## Measurements

This page shows the calculations we used to measure disparities on this website and provides additional examples.

## Raw numbers

If you select raw numbers as your measurement, the website will display the actual number of youth in that category. For instance:

- In California in 2017 (the latest year of available data for the one-day count, which is a snapshot of youth in detention): There were 2,283 youth of color detained on the one-day count.
- In California in 2014 (the latest year of available data for annual decision making data, which measures the volume of admissions over the course of the year): There were 17,763 youth of color admissions to detention.

## Rates

A rate is a quantity measured with respect to another quantity.

For this website, rates are calculated by dividing the number of youth involved in the juvenile justice system by either (i) the number of youth in the population or (ii) the number of youth involved at a prior decision-making point. The quotient is then multiplied by a number (for example 100,000 to give a “rate per 100,000.”)

Rate based on youth in population

For example, one-day count data includes youth detained on a given day. Use the following formulat to calculate the 2017 rate of detention in the U.S. per 100,000 Black youth in the population:

*Thus, on a given day in 2017, for every 100,000 Black youth age 10-17 in the United States, 141 were detained.*

### Rate based on prior juvenile justice decision-making point

In addition to calculating a rate per youth in the population, you may calculate the rate per prior decision-making point in the “decision-making points” section of the website.

Except for the point of arrest (which uses a rate per 1,000 youth in the population), the Relative Rate Index (RRI) calculates rates per 100 youth at the prior juvenile justice decision-making point. For example, detention rates are calculated per 100 referrals to court.

Use the following formula to calculate the detention rate per 100 referrals to court for Black Youth in Alameda County, CA in 2014:

*Thus, in 2014 in Alameda County, CA, for every 100 Black youth referrals to court, there were 47.3 admissions to secure detention.*

## Disparity gap

The disparity gap is a ratio of rates, or a “relative rate.” When calculating the disparity gap, we compare each race and ethnicity to White youth.To calculate the disparity gap, divide the rate for Youth of Color by the rate for White youth:

The rate of involvement for White youth is always the denominator. The “relative rate” for White youth is always 1, since we are comparing the rate for White youth to itself.

For this website, disparity gaps are calculated using either the (i) rate per youth in the population or (ii) rate per prior decision-making point.

### Disparity gap using rate per youth in population

Use the following formula to calculate the disparity gap in rates of detention for Black vs. White youth in the U.S. in 2017, based on the one-day count:

*Thus, on a given day in 2017, Black youth in the United States were 5.7 times as likely as White youth to be detained. The ratio is 5.7 to 1.*

### Disparity gap using rate per prior decision point

Use the following formula to calculate the disparity gap in rates of detention for Black vs. White youth in California in 2014, using the rate of detention based on 100 referrals to court:

*Thus, in 2014, Black youth in California who were referred to court were 1.6 times **as likely to be admitted to detention as White youth in California who were referred to court.*

*The ratio is 1.6 to 1.*

## Using Multiple Measurements

As you experiment with the state data map on this site, you may notice that some of the smallest states have the highest rates of incarceration and/or disparity gaps. It is important to interpret these data within context and use multiple measurements to understand the problem. This is best illustrated with an example.

In 2017, North Dakota had the fifth highest rate of detention for Latino youth in the country (78 per 100,000 Latino youth). In raw numbers, that represented only three youth. By comparison, Texas had the 20th highest rate of detention for Latino youth in the country (44 per 100,000 youth). Yet, in raw numbers, that represented 627 Latino youth--the second highest number of Latino youth detained on a given day in the nation.

All states should investigate disparities and work towards equity for youth in their systems. However, our example illustrates why it is also important to use multiple measurements to understand the problem. Although rates of detention for Latino youth are much lower in Texas, the raw numbers of youth involved are very different, and may lead to different strategies for reform.