Statistics 101 – Rates

A rate is a way of expressing how much one value changes in response to another. Whenever you’re driving to work, buying produce at the grocery store, or putting fuel in your car, you’ll likely be paying attention to rates, like your speed, the cost of veggies, and the price of gas. A rate simply shows the relationship between two different units of measure, such as kilometers per hour, dollars per kilogram, or cents per litre.

Another way we use rates is to understand how often something happens in a population. Take birthrates, for example. Birthrates are measured as the number of births per 1,000 people in a population. A large city like Toronto might count 30,000 births in a year, within its population of around 3,000,000 people. Converted to a birthrate, that’s 10 births per 1,000 people. A smaller city like Saskatoon might count 4,200 births in a year, within its population of around 350,000 people. Converted to a birthrate, that’s 12 births per 1,000 people. Even though Saskatoon is a smaller city with fewer births than Toronto, we can see that it has a higher rate of births among its population. Different populations are often different in size, and change year after year, so using a rate per 1,000 people gives us a standard way to compare data between them.

Here, at CSC, we often use rates per 1,000 people with our offender data. Offender populations differ by region and institution or parole office, and they change year after year. So, using a rate per 1,000 offenders gives us a standard way to compare data between these different populations. For example, in a given year, if one institution has 30 security incidents among its offender population of 270, and another institution has 40 incidents among its population of 550, calculating the security incidents as a rate per 1,000 offenders allows us to see and compare how often security incidents are happening in each population.
Next, let’s look at the rate of convictions on supervision for minor / moderate offences. In a given year, the rate at the national level might be 140 convictions per 1,000 offenders. At the regional level, we might expect to see similar rates. If, however, one region is showing a much higher or lower rate than the others, it might indicate a difference in the region’s offender profile characteristics. We can also filter and compare these rates by sex, race, district or parole office, and fiscal year to see if specific populations have higher, or lower, rates than the others.

CSC reports feature a number of different rates, such as weapon seizures, uses of force, supervision suspensions, drug-related seizures, and many more. And each of these rates is measured as the number of times that event happened per 1,000 offenders. Knowing how often these events are happening is important as it can help inform us where to allocate resources and help us better understand differences within our offender population. When observing CSC reports, be sure to watch for this icon so that you know when you are looking at rate data.