On Thu, 25 Jan 2001 09:23:02 -0500, Bruce Weaver
<[EMAIL PROTECTED]> wrote:
> Hi group,
> The unweighted means method for unbalanced ANOVA designs uses the
> harmonic mean of the cell sample sizes. I wonder if anyone can explain
> why the harmonic mean, as opposed to any other kind of "average" sample
> size. None of the books I've read comment on this--and I just know some
> keen student will ask me this next week!
It is almost "next week." So I will offer my shot at it.
Well, the number is an approximation, which is supposed to preserve
and represent how much information you have. For one thing, consider
the computation for the Student's t-test. For a given total N, you
have most power with the groups being equal. The power depends on the
average of the reciprocals of the Ns, not on the average of the Ns.
More generally, consider that you get different amounts when you
average different things. In the classic, race car example:
"To qualify for the next-day trials, suppose the car is supposed to
average 60 mph for two laps. If it averages only 30 mph for the first
lap, how fast does it need to go for the second lap?"
- You can't average "mph" when the necessary unit is Hours per mile.
When you have a Mean, increasing its N gives it a decreased error (or
an increased Precision): which is indexed by 1/N. Consider that you
are looking at the average of errors, and not an average of N.
- Sorry, that does not sound as useful as I had hoped it would....
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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