A Resource for Measuring Disparity

Effective system-wide research and policy interventions require evaluating disparity at each criminal justice point of contact.

What Constitutes a “Good” Metric?

An important factor in measuring disparity is to adjust actual numbers to a baseline population. Without this consideration, over-and under-representation is challenging to study. Presenting our data through percentage shares, ratios, and per capita rates can help us achieve this. We may refer to these as “global indicators” of disparity.

How Common Measures Relate

No disparity exists between a chosen baseline and a current point of contact when:

• A Ratio dividing two percentage shares = 1
• Two percentage shares are equal
• A Relative Rate Index (RRI) = 1
• Two per capita rates that are equal

Percentage Shares

Percentage shares can be useful in measuring disparity between groups. One of its strength is its ease of interpretation. In the next slide, we show a simple example of understanding percentage shares as a way of measuring disparity.

This group is over-represented at this point of contact (Point B).

Point A: Group representation as a share of the general population. Point B: Group representation at a particular criminal justice point of contact.

Current State of Disparity

Placing this in context to current data in Utah on racial and ethnic disparities (and as seen on the next slide), Minority individuals are over-representated in our prison system as seen by their higher share of representation in the prison population versus the general population count (22 vs 36%).¹ In contrast, Whites are under-represented as seen by their lower share of representation at prison in relation to their general population count (78 vs 59%).

Make-up of Utah’s Prison Population

Ratios

Simply put, a ratio can help us express whether there is parity (a 1:1 ratio) or disparity, (a > 1:1 ratio). If a ratio is measured at 2:1, then the group in the numerator is twice as likely as the group represented on the denominator to experience an event. While Ratios only need one number to convey either parity or disparity (rather than two percentage shares), they can be less straight forward to understand.

Ratios

The Relative Rate Index (RRI)

An advantage of the RRI is that it allows researchers to isolate disparity at a particular point of contact relative to the previous transitional point. This is because the baseline population is tied to the previous decision point.

The RRI: An Example

Let’s assume that we have 1,000 Minority individuals and 2,000 White individuals that make up our general population. Then let’s say that 100 are arrested for both groups. This means that 10% of the Minority population is arrested and 5% for the White population. Hence we see that Minorities are arrested at a higher rate than Whites and we see disparity between the general population count and at the point of arrests. If we divide 10 by 5, we will get 2 (our RRI). In other words, in our example, Minorities are twice as likely as Whites to be arrested when compared to their general population count.

The RRI: Using the Prior Decision Point as the Baseline

Then if we want to calculate the RRI between the point of Arrest and a Court referral we can do the following. Following our previous example, let’s assume that 50 individuals from each group get referred to Court, then there is no disparity between the points of arrest and court referral. This is because for both groups, 50% was referred, in other words, the same percent. In contrast, if 70% of individuals were referred for one group and 50% for one, that we see that the first group is being referred at a higher rate and we will see a RRI > 1.

Per Capita Rates

Many analysts use per capita measures to adjust a given number of interest relative to the general population count. This metric is calculated by taking the number of individuals at the point of arrest and divided by the general population for each group. Then this ratio is commonly multiplied by 1,000, 10,000 or 100,000 depending on the original size of the population.

Comparing the RRI and Per Capita Rates

There are 2 important distinctions between typical Per Capita and Relative Rate Index calculations. 1.) the RRI typically ties the baseline to the prior decision point while per capita calculations typically ties the baseline to the general population. 2.) The RRI then divides two rates to then produce one ratio.

Short Comings of Common Measures

While percentage shares, per capita measures, ratios and the RRI can point to overall group differences, they typically do not take into account individual factors that may be relevant in explaining differences between groups.

Are We Comparing “Apples to Apples”?

To make an “apple-to-apple” comparison and to further study group differences, we need to look beyond descriptive statistics. For example, let us consider evaluating disparity between different racial and ethnic groups at the point of arrest. If we wanted to know whether disparity persists, then we need to evaluate the average case characteristics to see if a 50/50% referral rate is truly representative of no inequities between groups.

Other Considerations

• Data Limitations
  • small sample sizes
  • data quality
• Weighted versus Unweighted Averages
• Statistical Significance

References

Utah Commission on Criminal and Juvenile Justice (2020). How Research Can Help Eliminate Racial and Ethnic Disparities