IN HER RESPONSE to my October article, Ruth Stotts indulges in and ad hominem attack that lacks cohesive logic. Within her 2 1/2 pages of typescript, Stotts accuses me of "violating [my] own methodology," of submitting an article that is "replete with factual errors," of harboning "prejudiced opinions," of distoring information for the purpose of supporting my opinions, of misrepresenting information, and of "violating the ethics of [my] profession." What happened to the canons of schoolarly debate?
What evidence or argument does Stotts offer in support of these accusation? First, she advances an alleged "error in methodology" resulting from my interpretation of a finding that average class size predicted just over 10% of the variation in 13-year-old' mean scores in mathematics in the 14 nations that "supplied reasonably comprehensive sampling frames for the 1991 IAEP study." I conclude that, "despite these results, it is difficult to believe that larger class size is generally associated with higher average student achievement. Perhaps a larger sample of nations would reveal a total absence of relationship."
It is important to note several facts. First, the methodology used was simple linear regression analysis. It was applied correctly, and the findings were accurately and factually reported.
Second, the same methodology was used in investigating the prediction of math achievement in the 1991 IAEP study, using average number of minutes of math instruction per week as the predictor variable, as well as the predictive value of a number of other variables. The method used was clearly described.
Third, both of the regression analyses cited by Stotts left more than 90% of the between-nation variation in 13-year-olds' average math achievement unexplained, a fact clearly noted in my article. The slopes of these regression lines did not differ significantly from zero when tested using a Type I error probability of .05. Thus the data at hand fully warrant the conclusion that the slope of the regression of 13-year-olds' math achievement on class size is equal to zero in the population of nations from which the sample of 14 nations might have been drawn.
Fourth, because of space limitations, only two of 28 figures contained in my original manuscript were included in the published Kappan article. Had my original Figures 14 and 15 (presented herewith as Figures 1 and 2) been printed, they would have shown clearly that Korea and Taiwan were outliers in the relationship between average class size and 13-year-olds' average achievement on the 1991 IAEP in mathematics - so much so that it seems reasonable to conclude that the positive regression line found in the analysis was not likely to generalize beyond the sample of 14 nations for which data on these two variables were obtained. Indeed, in the absence of Korea and Taiwan, the slope of the regression line is negative.
The screening of outliers is recommended practice in regression analysis. Note, in contrast to Figure 1, that in Figure 2 there are no outlying data values that would materially alter the slope of the regression line were they to be omitted from the data set.
Finally, a substantial research literature exists that supports the inverse relationship between average class size and student achievement. Although none of these studies used nations as its unit of analysis and the within-nation results often differ from between-nation results, it is not unreasonable to expect the regression of student achievement on class size to have a negative slope in light of the more than 75 studies summarized in this body of research. Having been a reviewer of Gene Glass' meta-analysis prior to its publication, my personal expectation, clearly stated as just that in my October Kappan article, is well justified. In sum, the first objection Stotts raises provides no support for her conclusions or for her attributions of bad faith on my part.
Stotts also objects to my statement well documented and with the source clearly indicated) that the U.S. was the leading nation in per-capita gross domestic product (GDP) in 1990, yet ranked "ninth among the world's industrialized nations in . . . per-student expenditure for K-12 education" (page 125). She accused me of being "intellectually dis-honest" in reporting these results. Curiously, her objection is based on her own subjective expectation: "The reader does not have to know very much about the economies of the nations of the world to question these statements. Is it reasonable that the U. S. could be number one in GDP and fall to ninth place in spending for education?" Apparently, commenting on an unexpected finding is permissible for critics, but not for authors.
Stotts justifies her second complaint by pointing out that the two statistics I cited were reported for different years and that the GDP data were reported in terms of purchasing power parity exchange rates. First, use of the most recent, reliable one can obtain is consistent with sound scientific practice. It is unfortunate that the major statistical agencies of many nations, and of major international organizations as well, require a number of years to analyze their data and report them. Data in the principal publications of the National Center for Education Statistics, as well as those of comparable agencies in other nations, are routinely out of date by three or more years. Furthermore, data for comparable years are often impossible to obtain from several agencies. Such was the case with data on GDP and educational expenditures.
