On Sun, 13 Apr 2008 07:12:25 -0700 (PDT), Rob <rt****lston@[EMAIL PROTECTED]
>
wrote:
> Rich,
>
> Thanks for you response. I've interspersed my comments below.
[snip, most]
RU > >
> > That is surely not the case. The most powerful
> > tests have equal group sizes; and cross-classifications
> > need cell sizes that are pro****tionate if the tests are
> > to remain independent and "unconfounded" with each
> > other. There still can be tests.
> >
> >
>
> I see. So fringe populations (eg short sighted, colour blind, wearing
> contact lenses against those who don't) are less powerful as the
> population is enormously mis-blanced? I presume this is because there
> might be a larger inter quartile range (or similar) within the small
> population because of the lower quantity of results?
No, that is not the reason.
When you compare two means, the test uses the
Standard Error of the two means - The SE is the Standard
deviation (pooled, or for equal variances) divided by
the square root of N. The mean and SE is considered
for each group. When you have a fixed N to divide
between two groups, the way to get the greatest precision
for both groups at once is to have equal Ns; when Ns are
unequal, the precision lost for the smaller N is worse than
the precision gained for the larger N. In fact, this problem
can be quantified by computing the "equivalent N" for the
analysis, using the <reciprocal of the average of the reciprocals>
That is, given Ns of 10 and 100, the average of .1 and .01 is
..055; the reciprocal of that is 18.2 -- Thus, allocating 110
people unequally gives the same power as comparing 18
versus 18.
Occasionally -- when variances are unequal -- there *can*
be an advantage in having a greater N for the group that
is more variable, if the test takes that into account, like
the "t-test for unequal variances." Then the ideal is to
achieve equal SEs for the two groups by varying the Ns.
[snip, rest]
--
Rich Ulrich
http://www.pitt.edu/~wpilib/index.html
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