Schooling Effects: Reply to Alexander and Pallas

Abstract

I am in error. Alexander and Pallas do consider the objective of both their analysis and mine to be the evaluation of the relative of Catholic sector secondary education to the overall achievement level of secondary school students in the United States. In my earlier comments (Kilgore, 1983), I assumed we agreed that such was not the objective. However, agreement clearly does not exist. In my previous response to their work, I submit that contribution to is an inappropriate statistic to evaluate the importance of Catholic sector achievement differences. Given, I argue, that R2 is a function of the to oVerall variance, any dichotomous variable which identifies very small portions of the population will contribute very little to R2. To illustrate, I report the R2 values for the same effect (coefficient) under two conditions: (a) under conditions where the proportion of the student population attending Catholic sector schools is equal to the proportion attending public schools (R2 =.05) and (b) under conditions that actually reflect the current enrollment pattern of 7 percent in Catholic sector schools (R2 = .013). The purpose of the exercise is to demonstrate the sensitivity of R2 to varying sizes of p where p is the proportion of students attending Catholic sector schools. However, in their response, Alexander and Pallas suggest that the likelihood of equal size enrollment in Catholic and public sector schools is quite remote. They ask: Who would ever anticipate such a radical transformation of our educational system? The answer is, neither I nor Alexander and Pallas. In raising this question, they have, however, clarified their position. They do consider the objective of our analysis to be the evaluation of the relative of Catholic sector education to the overall achievement level in the United States. With this objective, R2 is an appropriate yardstick to evaluate large versus small effects. Moreover, the assessment would be rather clear: the effect of Catholic sector education is small. What is evident, then, is that I was incorrect in assuming that we both reject this objective. It appears necessary to elaborate on my objection to this strategy. Let me begin with an example outside the domain of public and private school issues. If the past decade of research on achievement had been oriented toward the objective of identifying those factors which do the' most to raise or lower the overall achievement level in the United States, then one would not find a tremendous concern for the achievement level of blacks because their lower achievement level contributes very little (R2) to the overall variation in achievement. (Or, to move somewhat further away from education, in the Jencks et al. [1979] study of occupational status attainment, the R2 for race ranges from 0.010 to .006.1) The research has been formulated from a different perspective: issues of discrimination and relative advantage of subpopulations inform the framing of objectives and they rarely, if ever, include the evaluation of the overall of race to achievement levels in the U.S. Although it may seem curious to Alexander and Pallas, I view our research objective as an attempt to unravel school organizational processes that may affect achievement levels. Comparing organizational forms that are substantially different is helpful-not necessarily conclusive. Evaluating the relative achievement levels in each sector is only the first stage in that objective. If one finds a statistically significant difference (as in t test, not R2), then it is worthwhile to see if one can specify the organizational processes or properties that can account for the difference. Comparison of magnet schools with comprehensive high schools may prove to be similarly productive. But in both cases, assessing the relative of magnet schools or Catholic sector schools to the overall achievement level in the United States misdirects the inquiry. Alexander and Pallas are correct in pointing out that I failed to provide an alternative yardstick by which to evaluate Catholic sector effects. Allow me to do so now. In their original analysis, Alexander and Pallas reject the use of grade-level equivalencies, as was done in Coleman, Hoffer, and Kilgore [CHK] (1981b), on the grounds that our grade-equivalency scale was based on cross-sectional data that could be fraught with unknown biases. The