Question 4: Which method would you choose to test the null hypothesis that observed eye colour in not related to sex?
The chi-squared test for a contingency table should only be used if the sample is large enough. The usual criterion is that at least 80% of expected frequencies are greater than five and all are greater than one.
The expected frequencies are:
| Eye colour | Sex | Total | |
|---|---|---|---|
| female | male | ||
| black | 6.5 | 3.5 | 10 |
| brown | 51.4 | 27.6 | 79 |
| blue | 28.6 | 15.4 | 44 |
| grey | 7.2 | 3.8 | 11 |
| hazel | 9.1 | 4.9 | 14 |
| green | 13.0 | 7.0 | 20 |
| other | 3.3 | 1.7 | 5 |
| Total | 119 | 64 | 183 |
There are 14 expected frequencies, of which 9 are greater than five. This is 64%, less than the 80% we need, so the chi-squared test for a contingency table will not be valid.
We must either combine rows to increase the expected frequencies, which would change the null hypothesis, or use Fisher's exact test.
Fisher's exact test gives P = 0.309.
This calculation took 55 seconds in Stata running on a Pentium five PC in Windows XP.
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Last updated: 2 March, 2009.