' testing, the question becomes immaterial, anyway.
Cheers,
Jay
--
Jay Warner
Principal Scientist
Warner Consulting, Inc.
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