From: WLTPIRIE@VTVM1.BITNET (Walt Pirie)
Newsgroups: bit.listserv.edstat-l
Subject: Nonparametric tests for trend
Date: 4 Nov 92 13:58:17 GMT
Reply-To: Walt Pirie <WLTPIRIE@VTVM1.BITNET>
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU

Tony: I don't know how interested the MUG users' group would be
in your macro, but I wouldn't mind a copy.
As for your question, your options b) & c) are identical, and
a) is very close as far as efficiency is concerned. Here's how I
explain that in class.
The 2 well-known rank tests for ordered alternatives are
Jonckheere in the 1-way layout, and Page in the 2-way. I think J.
derived his as a generalization of the Mann-Whitney, but it can
be shown that it is also your option b), Kendall's test on the
ranks of the data and ranks of the ordered categories. Page, I
believe, actually developed his as the Spearman correlation for
each block between the ranks of the data and the ordered
categories, averaged over the blocks. Whether I'm right about
the origins or not, that's what the two tests are. I look at it
as historical accident that Kendall's test is used in the 1-way,
and Spearman's in the 2-way. Either approach works equally well
for either application, but tables exist for Jonckheere & Page
so that's what is used. As far as effectiveness, the efficiency
(ARE) between the 2 appears always to be very close to 1, so there's
not much to choose between the two.
I hope that helps.
Walt



Can anyone advise me about the relative virtues and drawbacks of the following
ways of testing for a trend (assuming that, for some reason, one is unhappy
about the equal-interval scaling or the Gaussian distribution of the
predicted variable):-

a)  Spearman's Rho: convert scores on the predicted variable to ranks
    and then correlate them with the ranks of values of the predictor
    variable (and if the predictor variable is, in itself, only a nominal-
    scale variable, assign ranks to its categories in terms of the ordered
    predictions its categories make for the predicted variable);

b)  Similarly, Kendall's Tau;

c)  The Jonkheere Test.

I'd be particularly grateful for advice about this in the situation where
the Jonkheere Test would seem a natural choice: i.e., where the predictor
variable has only a few values, e.g., 3 or 4, so that there are very
many ties on the predictor variable.

My motivation for asking is partly that, to meet some particular teaching
needs, I've written a Minitab macro to do the Jonkheere Test.  Now I'm
considering submitting it to the MUG macro library but I'm wondering
in what terms I should recommend it, and whether I was wasting my time!

(If anyone would like a copy of the macro, I'd happily forward a copy to
them.)

Tony Downing
Department of Psychology,
University of Newcastle upon Tyne,
England.

|==================================|============================|
|  Walter R. Pirie                 |                            |
|  Department of Statistics        |                            |
|  Virginia Tech                   |                            |
|  Blacksburg, VA 24061-0439       |                            |
|                                  |                            |
|  Tel. 703-231-5441               |                            |
|  Bitnet WLTPIRIE@VTFVM1          |                            |
|  Telnet WLTPIRIE@VTVM1.CC.VT.EDU |                            |
|                                  |                            |
|  Fax  703-231-3863               |                            |
|==================================|============================|
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU