http://spssx-discussion.165.s1.nabble.com/Fisher-Freeman-Halton-Exact-Test-or-Jonckheere-Terpstra-test-which-is-the-most-appropriate-tp5731524p5731537.html
Well, my default recommendation, given nothing too odd in the distributions,
was to use an ordinary Pearson r on the 1-5 scores, not on the rank-transformed
scores.
The Spearman rho is exactly the Pearson r, computed on appropriately
transformed scores (use the average rank for each group). The question of
transformation by rank, as I see it, is whether the transformed scores have
"better intervals" than the raw scores. The quality of the intervals is usually
a subjective matter (unless there is test-retest data on hand).
ON RANK-TRANSFORMATIONs
From the URl cited, I get marginal counts for several tables, Ns of 80, 40, and 80:
a. (1, 17, 20, 18, 2); (1, 9, 11, 18, 1); and (14, 46, 17, 3).
Average Ranks, cumulating left to right:
(2, 12, 30.5, 49.5, 59.5); (1, 6, 16, 35, 40); and (7.5, 37.5, 69, 79), respectively.
b. Intervals between adjacent categories:
(10, 18.5, 19, 10); (5, 10, 9, 5); and (30, 31.5, 10). [Or: 1221, 1221, 331]
Re-scored to simpler integers with highly-similar relative spacing:
c. ( 0, 1, 3, 5, 6); ( 0, 1, 3, 5, 6)<same>; and (1, 4, 7, 8).
Re-scored to intervals that are mostly integer:
d. (0.3, 1, 2, 3, 3.7); ( 0.3, 1, 2, 3, 3.7 ); and (0, 1, 2, 2.3).
The question I ask for considering the rank-transform is whether the scoring
in (c) or (d), which are equivalent to each other, is to be preferred on logical
grounds to the scores of 1-5 (or 0-4); or 1-4 (or 0-3). Lines (c) and (d) provide
less importance to the extreme scores when you conduct an ANOVA or correlation:
Is that desirable? On occasion, I say "yes" -- when the extremes are of doubtful validity.
ON J-T TEST, and other rank tests.
On the J-T, I read whatever SPSS has in its manual and I read another description on-line.
J-T described an approximate test for large samples, using estimates for variance. These
rank-test variance solutions were shown to be problematic by Conover in the 1980s. He
and his co-author showed that performing ANOVA on the rank-transformed scores is always
a very close approximation, and often is an improvement, over the test-size achieved by
the adaptions that are made for "ties" -- where a tie is what you have for two scores that
are identical. For small enough samples, of course, there originally were tables for p-values.
Computers can do better, if the problem is important enough that someone programs for it.
The worked-example I found used a nearly-continuous outcome and included formulas
(including, accounting somewhat for ties); I assumed that the there are the usual problems
with ties.
Rank tests were initially admired for their performance in continuous-scored samples;
how they do with ties is less admirable.
ON THE POWER OF J x K CONTINGENCY TESTS or Exact solutions.
Mantel flew in once a week to teach one of the stat courses that I took in grad school.
He passed out reprints of maybe 150 of his papers, and at least 100 of them were uses
of "tests using a 1 d.f. chi-squared"; his point, over and over, was that you have most
power when one test is carried by 1 d.f. If you are using 2 d.f. for your test (or more),
you are /almost always/ testing more than one hypothesis, at least implicitly.
--
Rich Ulrich
> Date: Mon, 15 Feb 2016 18:56:57 -0700
> From:
[hidden email]> Subject: Re: Fisher-Freeman-Halton Exact Test or Jonckheere–Terpstra test - which is the most appropriate?
> To:
[hidden email]>
> Hi Rich and Raimundas,
>
> Thanks for the comments.
>
> The total sample size for the two tests is 40 (tail vs wing) and 80 (tail vs
> foreneck). The marginal distributions for each test are shown in the graphs
> below.
> <http://spssx-discussion.1045642.n5.nabble.com/file/n5731529/SPSS_Discussion.png>
> These distributions are bell-shaped for Test 1, and unimodal with a positive
> skew for Test 2. So you've convinced me that it is more appropriate to run a
> rank correlation on the data, which is also more intuitive (i.e. a
> correlation).
>
> WRT to the Jonckheeere-Terpstra test, Rich you wrote "The JT test does not
> handle ties well ... I have not used it, but quick reading suggests that
> having a continuous outcome (and small N) are two of the expectations." I
> would like to read the text you refer to (this test may come in useful in
> the future, so I'm keen to learn more). I have not read anything about
> continuous outcomes, indeed the first reading I did about the JT test refers
> to its use in doubly-ordered contingency tables - i.e. ordinal dependent &
> ordinal independent
> (http://www.sussex.ac.uk/its/pdfs/SPSS_Exact_Tests_21.pdf). I'm also unsure
> what you mean by "ties".
>
> Thanks also for the advice regarding the lack of power of the FFH Exact Test
> through it ignoring the ordinal nature of the variables, something I didn't
> appreciate.
>
> Cheers,
> Dean
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