WASHINGTON—A sense of humor can serve a social scientist, who must distinguish mere correlations from causation, and must do so concerning subjects about which people have material interests and hence strong passions. To make such a distinction, Pat Moynihan, a scholar and senator who knows that pushiness is compatible with seriousness, postulates that a crucial determinant of the quality of American public schools is proximity to Canada.

He notes a positive correlation between states whose eighth graders achieve high scores on standardized math tests and the distance of the states’ capitals from the Canadian border. At least—here is the barb in the jest—that correlation is stronger than the correlation between high test scores and high per pupil expenditures.

In a 1992 book “America’s Smallest School: The Family,” Paul Barton argues that a more powerful measure of school quality than the pupil-teacher ratio is the parent-teacher ratio. He notes that in recent decades the proportion of children living in single parent families rose rapidly and school performance, measured by standardized tests, declined. The proportions of children in single-parent families very substantially among the states, so some conclusions are suggested by data such as:

In a recent year North Dakota had the nation’s second highest proportion of children in two-parent families, and the highest math scores. The District of Columbia ranked last on the family composition scale and next to last in text scores.

Empower America and the American Exchange Legislative Council this week released a report bristling with facts inconvenient for certain theories and factions:

Between the 1972-73 and 1992-93 school years, a 47 percent increase in spending on public education for grades kindergarten through twelve coincided with a 7 percent decline in school enrollment and a 35-point decline in SAT scores. As is usual with socialism (government control of the production and distribution of a product), public education is highly bureaucratized, so teachers’ salaries have declined as a percentage of total education spending, from 41.5 percent to 34.4 percent, as bureaucrats have proliferated. Nevertheless, during those two decades teachers’ salaries rose substantially and pupil-teacher ratios declined in all 50 states.

However, in 1992-93, none of the five states with the highest teachers’ salaries was among the 15 states with the top SAT scores. And the 10 states with the lowest per pupil spending included four—North Dakota, South one of the 10 states with the highest SAT scores.

New Jersey has the highest per pupil expenditure, an astonishing $10,561, which teachers’ unions elsewhere try to use as a negotiating benchmark. New Jersey’s rank regarding SAT scores? 39th.

North Dakota ranks 44th in per pupil expenditures ($4,423), and 49th in Dakota ranks last—51st—in teachers’ salaries ($24,125) but third in SAT scores and sixth in graduation rates. Utah ranks 51st in per pupil expenditure ($3,128) and has the highest pupil-teacher ratio (23.8) but is fourth in SAT scores. Washington, D.C., is fifth in per pupil expenditures ($7,967) and has a lower pupil-teacher ratio (11.9) than any state, yet ranks 49th in SAT scores and 50th in graduation rates.

Here are the five states with the highest SAT scores, and these states’ rankings in per pupil expenditures:

1. Iowa (27th)

2. North Dakota (44th)

3. South Dakota (42nd)

4. Utah (51st)

5. Minnesota (25th)

For understandable if insupportable reasons, the public education lobby has long argued for judging school quality not by cognitive outputs—standardized measurements of what students learn—but by monetary inputs, principally the number of teachers and staff and their earnings. Moynihan undermines the argument by having fun with a correlation that is coincidental, not causal.

By noting that proximity to Canada correlates more strongly with school excellence than does high spending on schools, Moynihan is not suggesting a solution—a proper posing of the problem. The problem is not an insufficiency of appropriations.

Being droll in order to be didactic, Moynihan suggests that states wishing to improve schools might try moving closer to Canada. “this would be difficult, but so would it be to change the parent-pupil ratio.”

The fact that the quality of schools correlates more positively with the quality of the families from which children come to school than it does with education appropriations will have no effect on the teachers unions’ insistence that money is the crucial variable. The public education lobby’s crumbling last line of defense is the miseducation of the public.