using Fishers Exact with 7 Race Categories?

[Ellen Kiley]

So when using Fisher's exact to tabulate association between Race and Screening I got an error message saying "exceeded memory limits" when it gets to the final enumeration of 'sample-space combinations' and in the help it says to try using exact(2), which I did and got the same error message. Any ideas?

tab RaceEthnicityCoding ScreeningDone_Dummy, chi column exact(2)

+-------------------+
| Key |
|-------------------|
| frequency |
| column percentage |
+-------------------+

Enumerating sample-space combinations:
stage 7: enumerations = 1
stage 6: enumerations = 11
stage 5: enumerations = 321
stage 4: enumerations = 9730
stage 3: enumerations = 257651
stage 2: exceeding 1x10^6 enumerations
exceeded memory limits using exact(2); try again with larger #; see help tabulate for details

Race + |
Ethnicity | Screening Done_Dummy
Coding | 0 1 | Total
-----------+----------------------+----------
1 | 36 44 | 80
| 11.01 8.10 | 9.20
-----------+----------------------+----------
2 | 19 38 | 57
| 5.81 7.00 | 6.55
-----------+----------------------+----------
3 | 17 18 | 35
| 5.20 3.31 | 4.02
-----------+----------------------+----------
4 | 131 300 | 431
| 40.06 55.25 | 49.54
-----------+----------------------+----------
5 | 5 5 | 10
| 1.53 0.92 | 1.15
-----------+----------------------+----------
6 | 76 116 | 192
| 23.24 21.36 | 22.07
-----------+----------------------+----------
7 | 43 22 | 65
| 13.15 4.05 | 7.47
-----------+----------------------+----------
Total | 327 543 | 870
| 100.00 100.00 | 100.00

Pearson chi2(6) = 37.2129 Pr = 0.000
r(910);

[Nick Cox]

I doubt you're missing much -- except a different very small P-value.

The chi-square test is best taken forward to look at the pattern of discrepancies. Here's tabchii from tab_chi on SSC with extra Pearson residuals, namely (observed MINUS expected) / sqrt(expected). First off, the P-values are of the order of 1 in a million and so clear-cut. I would bet that the Fisher test wouldn't contradict that. Second, rows 4 and 7 are those most out of line with a null.

.

 tabchii 36 44 \ 19 38 \ 17 18 \ 131 300 \ 5 5 \ 76 116 \ 43 22, pearson

          observed frequency
          expected frequency
          Pearson residual

----------------------------
          |       col      
      row |       1        2
----------+-----------------
        1 |      36       44
          |  30.069   49.931
          |   1.082   -0.839
          |
        2 |      19       38
          |  21.424   35.576
          |  -0.524    0.406
          |
        3 |      17       18
          |  13.155   21.845
          |   1.060   -0.823
          |
        4 |     131      300
          | 161.997  269.003
          |  -2.435    1.890
          |
        5 |       5        5
          |   3.759    6.241
          |   0.640   -0.497
          |
        6 |      76      116
          |  72.166  119.834
          |   0.451   -0.350
          |
        7 |      43       22
          |  24.431   40.569
          |   3.757   -2.915
----------------------------

1 cell with expected frequency < 5

         Pearson chi2(6) =  37.2129   Pr = 0.000
likelihood-ratio chi2(6) =  36.4749   Pr = 0.000

. ret li

scalars:
                  r(N) =  870
                  r(r) =  7
                  r(c) =  2
               r(chi2) =  37.21292707219945
                  r(p) =  1.60034046607e-06
            r(chi2_lr) =  36.4749305559922
               r(p_lr) =  2.22847158301e-06

[Ellen Kiley]

Thanks. I"m doing this for a med student who has to present the data at a conference this weekend and I can tell her not to worry about it but I just want to be able to explain to her what is happening and what to say if anyone asks her about it. Should she just report the p val of .000 for fishers exact and leave it at that? I don't want anyone to get called out for an error.

[Nick Cox]

You don't have a P-value for FIsher's exact test. At most you have my guess that it would be very small.

I'd never report P-values of 0,000 because they are all too likely to be misunderstood. I would report the attained value for chi-square P-value, but using 3 or 4 significant figures. You could say P < 0.0005.

It should be much more interesting to comment on why there is an apparent departure from null expectation and how far it is clinically interesting.

PS Not a medic. Not a medical statistician.

[Nick Cox]

Ellen Kiley posted this in another thread

Or I can just use Pearson's (which runs without error) because while 2 cells have only 5 observations, only 1 of the expected has <5 and that is way < 20%?

That's a rather ancient rule of thumb (Cochran 1952???). I tend to go with a simpler rule, which can be found in the work of Harold Jeffreys and more recently of Stephen Fienberg, which is to worry only if expected frequencies fall below 1.