Nearly every day of my professional life I am engaged in some manner of discussion about the “quality” of education, either at the Calhoun School or elsewhere. Whether as seen in broad educational policy research, in independent school admissions, or in U.S. News and World Report college rankings, our society grapples constantly with the elusive process of assessing schools. The waters of social science research are generally murky, but educational research is particularly confusing.

Perhaps the greatest fallacy in educational assessment is the nearly unchallenged idea that you can judge the quality of the process by the product. For example, conventional wisdom holds that the median SAT scores and college acceptances at a particular secondary school serve as an unquestioned barometer of the quality of the education. I propose that SAT scores and college acceptances have almost nothing at all to say about the quality of education in secondary schools.

Consider this analogy: Let us imagine that the most important measure of success in school or life is not SAT scores or colleges attended, but foot speed. Most parents with the luxury to choose will naturally seek a school that seems to produce fast runners. One way, arguably the primary way, that a school might achieve this end is to begin with an admissions process that seems a fair race: Line 1,000 young applicants up at one end of a football field and have them sprint to the other. Admit the 50 who finish first. Next year do the same.

Furthermore, at the end of each subsequent year, line up the students in each grade and have them race again. Kick out (politely, of course) the five or 10 who finish last. Perhaps they lagged in growth, gained a few pounds during puberty, or peaked early and really weren’t born to run fast. Hold races among new applicants to fill the vacated slots. This process will inevitably produce one of the fastest on foot graduating classes in town.

I hope the parallel is obvious, even if the variables are more complex. Many of the supposed “best” private schools admit students with the highest demonstrated test-taking ability, usually the ubiquitous ERBs. Other predictors of high SATs and Ivy League admission also are carefully analyzed: Colleges attended by the parents, ambition of parents and children, social and economic standing (the most reliable predictor of all), prior evidence of a high level work ethic, etc.

Having thus pre-selected students with the most powerful predictors for the predetermined measures of success, all a school must thereafter do is line them up and reassess from time to time, culling out those whose predictors lag as they grow. At the end of this process, pop the champagne and celebrate the inevitable. This does not mean, of course, that schools whose graduates boast 1,400 median SATs and 50% Ivy acceptances are bad schools. Most of them are very fine schools. But the self-fulfilling results don’t make the case either way. Those scores and college acceptances would be likely whether or not the education was indifferent and unimaginative or inspirational and dynamic.

The same fallacious reasoning distorts perception and policy from college rankings to the assessment of public education. The reputations and rankings of schools like Harvard, Yale, and Stanford soar on the achievements of their graduates: Elite graduate schools attended, earning power, subsequent professional achievement, and so on. Again, no disparagement intended, but such schools are even more fastidious in their pre-selection of only those who are the very most likely to succeed in the precise way that success has been pre-defined.

It is rather like a great violinist (a Juilliard graduate) friend of mine who said this about the Juilliard School. “It’s not like the students learn how to play there. The greatest thing Juilliard can do is to not ruin them.”

Suburban public schools in wealthy neighborhoods are “good” because 90% of graduates go to college. Urban public schools are “bad” because 90% don’t go to college. Powerful social dynamics produce self-fulfilling results just as do private school admissions, by sorting America’s families into neighborhoods by the very same predictor variables: College degrees among parents, social and economic standing, and so on.

What all schools should do is expose each child to rich sensory stimulation, constant respect and affection, and develop her own, unique expressive and analytic capabilities. What all schools should seek is to sustain curiosity, to kindle deep passion and sharp skepticism, to encourage cooperation and compassion over self-interest and competition, and to guide each child to discover himself and his place in a just world.

The self-fulfilling, Darwinian process in education and its assessment in America today tends to do just the opposite.

Mr. Nelson is the head of the Calhoun School in Manhattan.