Claire Corlett

Fish Food, Fish Tanks, and More
Association between two variables Fisher’s exact test

Association between two variables Fisher’s exact test


So in this last section for
this last lesson, I want to discuss Fisher’s exact test. Now look at this little example we have. We have patients who took a placebo drug,
and patients who took a test drug. And we have patients who improved, and
patients whose disease remain static. So five patients improved,
three patients remained static, and four patients each took the placebo or
the test drugs, quite small values there. Now remember I said the Chi-square
test statistic only follows the Chi-square distribution if
the expected values are quite large. And there’s actually this old
rule called Cochran’s rule. And it says if you look
at the expected table, that more than 80% of those
values in each of those cells, have got to be larger than five, and they
definitely all have to be larger than one. So, if there isn’t that rule of thumb,
then you really can’t expect the Chi-square test statistic,
your sample statistic. You will need to follow
Chi-square distribution. If that is so you’ve got a few choices. Number one is, we do the study. Look at the study and
get the numbers larger. The other thing that you could also do,
is combine columns and rows. So, you might have a contingency
table where there are many rows and many columns, and
you could combine some of those values. Add some of them up. It’ll make those tables smaller, but at
least you can follow Cochran’s rule then. That would state that all of the expected
values got to be larger than one, and at least 80% of them larger than five. Now there’s a lot of mathematics and
statistics taught around the two, and isn’t really so, but
it’s probably safe to follow. So if we looked at the expected
values table from our example here, you see that at least all of
the values are larger than one, but certainly none of them
are larger than five. So definitely not more than 80% of
them are larger than than five. So in this instance we
can combine all of them, we can combine some of them at least
to get to those kind of values. So we’ve got to move over
to Fisher’s exact test. And what Fisher’s exact test just asks,
how many combinations can you make, how many randomizations would give
you those same column and row totals. And it really uses factorials and it will give you a p-value
that is much more appropriate than you would have gotten under the same
circumstances using a Chi-square test. Only thing to remember though
Fisher’s exact T-test, it’s going to give you a one-tail p-value,
and there isn’t really consensus as to
how to make this a two-tail test. Most of the time you can just
multiply that by two and that would be acceptable though.

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