Neither test appears to be appropriate. The FFH Exact Test does not consider
that either variable is ordinal. 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.
What is your total N? How even, and how regular, are your marginal distributions?
If the distributions are either fairly uniform or bell-shaped, I would have no hesitation
of using the Pearson r as my main test.
Other comments on your post: The problems with (Expectations < 5) for contingency
chi-squared owes to the generation of overly-BIG values when Expectations are too small,
thus providing a misleadingly large total. If your overall contingency chi-squared is small,
you could accept that there is No Effect, if you were doing a proper test of your hypothesis.
However, this is a very weak test of your hypothesis because it does not account for ordering.
Is the X2 test value large enough that a one d.f. X2 test would be significant? In that case, a
test that accounts for ordering has a chance of being significant. - If the overall X2 is /really/
small, like, less that 3.83 needed for a 5% test, you could, indeed, fairly conclude that "There
is nothing here," regardless of the number of cells with tiny Expectations.
An Exact Test derived from the FET is not harmed by observed zeroes; it lacks power for you
because of it ignores the ordering (as I mentioned already). Generally, one should keep in
mind that "Exact testing" for r x k tables is not a magic bullet, and not a unique proposition --
other methods (X2 contribution, instead of smallest likelihood used by Freeman-Halton) can
give other results, especially when there are highly skewed distributions.
--
Rich Ulrich
> Date: Sun, 14 Feb 2016 23:50:21 -0700
> From:
[hidden email]> Subject: Fisher-Freeman-Halton Exact Test or Jonckheere–Terpstra test - which is the most appropriate?
> To:
[hidden email]>
> Hi,
>
> *Analysis question*: I am seeking to determine whether there is a
> relationship between the extent of pigment in tail feathers of a particular
> bird species and the extent of pigment on 1) the foreneck (5 x 5 table, n =
> 40) and 2) the wings (4 x 5 table, n = 80). Pigment was scored on an ordinal
> scale from least to most pigment for each body region (5 levels for tail and
> foreneck, 4 levels for wing). Because of the small sample size. A chi-square
> contingency table is inappropriate because of the high proportion of
> expected values <5.
>
> *Option 1 - Fisher-Freeman-Halton Exact Test*: Both contingency tables have
> a high number of zero cells: 12 in the 5 x 5 table, 6 in the 4 x 5 table.
> /Is this a problem for this test?/
>
> *Option 2 - Jonckheere–Terpstra test*: At first glance, this test is
> appropriate since both my variables are ordinal variables and I expect a
> positive relationship (i.e. birds with more pigment on the tail are
> predicted to have more pigment on the foreneck or wing). However, I am not
> postulating a causal relationship between variables (i.e. pigment on tail vs
> pigment on foreneck/wing). /Is this test appropriate for analyses where the
> independent and dependent variables are interchangeable?/
>
> Any advice as to which option is the most suitable, and any other issues
> that I have not identified, is most welcome!
>
> Thanks,
> Dean
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