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StatXact Example 9
Did Entrance Exam for Firefighters Discriminate Against Minorities?
Pearson Chi-Squared Test Says NO! But Exact Test Says YES!
Suppose you had to testify in a minority discrimination suit with the following data from an entrance exam for firefighters in a small township:
| |
Results of Entrance Exam |
|
Racial Group |
Pass |
No Show |
Fail |
Totals |
| White |
5 |
0 |
0 |
5 |
| African American |
2 |
1 |
2 |
5 |
| Asian American |
2 |
0 |
3 |
5 |
| Hispanic |
0 |
1 |
4 |
5 |
| TOTALS |
9 |
2 |
9 |
20 |
Do the data suggest that entrance exam results are related to race? The StatXact output is shown below:
 
The Pearson chi-square statistic is 11.56, which, when referred to a chi-square distribution with 6 degrees of freedom, yields an asymptotic p-value of 0.0727, failing to confirm discrimination. But with data this sparse can you really trust the asymptotic p-value? Would you be prepared to defend that p-value in court?
Fortunately you don’t need to. StatXact tells you that the exact p-value of the Pearson chi-square statistic is 0.0398. You may thus feel secure that your data do indeed yield a statistically significant difference in pass rates among the four racial groups, notwithstanding the small sample size.
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