My thirteen year-old son is just finishing middle school and it’s time to think about high school. There are three choices in the School District, or four if you count home-schooling. Clover Park High School is the default school for where we live. It’s a prison-like building, which puts a high premium on sports. Indeed it’s the home of the Warriors, and every week I can hear the Star Spangled Banner blasting from their stadium. Another high school is Lakes. It’s the school that all my son’s friends are going to, and they teach rudimentary German and Japanese there. Finally there’s Harrison Preparatory School, Harrison Prep for short. Its big advantage is that they don’t do sports, but they do have a waiting list. The school claims that they prepare students for college, and they are very proud of their International Baccalaureate program.

So how do we make our choice? One method is to use test results. Every year the State of Washington gives children a standardized test, called the Smarter Balanced Assessment, SBA for short. The tests are in English Language Arts (ELA), mathematics, and science, and they are designed to test whether children have reached state standards for their grade level.

The State have published statistics for 2016-2017, on the website of the Office of Superintendent of Public Instruction. You can look up all the School Districts in the state, and you can then compare the good, the bad, and the ugly. The SBA has four levels, 1 to 4. Level 4 is Advanced and Level 3 is proficient. In other words, the kid with a 3 or 4 has met the state standards. Levels 2 (Basic) and 1 (Below Basic) are below standard.

Let’s look at some examples. In the Tacoma School District there is a school called the Science and Math Institute. It’s a great shame we don’t live in Tacoma, because that would be just the school I’d want my son to go to. Nonetheless, I’ll check the SBA scores. For ELA it’s not too bad, with 73.2% of 11th Graders reaching the standard, with a 3 or a 4. And one has to remember that it’s a science and math institute, so the kids are going to be more focused on numbers than words. Turning to the math scores… and 25 eleventh graders out of 80 at the Science and Math Institute have met the state standards. That’s 31.3%, or 35.2% if you count previous sittings of the test. That’s weird… either the students need more practice taking tests or the school needs a name-change. Another example is the International School, in Bellevue School District. Bellevue is where the money and the tech companies are, and this is reflected in the school’s SBA scores. Of the 11th graders that took the math SBA, 93.6% reached or exceeded state standards.

We now have to consider my son’s School District. I created a table, listing the number of 11th graders in Clover Park, Lakes, and Harrison Prep who were above and below state standards in math:

There are real differences between the three schools, and if one does a *Χ ^{2 }*test one gets a significant result. However, are the results enough to show that Harrison Prep is the better school, at least for mathematics? They suggest that for the student of average ability it probably is. For children who are markedly above or below average, the situation isn’t so clear. Both Clover Park and Lakes have a lot of students who are above standard – indeed enough to fill two whole class rooms, in each school. And From the Washington figures we have no way of knowing how well these above-standard students are catered for.

As a final thought, we can estimate the effect size of *Χ ^{2}*. We divide

*Χ*by the total number of students in the table, and square-root the answer.

^{2}*Χ*is 40.775, and when we divide this by 486 we get .084. And the square root of .084 is .2897. We can therefore say that differences between the three schools explain 28.97% of the differences between the math scores. This leaves us with an unexplained 71.03%. So maybe it doesn’t really matter which high school my son goes to. Or maybe he should be home-schooled?

^{2 }