1. i think when ns are the same and the variances are the same ... the standard errors are the same using pooled or non pooled estimates ...
2. when ns are the same but variances are different, the standard errors are the same
3. when ns are different and the variances are the same, the standard errors are the same
4. ONLY when ns are different AND variances are different are the standard errors different
http://roberts.ed.psu.edu/users/droberts/papers/twosampt.PDF
so, the only time the actual test statistic will be different is for #4 above ...
but, that does not solve the issue of what will be used for a critical value? (ie, dfs to look up the critical t) ... and, i don't think there is any hard and fast rule for this (just don't use MORE than n1-1 + n2-1) ... there are even thumb rules about in the case of differing ns ... when variances are not the same ... use the df for the SMALLER group ...
these kinds of trivial points pale in comparison to justifying that we are using the .05 level or the .01 level .. when deciding whether to reject/retain the null
in addition, since the null is never true (in most likelihood) ... the notion of having to decide about rejecting is rather silly ...
p values are really fairly useless ... and since about the best we can infer from them is evidence AGAINST the null and, if we know that the null CAN'T really be true (exactly) ... garnering evidence against the null is like adding more or more evidence that the ocean has water in it ...
At 09:13 PM 1/12/03 -0500, Karl L. Wuensch wrote:
It is NOT true that with equal sample sizes the separate variances and the pooled variances t tests are equivalent (except in one case, where the sample variances are identical). The computed values of t will be identical with equal sample sizes, but the degrees of freedom (and thus the value of p and the width of the confidence interval) will not. With equal sample sizes one still must make an assumption of homogeneity of variance to use the pooled degrees of freedom. Zimmerman did not seem to think it unreasonable to consider the observed variances when deciding between pooled and separate degrees of freedom when the sample sizes are equal.Karl W. ----- Original Message ----- From: "Howard Kaplon" <[EMAIL PROTECTED]> To: "Karl L. Wuensch" <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]> Sent: Sunday, January 12, 2003 9:03 PM Subject: Re: When to use a separate variances standard error One can show algebraically that when the sample sizes are equal, the pooled variance t test and separate variance t test are equivalent. So that if you agree with the work by Donald Zimmerman below and Karl's thinking, there is no reason to ever use the pooled variance t test. Howard Kaplon . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
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