Solved – Effect size for Fisher’s exact test

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Does anyone know a way to calculate the effect size of a Fisher's exact test? Does that even make sense?

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Fisher's exact test is usually used for 2x2 tables. In such a table, you have a few choices for effect size.

One is the odds ratio, which can be calculated by hand pretty easily. If the four cells are $A_{11} A_{12} A_{21} $ and $A_{22}$ then the OR is $A_{11}*A_{22}/A_{21}*A_{12}$.

Another is the difference in proportions in the two rows or two columns: $A_{22}/(A_{12}+A_{22}) -A_{21}/(A_{21}+A_{11})$ or vice versa.

There are others; see any good book on categorical data analysis, such as Agresti's Categorical Data Analysis.

If you have a table that is bigger than 2 x 2, things get more complex, and it depends on whether either row or column is ordinal and on what you are interested in, as well.

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Solved – Fisher’s exact test

The massive 58 amid much lower frequencies signals that any test is just quantifying a major failure of independence. I did this in Stata. The command ret li (short for return list) obliges Stata to show results as exactly as it knows them, but both tests yield P-values that are 0.000 to 3 d.p. It is right to be a little cautious about low expected values (for row 1 here in particular) but the test results are overwhelming.

. tabi 0  2 \ 5 58 \ 4 3 \ 4 3 

            |          col
        row |         1          2 |     Total
 -----------+----------------------+----------
          1 |         0          2 |         2 
          2 |         5         58 |        63 
          3 |         4          3 |         7 
          4 |         4          3 |         7 
 -----------+----------------------+----------
      Total |        13         66 |        79 

      Pearson chi2(3) =  20.5779   Pr = 0.000

. ret li 

scalars:
              r(p) =  .0001288081813192
           r(chi2) =  20.57794057794058
              r(c) =  2
              r(r) =  4
              r(N) =  79

. tabi 0  2 \ 5 58 \ 4 3 \ 4 3 , exact

Enumerating sample-space combinations:
stage 4:  enumerations = 1
stage 3:  enumerations = 3
stage 2:  enumerations = 17
stage 1:  enumerations = 0

             |          col
         row |         1          2 |     Total
  -----------+----------------------+----------
           1 |         0          2 |         2 
           2 |         5         58 |        63 
           3 |         4          3 |         7 
           4 |         4          3 |         7 
  -----------+----------------------+----------
       Total |        13         66 |        79 

       Fisher's exact =                 0.000

. ret li 

scalars:
        r(p_exact) =  .0003124258226793
              r(c) =  2
              r(r) =  4
              r(N) =  79

SPSS – Understanding Fisher’s Exact Test Value

The test statistic is, as you say, like the chi-square test statistic (or any other). Although not everyone reports it, I think you should. It is the result of running the test; the calculation (on larger than 2x2 tables) is pretty involved but that is what computers are for.

I would not report the chi-square statistic, unless you correct somehow for small sample sizes (e.g. by simulation). I don't know what options SPSS offers, but Fisher's is not the only option.

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Solved – Fisher’s exact test

SPSS – Understanding Fisher’s Exact Test Value

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