Second, as noted in the source I cited in my Kappan article and in numerous research-based comparisons of national economies, exchange-rate conversion of currencies for purposes of GDP comparisons provides less trustworthy results than does purchasing power parity (PPP) conversion. The reason is that comparable amounts of money purchase markedly different amounts of goods and services in different nations. The per-capita GDP data I cited, showing that the U. S. leads the industrialized world, were thus reported in a metric that is widely regarded by leading international economists as the most trustworthy. Had current educational expenditure data been available in a comparable PPP metric, they would have been preferable to the data I reported, and I would have cited them.
Unfortunately, these data were not available. The most recent, partially relevant information that I could obtain was reported by Irving Kravis and his colleagues in their analyses of data collected on behalf of the United Nations and the World Bank in 1975. Among 151 elements of the economies of 34 nations, they included the salaries of "first- and second-level teachers." They reported these amounts on a per-capita basis, valued at "international prices" in 1975 for the 10 nations that then enjoyed the highest levels of economic development in the world. With the exception of Belgium (with a value of 100.4), the per-capita international-price cost of teacher salaries was reported to be higher in the U.S. (98. 1) than in any other major industrialized nation. Corresponding figures were 87.2 in the United Kingdom, 70.8 in Japan, 86.1 in Austria, 82.2 in the Netherlands, 92.9 in France, 76.2 in Luxembourg, 77.7 in Demnark, and 69.0 in Germany.
Granted, these data are now 17 years old. However, they were the most recent figures obtainable that offered results in a PPP metric for the major cost of providing public education. These data suggest that education dollars bought less in the U. S. in 1975 than in the other economically wealthy nations compared, including Germany and Japan. If these comparisons still held in 1988, the exchange-rate data for per-pupil expenditure I cited would credit the U.S. with greater investment in education than is warranted, not less, as Stotts seems to claim. Unfortunately, in the absence of more-recent data on PPP per-capita expenditures, we can only wonder whether the findings reported for 1975 are applicable to 1988. More to the point, however, no available data suggest that the findings of Rasell and Mischel misrepresent the conclusion that the U.S. ranks below many other industrialized nations in its per-pupil investment in K-12 education cation, despite its top rank in wealth.
These are the facts. At its best, scholarly critique illuminates an issue. Regrettably, Stotts' reaction to my Kappan article provides little light and substantial heat. [1.] Marija J. Norusis, SPSS Advanced Statistics Student Guide (Chicago: SPSS, 1990), p. 27; and Elazar J. Pedhazur, Multiple Regression in Behavioral Research (New York: Holt, Rinehart & Winston, 1982), pp. 37-39. [2.] For a summary of case studies, see Leonard Cahen et al., Class Size and Instruction (New York: Longman, 1983); for extensive meta-analyses, see Gene V. Glass et al., School Class Size: Research and Policy (Beverly Hills, Calif.: Sage Publications, 1982); and for a recent large-scale experimental study, see Jeremy D. Finn and Charles M. Achilles, "Answers and Questions About Class Size: A Statewide Experiment," American Educational Research Journal, vol. 27, 1990, pp. 557-77. [3.] See Michael Ward, Purchasing Power Parities and Real Expenditures in the OECD (Paris: Organisation for Economic Cooperation and Development, 1985), p. 11; Irving R. Kravis, Alan Heston, and Robert Summers, World Product and Income: International Comparison of Real Gross National Product (Baltimore: Johns Hopkins University Press, 1982), Chs. 1 and 2; and J. Salazer-Carrillo and D. S. Prasada Rao, eds., World Comparison of Incomes, Prices, and Product (Amsterdam: Elsevier Science Publishers, 1988). [4.] Kravis, Heston, and Summers, p. 223.
RICHARD M. JAEGR is Excellence Foundation Professor of Educational research methodology and director of the Center for Educational Research and Evaluation in the School of Education, University of North Carolina, Greensboro.…