Sunday, April 19, 2015

Looking at Disproportionality

The concept of disproportionality underlies much of the reform movement for education in the United States. Sometimes referred to as the achievement gap or opportunity gap, the basic idea is that outcomes for all students are not equitable. While much of the conversation focuses on race, disproportionality applies to any subgroup: gender, special education, English language learners, free/reduced lunch, and so on. Over the past several years, much of the conversation about disproportionality has focused on student achievement---and test scores in particular. But just as there is more we need to look at in addition to race, there is more to children than representing them as test scores. We can look at disproportionality as it relates to sports or after school activities, student discipline,  attendance, and other factors.

If you want to examine disproportionality within your system, there are a few pieces of data that you will need to know. In the example below, I'm going to use gender (male, female) as subgroups. (Note: I realize this is a very heteronormative view of gender. Our data systems need to catch up with our increasing understanding as a society about gender identification; however, right now, most school data systems are set up to only capture the binary male/ I'm going to use it as an example.)

First, you need to know the enrollment numbers and percentages for each subgroup. In other words, how many possible students are there who could participate in an athletic program, be subject to suspension/expulsion consequences, fail Algebra, or yes, pass the state test? Many schools report gender as close to 50/50 percent, as one might expect, but variations do exist. Don't assume that you're starting off with equal pools of participants.

Secondly, you need to know the participation numbers and percentages for each subgroup. Just because everyone is eligible to pass the state test doesn't mean that they do. So, how many males/females met the standards? How many in each subgroup were suspended? Enrolled in Physics or Calculus? Turned out for basketball?

In this example, we have a school with 250 males and 275 females, with 50 from each group enrolled in Algebra. Now we need to calculate the disproportionality.

To determine the number of males required to achieve proportionality for the total population, we use the first equation described above (n males for proportionality = (50 * .52) / .48) for a result of 45.5 males. The second equation gives us 55 females needed for proportionality.

Next, we take these two and compare them with the number of students in each subgroup that are participating. For males this would be 50 - 45.5 = 4.5; for females 50 - 55 = -5. That -5? It means that we need five more females enrolled in Algebra to achieve proportionality.

While it may not be entirely realistic to achieve perfect proportionality within a system for all programs, subgroups, and outcomes, it is still important to review these data to reflect on areas where institutionalized racism or policies may be contributing to disproportionality. Another factor to consider is the size of the subgroups that you are reviewing. For example, if you only have two or three American Indian students in a grade level, it's unreasonable to expect that they are represented in everything---but you should look to be sure that they are represented somewhere among school offerings. In that case, it may be more helpful to use longitudinal data to get an idea for participation.

Here's an Excel workbook that allows you to easily compare gender equity in sports programs. I built it a couple of years ago for a program that needed it, based off an idea of Debra Dalgleish. See her site for even more ideas on data entry forms...and feel free to modify mine to suit your needs.


  1. You might want to look at the evaluating the goodness of fit using the Chi-Square method. The example given is an perfect match for the technique. You can then find out if the observed dis proportionality is a chance occurrence or a real phenomenon.

  2. You could apply the Chi square test here, but we would still need to have a way to determine the expected results in order to compare them with the observed. Seems like that would be a good second step after calculating the disproportionality.

  3. Right. I intended it to be the next step to what you proposed