On 28-Jul-99 Jenny Keating wrote:
> Can anyone help with a reference +/ or formula for determining power
> when using a MannWhitney U test. I have been told to use the power
> calculations for the parametric equivalent and add 10%, but would
> prefer the formula for direct calculation
Strictly speaking there's no such thing (at any rate in a form that would
be useful to you).
Since the Mann-Whitney is a non-parametric (more exactly, distribution-
independent test, i.e. the SIZE of the test is guaranteed to be exact
under the Null Hypothesis that both samples are from the same
distribution, whatever that distribution may be), and since also the
concept of Power embodies a specific measure of difference between
the distribution of one sample and the distribution of the other,
you can only formulate a power calculation once you have settled what
this difference is to be.
Unfortunately, this is very slippery. Suppose, for instance, that
the alternative hyppothesis is that Sample II is distributed like
Sample I but shifted by a given amount. Then the power of the M-W
test depends on what the distribution of Sample I specifically is,
even though the size of the test is independent of what the
distribution is. In fact, any exact power calculation depends on an
assumption about what the distribution is.
If you're going to assume that, you might as well use the appropriate
parametric (i.e. distribution-specific) test in the first place.
However, approximate power calculations can depend on an assumption that
[words to the effect that] "the distribution of the data are unlikely to
be sufficiently non-Normal to grossly affect the power of the test".
Whether the recommendation you have been given is a good one is not clear
to me: maybe others can comment on this.
Best wishes,
Ted.
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E-Mail: (Ted Harding) <[log in to unmask]>
Date: 29-Jul-99 Time: 09:45:53
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