In a 1992 study entitled America's Smallest School: The Family, Paul Barton came up with the elegant and persuasive concept of the parent-pupil ratio as a measure of school quality. Barton, who was on the policy planning staff in the Department of Labor in 1965, noted the great increase in the proportion of children living in single-parent families since then. He further noted that the proportion "varies widely among the states" and is related to "variation in achievement" among them. The correlation between the percentage of eighth graders living in two-parent families and average mathematics proficiency is a solid .74. North Dakota, highest on the math test, is second highest on the family compositions scale - that is, it is second in the percentage of kids coming from two-parent homes. The District of Columbia, lowest on the family scale, is second lowest in the test score.
A few months before Barton's study appeared, I published an article showing that the correlation between eighth-grade math scores and distance of state capitals from the Canadian border was .522, a respectable showing. By contrast, the correlation with per pupil expenditure was a derisory .203. I offered the policy proposal that states wishing to improve their schools should move closer to Canada. This would be difficult, of course, but so would it be to change the parent-pupil ratio.
This parent-student ratio concept is worth remembering.
As is commenter Rob S's revision of the now-cliched "Correlation does not imply causation" into the less euphemistic "Correlation does not imply Caucasian," because we definitely wouldn't want you to draw that lesson!