Fisher's exact test

Question

I am an archaeologist (PhD candidate) that has recently learned how to perform chi squared tests. However, I am told that for the table below, I would need a Fisher's exact test since some of the bins have <5 in them.

I know that this test is usually for 2x2 tables but that it's possible to use it for larger tables too and I have found a number of sites that allow you to enter the data and give you a P value for 2x4 tables such as mine.

However, I know that in citing the results of a chi-squared test, I must quote the test statistic and the df and presume that I would have to do so for this test also.

I know how to work out the df for chi-squared tests (Row-1)*(Columns-1) but wondered if it was the same foe the Fisher's exact test.

As for the test statistic, I would have no idea where to start. Any help would be much appreciated.

Apologies if this is an old question. I think another person may have asked about this already, although the terminology used in both the question and the answer made it hard to be certain!

Grade 1:    0       2    |   2  
Grade 2:    5      58    |  63  
Grade 3:    4       3    |   7  
Grade 4:    4       3    |   7  
           --------------+----- 
TOTAL:     13      66    |  79  

Answer 1

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