The Problem

The percentage of Missouri citizens who identified themselves as African-American in the US 2000 census was 12%, while a similar percentage of inmates in the state’s correctional facilities was 50%. Of the individuals who are incarcerated, approximately 50% are there because of drug offenses. To explain the racial disparity between the percentage incarcerated and the general population, two different hypotheses have been put forth.

The first is that the percentage of African-Americans in the state’s prison system is simply reflective of the crime rate. African-Americans commit 50% of the crimes in the state of Missouri, so one would expect that 50% of prison population would be African-American.

The second hypothesis is that the crime rate for African-Americans and non African-Americans is approximately equal and that the difference in prison percentages relative to the general population is due to a differing stop and search rate. That is, the police officer on the street is more likely to stop and search an African-American because he or she expects to find some sort of criminal activity. Because African-Americans are more carefully scrutinized, more criminal activity is discovered and more are convicted. This in turn leads the police officer on the street to even more strongly believe that African-Americans commit more crimes and even more carefully scrutinize their activity. The different incarceration rate thus becomes a self-fulfilling prophecy.

In order to differentiate between these two hypotheses, the base rate of criminal activity by different racial groups must be estimated independently of the number of individuals who are actually convicted of a crime. This becomes difficult because by the very nature of the activity, it is usually not directly observable and seldom admitted.

The Legislative Solution

In an attempt to assess the dimensions of the problem, the Missouri Legislature passed a racial profiling statute (Chapter 590 in the Missouri Revised Statutes) in 2000 requiring peace officers to record age, gender, race, and other information each time he or she stops a driver of a motor vehicle. The state attorney general disseminates this information as a report for each city in the state.

The same statute (Section 590.650.5) also requires each law enforcement agency to “(a) Determine whether any peace officer of the law enforcement agency have a pattern of stopping members of minority groups for violations of vehicle laws in a number disproportionate to the population of minority groups residing or traveling within the jurisdiction of the law enforcement agency; and ” “(b) If the review reveals a pattern, require an investigation to determine whether any peace officers of the law enforcement agency routinely stop members of minority groups for violations of vehicle laws as a pretext for investigating other violations of criminal law; “ “(c) Provides for appropriate counseling and training of any peace officer found to have engaged in race-based traffic stops within ninety days of the review”.

The Statistical Problem

If the rate of minority stops and searches is examined for each peace officer and action taken on their basis, then statistical issues become important. For example, suppose the proportion of a minority in a city is .10 (10%). Should every peace officer who stops 100 motorists stop exactly 10 members of the minority population? From a statistical perspective the answer is “no”, because by chance some might stop fewer than 10 and some might stop more. Is 12 too many? How about 15? At what point is the number of minority stops unlikely? In a related issue, is the officer who stops 2 minorities out of 10 as likely to be racially profiling as the officer who stops 20 out of 100 or 200 out of 1000? Again the answer is “no”.

Fortunately a statistical model in the form of the binomial distribution can assist in answering the above questions. Given the proportion of minorities in a given population and the number of traffic stops, the model can provide the theoretical probabilities for each number of minority stops. For example, the following distribution illustrates the distribution of stops for a minority proportion of .10 and 100 total traffic stops.

The height of each line indicates the relative likelihood of that number. For example, both 12 or 15 minority stops are fairly likely, while 17 or more are fairly unlikely. The sum of the probabilities for all numbers of minority stops must equal one.

A similar analysis of a minority proportion of .10 and 10 total traffic stops shows that 2 minority stops are fairly likely, given that the officer is not racially profiling.

The Binomial Calculator

The calculator provided as part of this web page will automatically calculate the probability of making a given number of minority traffic stops out of a given number of total stops for a given minority population proportion. To use the binomial calculator, simply enter the minority proportion, number of minority stops, and total number of stops in the appropriate text boxes, followed by clicking on the “->” button. The likelihood of that number of minority stops or greater will then be displayed in the “likelihood” box as well as a visual representation of the distribution. The following illustrates the results of entering a proportion of “.10” with 7 minority stops out of 50 total stops. The likelihood of 7 or more minority stops out of 50 given a minority ratio of .1 is .2298.

The likelihood may be interpreted as the probability of stopping 7 minorities out of 50 total stops given chance alone (no racial profiling) was operating.

Issues

Two issues are present in the use of the binomial calculator to identify peace officers who may be racially profiling. The first is the point at which the line is drawn between chance and real effects and the second is the selection of the target proportion.

The probability of identifying a peace officer as a “profiler” when if fact chance alone was responsible for the number of minority stops is called the significance level or alpha. In the social sciences, a de facto standard of .05 is widely accepted as the point at which the line is drawn between real effects and chance. Using a value of .05 would generally shield the decision-maker from criticism and is recommended. It means that over the long run 5 out of every 100 peace officers would be incorrectly labeled as profilers when in fact they simply had the misfortune of stopping too many minorities. Setting the cutoff value of alpha lower then .05 would result in fewer errors of this type. Setting a very low value for alpha does not come without a cost, however, as it would be more likely that true profilers would be missed.

The second issue is the correct value for the target proportion or base rate. The state attorney general, in setting the target proportion differently for each district or city, has acknowledged that different base rates are appropriate for each area. In a similar vein, it would seem unreasonable to use the same base rate for all peace officers. An officer patrolling a mostly white part of the city would be expected to have fewer minority stops than an officer patrolling a mostly non-white area. The difficulty is finding the appropriate proportion given that each peace officer patrols different parts of the city during the data collection period is obvious.

In arguing that the proportion of minority traffic stops should approximate the proportion of the minority population, one must make the assumption that minority and non-minorities commit the traffic offenses at the same rate. The reasonableness of this assumption must be assessed independent of a political agenda or preformed bias. I have attempted to obtain statistics relating to the proportion of individuals of each racial group who fail the written part of the driver’s license exam without success as information about race is not collected at that point.

As a statistician I step back in wonder at the hypocrisy in the ready acceptance of different proportions of traffic stops for males (.66) and females (.34) as attributable to different base rates of traffic and criminal offences, but the reluctance to do so with minority populations.