Saturday, April 23, 2016

Prep Schools and Test Scores
How do we rate teachers and schools?  One way, which has the advantage of being objective, but which is still controversial, is to consider their students’ test scores, and how much they go up while the students are being taught by a given teacher or at a given school.  The No Child Left Behind Act has likewise mandated tests for most public school students at a few points in their schooling.  We don’t have such mandated tests at private schools, but many private high schools (“prep schools”) require Secondary School Admission Tests (SSATs) of all their applicants, and have graduates who almost uniformly are applying to colleges and taking the SAT test.

This scatter graph shows information on the students’ testing at several prep schools which might be of interest to a student living in Massachusetts or New Hampshire, and which have released testing information to Boarding School Review (n.d.).

For each school, the horizontal location of the bubble marking the school shows how well the school’s students tested when they applied to the school (the average SSAT score, measured as a percentile, of incoming students).  And the vertical location of the bubble shows how well the school’s students test in their senior year at the school (the average SAT score, on a scale which goes to 2400) of graduates.

Since the SSAT and SAT test essentially the same thing (preparation for academic schoolwork, a combination of intelligence and learning measured mostly with regard to mathematical understanding, vocabulary and reading skill), we should not be surprised to see a fairly strong correlation between the two statistics.  This correlation can be expressed by an r2 of 78%, or by noting how nearly the schools’ bubbles fall along the best-fit diagonal trend line, as shown:

To the extent each school deviates above the trend line, we can say that the school is doing an above-average job of educating its students (at least, to the extent that SAT scores reflect education), and schools below the trend line appear to not be doing so well on this measure.  (The size of each circle indicates the number of students at the school; the color green indicates a girls-only school, blue a coed school, orange a day school.)

However, the information in this graphic should be a rather small part of judging a school’s academics, and academic strength may not be the most important factor when judging how happy or successful a particular child will be at a particular school.

Further, the height of the dots above the diagonal line may not be as important in choosing a school as is where the school falls along the diagonal line.  Although most people want to go to the most selective prep school (or college) that they get into, it is unclear whether this is the ideal choice in terms of academic progress, let alone social life.  Imagine a student who scores at the 90th percentile on the SSAT.  At a school near the center or on the left of the chart she will be among the stronger students; this may lead to increased self-confidence and self-identification as a scholar; on the other hand, it may instead lead to laziness as a moderate effort may be all that is necessary to have average or even above-average grades.  At an academically tougher school on the right of the chart, the 90th-percentile scorer will likely not be among the stronger students; this may lead to harder work to keep up with peers, or it may lead to frustration and burnout.  So in choosing a school, one might have to guess whether one’s child is more likely to suffer from laziness or from low self-esteem.

A final caveat: With any system of measurement, the accuracy of the measurement goes down to the extent that the measured entity or the measurer has a stake in the outcome.  And as with public schools, colleges and law schools, prep schools have in the past sometimes fudged input and outcomes statistics.  One wouldn’t want to penalize a school for being honest.


Boarding School Review. (n.d.). Retrieved from (2013). Scores: How to read your score report. Retrieved from