From: nichols@spss.com (David Nichols)
Newsgroups: bit.listserv.stat-l
Subject: Re: Wanted: Rank test
Date: 24 Nov 92 01:15:03 GMT
Organization: SPSS Inc.

In article <STAT-L%92112311112401@VM1.MCGILL.CA> Walt Pirie <WLTPIRIE@VTVM1.BITNET> writes:
>For the problem below, two ideas come to mind. One is Kendall's Test of
>Concordance. Some Nonparametric books include it, or look in Kendall's
>Rank Correlation Book. The other is the General Linear Models by Ranks
>procedure by Hettmansperger and McKean, but I don't know if there is
>a general software package for that. It's much too complex to do by hand.

I don't think that Kendall's coefficient of concordance addresses the
question asked here by Gene Glass. He wants to know (on my interpretation)
if the men and women rank things differently. The Kendall coefficient of
concordance will test whether the rankings of all raters, male or female,
are unrelated. I just looked through Kendall's book, and I don't see any
test in there to address this question. He makes reference near the end
to several people who have developed tests for this situation in which
multiple ranks are generated by raters forming groups, but does not
discuss any such test in the book (unless I missed it).

>    I can't believe it! I'm too old for this. I had a student gather a
> bit of data thinking that when the time came I would just pick up
> Siegel or some other hoary text and look up the proper significance
> test. Now I can't find any test that addresses the problem.
>
>   A group of 5 men ranks four things; and a group of five women do also:
>                  Thing1  Thing2  Thing3  Thing4
>       Man 1 :      4        2      1       3
>       Man 2 :      4        3      2       1
>        .
>        .
>        .
>     Woman 1 :      3        2      4       1
>     Woman 2 :      3        4      1       2
>        .
>        .
>      etc.
>
>      Now, I'm not obsessive about being fooled by chance, but I would
>  like to know whether the disparity in the rankings between the men and women
>  is of suffucient size that it is unlikely to have arisen solely from the
>  chance selection of these two samples from populations in which men and
>  women rank the four things similarly (or identically or something).

If there were no structure on the raters (no gender/sex designation),
Kendall's coefficient of concordance could be used to test the null
hypothesis that the rankings are unrelated. Friedman's test could also
be used to test the null hypothesis that Thing1 to Thing4 all have the
same ranking in a population of interest. But as far as I can tell,
neither of these is really what is wanted here.

SPSS basically has Siegel's set of nonparametrics in our package. We don't
have anything that would address this question in the manner posed (at
least as I read it). Unless I'm misinterpreting the question, this is
somewhat analogous to a repeated measures ANOVA with two groups, except
that instead of having means of four correlated variables to compare,
we have four ranks. The question of interest here would seem to be the
status of what would commonly be called the interaction term; that is,
is there a difference in the ranking orders between men and women (the
standard group term here wouldn't come into play, because the ranks
sum to 10 for each rater). I've not seen a test for this, though I
would bet that one must exist. 

--
 David Nichols        Senior Statistical Support Specialist         SPSS, Inc.
 Phone: (312) 329-3684     Internet:  nichols@spss.com     Fax: (312) 329-3657
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 Any correlation between my views and those of SPSS is strictly due to chance.