comment inline
David Winsemius wrote on 24.01.2015 21:08:
On Jan 23, 2015, at 5:54 PM, JohnDee wrote:
Heinz Tuechler wrote
At 07:40 21.06.2009, J Dougherty wrote:
[...]
There are other ways of regarding the FET. Since it is precisely
what it says
- an exact test - you can argue that you should avoid carrying over any
conclusions drawn about the small population the test was applied to and
employing them in a broader context. In so far as the test is concerned,
the
"sample" data and the contingency table it is arrayed in are the entire
universe. In that sense, the FET can't be "conservative" or "liberal."
It
isn't actually a hypothesis test and should not be thought of as one or
used
in the place of one.
JDougherty
Could you give some reference, supporting this, for me, surprising
view? I don't see a necessary connection between an exact test and
the idea that it does not test a hypothesis.
Thanks,
Heinz
Fisher's Exact Test is a nonparametric "test." It tests the distribution in
the contingency table against the total possible arrangements and gives you
the precise likelihood of that many items being arranged in that manner.
That's not the way I understand the construction of the result. The statistic
gives rather the ratio of the number of permutations as extreme or more extreme
(as measured by the odds ratio) while holding the marginals constant which is
then divided by the total number of possible permutations of the data.
No
more and no less. You could argue about the greater population from which
your sample is drawn, but FET makes no assumptions at all about any greater
sample universe.
It is conditional on the margins, so that is the description of the "universe".
Also, since the "population" being used in FET is strictly
limited to the members of the contingency table, the results are a subset of
a finite group of possible results that are relevant to that specific
arrangement of data. You are not "estimating" parameters of a parent
population or making any assumptions about the parent distribution. You can
designate a "p" value such as 0.05 as a level of significance, but there is
no "error" term in the FET result. Fisher stated that the test DOES assume
a null hypothesis of independence to a hypergeometric distribution of the
cell members. But that creates other issues if you are attempting to use
the results in conjunction with assumptions about a broader sample universe
than that in the test. For instance you have to carry the assumption of a
hypergeometric distribution over in to the land of reality your sample is
drawn from and you then have to justify that.
In this respect I agree. A real world situation with a universe of fixed
margins seems unusual to me.
And this is off-topic on Rhelp .....
Sorry for asking a question off-topic more than five years ago. A nice
surprise to get an answer.
Thanks,
Heinz
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David Winsemius
Alameda, CA, USA
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