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Let's say I have 4 plants and I measure something under 2 conditions. For example:

The entries in the table show how many times I saw something under condition (C1 or C2) for plant (P1, P2, P3 or P4). 

     P1,  P2,  P3,  P4 
C1    0   20    0   19 
C2  100   80  180  150

Now I would like to answer the question "what is the probability that these 39 times of seeing something is unevenly distributed between these 4 plants"?

I am much interested in observation like this, rather than, say:

     P1,  P2,  P3,  P4 
C1   25   20   15   19 
C2  100   80  180  150

Is it right to use Fisher's exact test for this? I just extended the question from a 2*2 table to 2*4.

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  • $\begingroup$ No. Fisher wouldn't answer your question. And I am not sure you asked what your real question is. Further reading: en.wikipedia.org/wiki/Fisher's_exact_test $\endgroup$
    – Tal Galili
    Aug 8, 2011 at 13:06
  • $\begingroup$ I already read that and framed the question from that. Maybe it goes something like this. For example 1, "Knowing that 39 out of 549 times I see something under C1, and that 100, 100, 180 and 169 of them are from P1, P2, P3 and P4 respectively, What is the probability that these 39 something are so unevenly distributed between the 4 plants? And this is what I desire. I agree the second table is a bit misleading. It might or might not be significant (depending on the parameters that fisher's exact test computes). $\endgroup$
    – Arun
    Aug 8, 2011 at 13:25
  • $\begingroup$ Or in other words, if I were to find 39 something under C1, what is the probability that there are none of them from P1 and P3 and 20 and 19 of them from P2 and P4? This I suppose would be far from random distribution and hence a very significant p-value. Did I misunderstand something here? $\endgroup$
    – Arun
    Aug 8, 2011 at 13:31

1 Answer 1

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There's no reason you can't apply Fisher's exact test to this problem. Or you could use a standard chi-squared test for independence, as the expected cell counts aren't that small.

Neither approach will answer the question "what is the probability that these 39 times of seeing something is unevenly distributed between these 4 plants" though. That would require a fully Bayesian analysis.

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    $\begingroup$ Why is a Bayesian analysis called for here? This is phrased as a straightforward probability question. $\endgroup$
    – whuber ♦
    Aug 8, 2011 at 13:32
  • $\begingroup$ onestop, Thanks for your answer, however doesn't fisher's exact test answer the same question for a 2*2 table? or am I wrong even there? From the wiki page, under example, this is the question they ask: "what is the probability that 9 of them would be among the 12 women, and only 1 from among the 12 men"? $\endgroup$
    – Arun
    Aug 8, 2011 at 13:35
  • $\begingroup$ whuber, I thought so as well. $\endgroup$
    – Arun
    Aug 8, 2011 at 13:36
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    $\begingroup$ Arun, my understanding is that Fisher's exact test is not limited to 2x2 tables, even if the original example was of that size. See for instance, C.R. Mehta and N.R. Patel(1986) Algorithm 643. FEXACT: A FORTRAN Subroutine for Fisher's Exact Test on Unordered r x c Contingency Tables, ACM Trans. Math. Soft. vol. 12, p. 154-161. $\endgroup$
    – F. Tusell
    Sep 7, 2011 at 16:38

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