Question 3: How would you choose between these methods to test the null hypothesis that observed eye colour in not related to sex?
We could always do the Fisher's exact test, whatever the data, provided we had the computing facilities.
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.
For testing, we can drop the 'missing' row from the table. The expected frequencies are then:
| 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 |
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Last updated: 2 March, 2009.