Which of Two Schools is "Best" for a Particular Child?

If a school gets terrific scores on the state standardized tests, does that mean it's a great choice for your child?

Maybe, maybe not. Averages hide a lot of details.

Take two high schools as an example, Adequate High and Leafyburb High.

Adequate High is a typical high school in a middle-class neighborhood that does a decent if unremarkable job with its students. It's in a stable neighborhood without big gang or drug problems, and it has many well-liked teachers and a facility in good condition.

Leafyburb High is in an upper-class suburb and its highly ballyhooed program is supported by sky-high taxes. Its top-track students attend classes that go way beyond typical AP courses to rival the best college experiences, and those kids often go on to prestigious colleges and careers, a fact that Leafyburb heavily promotes. In addition, Leafyburb has a superlative program to help students with learning challenges, with a large support staff.

The state scores are no surprise. Leafyburb High has "meet" and "exceed" scores that beat everyone else around, including Adequate High.

But does that mean that Leafyburb High would be a better school than Adequate High for your child? This is where the state averages fail to provide much guidance.

Suppose we had access to more detailed information on standardized scores for each individual student just before they entered high school, and then again as they near the end of their high school careers. We could then draw an XY plot of these input scores versus the output scores. For all of the plotted points for all of the students in a school, we could compute a curve of best fit (using curvilinear regression) through the plotted points. By overlaying curves for individual schools, we would have a much better idea of how well schools might deliver for each student.

We might wind up with a plot like this:



Looking at the right side of the plot, we see that kids leaving 8th grade with very high scores might benefit from the excellent top-tier academic track at Leafyburb High. On the left side of the plot, we see that kids struggling with weak grades in 8th grade might be greatly aided by the intense program for learning disabilities at Leafyburb.

But what about the kids in the middle? Leafyburb may reserve its very best, motivating teachers with multiple degrees for the top tier classes, and provide fairly straightforward coursework in middle tiers. In addition, all the emphasis and boasting about the superlative students may mean it's a daily struggle for the average kids to feel they are doing well.

As a result, perhaps students of middling achievement in 8th grade might actually grow more and learn more if they attend Adequate High! For that middle tier, the plotted curve for Adequate High is above that of Leafyburb.

Is this true in the real world? Can we demonstrate these possibilities with real data? Sadly we cannot. The data required for this analysis simply isn't available. Or, if the data exists at all, it's closely held by individual schools and seldom if ever revealed to outsiders, even in an aggregated form.

Conclusion

Parents cannot rely on great-sounding averages to choose the right school for a particular child. To do that, they would need more information on patterns of what schools accomplish for kids with different levels of achievement going in. And that simply isn't available.