On 18 May 2001 07:51:21 -0700, [EMAIL PROTECTED] (Robert J.
MacG. Dawson) wrote:
[ ... ]
> OK, so what *is* going on here? Checking a dozen or so sources, I
> found that indeed both versions are used fairly frequently (BTW, I
> myself use the pooled version, and the last few textbooks I've used do
> so).
>
> Then I did what I should have done years ago, and I tried a MINITAB
> simulation. I saw that for (say) n1=n2=10, p1=p2=0.5, the unpooled
> statistic tends to have a somewhat heavy-tailed distribution. This makes
> sense: when the sample sizes are small the pooled variance estimator is
> computed using a sample size for which the normal approximation works
> better.
>
> The advantage of the unpooled statistic is presumably higher power;
> hoewever, in most cases, this is illusory. When p1 and p2 are close
> together, you do not *get* much extra power. When they are far apart
> and have moderate sample sizes you don't *need* extra power. And when
[ snip, rest]
Aren't we looking at the same contrast as the t-test with
pooled and unpooled variance estimates? Then -
(a) there is exactly the same t-test value when the Ns are equal;
the only change is in DF.
(b) Which test is more powerful depends on which group is
larger, the one with *small* variance, or the one with *large*
variance. -- it is a large difference when Ns and variances
are both different by (say) a fourfold factor or more.
If the big N has the small variance, then the advantage
lies with 'pooling' so that the wild, small group is not weighted
as heavily. If the big N has the large variance, then the
separate-variance estimate lets you take advantage of the
precision of the smaller group.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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