Suppose that a plane has just landed and a flu pandemic may be emerging.  You have the time and resources to check some but not all of the arriving passengers for signs of influenza.  A small fraction of the passengers are arriving from Mexico where the pandemic originated and the others have not been to Mexico.  How do you allocate your searches?

Efficient screening means that the probability of finding an infected passenger should be equalized across the groups that you screen.  And if searches of one group yield a higher infection rate than another then you should allocate your searches to the first group.   Since the passengers arriving from Mexico are much more likely to be infected, you will probably use all of your searches on them.

Even though the passengers from Mexico are being searched disproportionally more often than the others, this is not because you are discriminating against them.  Your motive is simply to use your limited resources most effectively to stop the spread of the virus.

These ideas should be kept in mind when you read articles like this one (via The Browser) which claim that the disproportionate number of searches of black motorists on the highways indicates that the police are racially biased.  The police probably are racists, this would not surprise anybody.  But the fact that they stop and search black motorists more often than whites is not evidence of racism, unless it can be shown that the proportion of stopped black motorists who are found to be committing a crime is smaller than the proportion of stopped white motorists.

In fact, this 2001 paper by Knowles, Persico, and Todd test for this using one particualar data set and find no evidence of bias.  I don’t know where the literature has gone since then, probably there have been other studies with other findings, but its important to know what the right test is.