| Population Groups | Expected | Observed frequencies | Observed Percent |
| White (82.5% of pop.) | 75075 | 71,718 | 78.8% |
| Black (6.4%) | 5824 | 11,182 | 12.3% |
| Asian (10.2%) | 9282 | 7,495 | 8.2% |
| Other (0.9%) | 819 | 605 | 0.7% |
| Total | 91,000 | 91,000 | 100% |
Now, are those "expected" numbers significantly different from the Observed
Numbers? To find out, solve the formula for Chi Square from any statistics
book and look the result up in the table of values of the chi square distribution
in the back of the book.... OR... use a handy WEB chi
square calculator at Georgetown
University (or, for expected and observed problems only, not
cross-tabulations, the one at Vassar;
there are others also).
| Expected | Observed | Total | |
|---|---|---|---|
| White | 75075 | 71718 | 146793 |
| Black | 5824 | 11182 | 17006 |
| Asian | 9282 | 7495 | 16777 |
| Other | 819 | 605 | 1424 |
| Total | 91000 | 91000 | 182000 |
Degrees of freedom: 3
Chi-square = 1987.3929347748
p is less than or equal to 0.001.
The distribution is significant.
What is the chi square value? 1987.39
What is the probability of this relationship occurring by chance?less than or equal to 0.001.
Is this finding statistically significant? yes
Would this be considered evidence for or against allegations of racial profiling? This would count as evidence for the allegations of racial profiling. Black motorists are being stopped significantly more frequently than their percentage in the population would suggest. Of course, this evidence is not conclusive. First of all, I made the numbers up! Second, there may be good reasons that the police stop more black motorists, e.g, they may be out more late at night, or speed more, or have more defective tail lights, or whatever). Or it may be that the population statistics we used do not reflect the number of motorists on the roads the San Diego police patrol. And so on. In real cases, all these issues must be addressed. Statistics such as these are routinely used in lawsuits, such as the ones against the New Jersey State Police.