On 26 Feb 2001 12:26:19 -0800, [EMAIL PROTECTED] (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?
Neither extreme is better than the other. Student's t-test and that
Satterthwaite test have their problems in the opposite directions.
With unequal Ns and unequal variances, and a one-tailed test,
- one t-test will be too small (rejecting, approximately, never) and
- the other will be too big (rejecting about twice as often);
- making the TWO-tailed versions come out 'robust'! for size.
Neither direction is better until you decide what bias you want.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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