Re: How to test means when there's no variance?
- From: tim_witort@xxxxxxxxxxx (Tim Witort)
- Date: Mon, 05 Mar 2007 11:18:43 -0600
Richard Ulrich seemed to utter in news:jo7iu2pig4tn4u483m89cvaufph3qeev9h@
4ax.com:
On Thu, 01 Mar 2007 23:10:03 -0500, Richard Ulrich
<Rich.Ulrich@xxxxxxxxxxx> wrote:
On Thu, 01 Mar 2007 16:48:14 -0600, tim_witort@xxxxxxxxxxx (Tim
Witort) wrote:
I have an application that compares the mean pay of men and[ snip, rest]
women using a T-test. The goal being to determine if the mean
pay of men is greater than the mean pay of women at a two standard
deviation confidence level. This has worked well for years, but
I came across an odd sample of pays where all of the men
were paid one salary and all of the women were paid another.
As a result, the variance in both samples was zero. This,
in turn gives me a divide by zero when trying to compute
the t-stat.
I've looked through a couple of statistics books for guidance
on how two samples can be compared when there is no variance,
but none of the books address this case.
Speaking somewhat generally -
If the Universe of scores only contains two values, then
you have nothing more available than a sign test.
Uh-oh. Sign test does not fit what I had in mind.
The sign test assumes p= 0.50. The proportion is 0.50 only
if there are equal numbers of men and women (or whatever the
two samples). It could still a binomial test, but with unequal
proportions.
If these numbers are two groups within a larger universe,
such as a dozen sets of pairs of groups being compared for
salary, then it might be more sensible to do something like this -
Pool the data (at least, the ones that are reasonably in the same
range... if you don't want to argue about other differences in
standard deviations); get the common variance; and test each
pair as a contrast using the common variance.
From later posts by the OP -- It sounds as if each comparison
is presently being done by t-tests on single classifications.
Well, that is (arguably) not as robust as using pooled variances.
The present system might face strong *legal* challenge, if all
the Ns are too small to offer any power, or if the variances are
too large.
The company probably should bring in a statistician who has
argued discrimination cases, and find out what is *acceptable*
for small Ns, for zero variance, and so on.
Not bad advice. We do have access to a statistician in this
area. Maybe I will run this past him. Thanks.
-- TRW
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- From: Tim Witort
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