### Analysis of Ontario Primary School Class Sizes Part One: Verifying Ministry Claims

#### by Joseph Ryan Glover

*To practice my skills as a data analyst I decided to look into some of Ontario’s Open Data data sets. The primary school class size data set interested me because I have children in the primary grades and the topic is often in the news. *

**Summary of Analytical Findings**

- The Ministry of Education website claims all 2013-14 Grade 1, 2 and 3 classes have 23 or fewer students. The data reveals 7 classes in the 2013-14 school year with more than 23 students.
- The Ministry of Education website claims that 90% of all 2013-14 Grade 1, 2, and 3 classes have 20 or fewer students. An analysis of the data reveals that 89.89% of classes have 20 or fewer but this result requires the exclusion of 412 JK/K/Grade 1+ split classes and 2,213 Primary/Grade 4+ split classes. Including the Primary/Grade 4+ classes reveals that 83.71% of all classes have 20 or fewer students.

**Introduction to the Analysis**

Like many parents of children in the primary grades (JK, K, Grades 1, 2 & 3) I am familiar with the Ontario Government’s 2003 class size reduction initiative (PDF) which sought to have 20 or fewer students in 90% of all primary classes and 23 or fewer students in every primary class by the 2008-09 school year. To monitor their success the Ontario Ministry of Education maintains a Class Size Tracker website for visitors to browse class size data by school and school board. On the home page of the website (as of August 20, 2014) is the following claim for the 2013-14 school year:

The Ontario Government also supports an Open Data program from which they serve over 1000 data sets related to Government operations. On February 1, 2014 they published the latest Primary Class Size data set in the form of an Excel spreadsheet that lists the class enrolment details for every primary class in Ontario going back to the 2007-08 school year. I decided to check if the published data supported the claims on the homepage.

**All primary classes have 23 or fewer students**

The first claim, that all 2013-14 classes have 23 or fewer students was straightforward to investigate because each class in the Open Data Excel file indicates how many students of each grade are in the class. Class size is calculated by summing these numbers. After sorting the new class size column I found 5,438 classes with more than 23 students.

I was confused until I noticed that the Government excludes full-day kindergarten classes from the analysis because these classes have both a teacher and an early childhood educator and are permitted to go over 23. To account for this I excluded every class that had a JK or K student and in doing so also excluded 412 Grade 1+ split classes that had JK or K students.

Further close reading of the Ministry website indicated that only JK through Grade 3 classes are considered primary grades. The Open Data data set includes a column labelled G4To8 which is the number of grade 4 and up students that are split with primary students. By excluding the 2,213 classes that include at least one grade 4+ student I was left with a final count of 19,586 classes down from the original 33,523.

Sorting these remaining classes by class size I found 7 classes with more than 23 students which means that 99.96% of the 2013-14 classes defined as primary classes by the Province have 23 or fewer students. Re-running the analysis and including the Primary/Grade 4+ split classes resulted in 14 classes having more than 23 students and 99.94% of classes having 23 or fewer students.

Using all the data results in the aforementioned 5,438 classes with more than 23 students which translates to 83.78% of classes with 23 or fewer students, which is a better percentage than is published in the Ministry’s FAQ where they claim the number is 73.1%.

I understand the reasoning behind excluding JK and K classes from the calculation; two supervising adults should allow the number to be higher. I can also understand the exclusion of the JK/K/Grade 1+ splits if those splits also have an early childhood educator. I don’t think it is reasonable to exclude a primary class (typically a Grade 3 class) from the calculation because it happens to have some Grade 4 students in it. Admittedly, the difference between the two results is tiny for this claim but it plays a larger role in the next one.

**90.0% [of primary classes] have 20 or fewer [students]**

The second claim required a frequency analysis. After first eliminating the JK and K classes, the JK/K/Grade 1+ splits and the Primary/Grade 4+ splits I created a histogram of classes sizes. From that histogram I created a cumulative distribution function chart of class sizes.

The labelled data point is for a class size of 20 and the chart states that, for 2013-14, 89.89% of classes have 20 or fewer students. I suspect that the Ministry analysts rounded this 89.89% up to 90% (never round up to important breakpoints) to support their claim.

Re-running the frequency analysis but including the Primary/Grade 4+ split classes results in the following chart:

Here the class size of 20 occurs at 83.71%, which is meaningfully different from 90%. The percentage point drop occurs because of the inclusion of all 2,213 Primary/Grade 4+ splits but even if I only include those Primary/Grade 4+ split classes with as many or more primary students than Grade 4s — 1,120 of the 2,213 — the 20 or fewer breakpoint occurs at 86.66%. It seems that only by excluding primary classes split with Grade 4s can the province make its 90% number.

*This analysis just scratched the surface of the data set and revealed that you have to look closely at the assumptions behind the numbers to really understand what’s going on. I’m planning a second analysis that looks at the prevalence of split classes in the coming weeks. *