Re: Nonparametric tests with unequal group sizes

From: Ray Koopman (koopman_at_sfu.ca)
Date: 07/16/04

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    Lance Hoffmeyer <lance-news@augustmail.com> wrote in message
    news:<Y8ydnVTIE5SdfGvd4p2dnA@august.net>...
    > I have 2 groups with very unequal base sizes. Group1=15, Group2=250.
    > I was thinking of using a Mann-Whitney or Kruskal-Wallis non-parametric
    > test.
    >
    > How do the unequal group sizes would affect these tests, if at all?
    >
    > Any suggestions?
      
    Contrary to popular opinion, the Mann-Whitney test (which is the same
    as the two-group Kruskal-Wallis) resembles the usual t test in the way
    it becomes increasingly sensitive to the ordinal equivalent of hetero-
    scedasticity as the sample sizes become more different. With sample
    sizes such as yours, I would use the M-W only if I were certain that
    the only difference between the groups was the ordinal equivalent of
    a simple shift in location -- which translates to "almost never".
      
    The current best ordinal comparison of two independent groups is given by
    eq 5.12, p 140, in Norm Cliff's 1996 book Ordinal Methods for Behavioral
    Data Analysis. For a corroborating opinion, see the comments re FPC3 on p
    500 of H.Delaney & A.Vargha, Comparing several robust tests of stochastic
    equality with ordinally scaled variables and small to moderate sized
    samples, Psychological Methods, 7 (2002), 485-503.

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