There is currently a debate within the literature as to whether class size influences academic achievement. The debate was perhaps first sparked by a review of the literature by Glass and Smith (1978). Using meta-analytic techniques Glass and Smith reviewed approximately 80 class-size studies conducted between 1900 and 1978. The researchers concluded that reductions in class size resulted in increases in academic achievement. To achieve a significant increase in academic achievement however required a dramatic reduction in class size. Class sizes of 15 or fewer students could be expected to increase achievement scores by approximately half a standard deviation.

The assertions made by Glass and Smith were challenged by the Educational Research Services (ERS) (1980), which maintained that many of the studies analyzed by Glass and Smith were methodologically faulty. The ERS pointed out that many of the achievement gains were based on tutorials or extremely small classes. The ERS concluded that the analysis by Glass and Smith actually supported few achievement differences for classes ranging from 20 to 40 students.

Of the studies that have found smaller class sizes producing gains in student achievement, most are for the early primary grades (e.g., Robinson & Wittebols, 1986). Robinson and Wittebols found that the effects for smaller class size decreased from grades K-3, to 4-8, and were almost nonexistent for grades 9-12.

The purpose of this investigation was to examine the degree to which class size influences student achievement. Student achievement was measured by the Iowa Test of Basic Skills (ITBS) and scores were reported in Normal Curve Equivalents (NCE). Achievement measures were also grouped according to content. The math score represents the mean NCE score for three math subtests of the ITBS. The English score represents the mean NCE score for the reading, vocabulary, and usage and expressions subtests of the ITBS. The amount of shared variance between these variables allowed for the creation of these combined scores. Attendance rate, math grades, and English grades were also analyzed and their influence on achievement was compared with class size.

Analyses included Pearson Product-Moment correlations between attendance, class size, course grades and corresponding measures of academic achievement. Finally, step-wise multiple regression analyses were run to determine the amount of academic achievement variance explained by class size, course grades, and attendance rate. The analyses performed in this study differ from those performed in many previous investigations. Except for studies that used meta-analysis or cluster-analysis to analyze previous research findings, most used an analysis of variance (ANOVA) model. Use of ANOVA was suggested by the methodology used in a number of these studies (e.g., Finn & Achilles, 1989). The use of ANOVA is suggested by a methodology that uses random assignment to control for extraneous influences on the variables of interest. This method of randomly assigning students and teachers to class rooms was not possible in this study. Instead, analysis of the impact of class size on student achievement had to be carried out post hoc.

While it is desirable methodologically to randomly assign teachers and students to classes of various sizes, given that random assignment was not possible in this study, the use of linear regression model seemed the most appropriate choice for a statistical model. Using an ANOVA model would have required an arbitrary decision as to the number of students that would constitute a small, medium, or large classroom, a decision that is not required when using a regression model. In addition, use of the linear regression model produces a direct measure of the strength of association between any two variables with the influences of additional variables removed or partialed out. Finally, all statistical tests of significance using the ANOVA model are also possible with the regression model.

The student pool on which analyses were performed consisted of 4370 forth graders, 4196 seventh graders, and 3166 tenth graders. The off grades five through twelve, ranged from seven students in grade twelve to 805 students in grade six. All students took the ITBS at the end of the 1992-93 school year.

Students in grades four through six were largely confined to a single home room so that the english and math class sizes were equal. Students in the middle grades and high school were able to take a variable number of math and English classes. To address the problem of multiple courses, class size was averaged for those students who had taken more than on english or math class. In addition, final grades represent mean grades for students taking more than one math or english class. For grades four through six English and math grades were not available.

Separate analyses were run for the primary grades four through six, and for grades 7 - 12. The rationale being that a number of studies have found class size to have a positive effect on academic achievement for grades K-2 (e.g., Achilles, Bain, and Finn 1990). In a synthesis of research on the effects of class size Robinson (1990) found that 50% of the studies concluded that smaller class sizes had a positive impact on student achievement for grades K-3, while 38% of the studies reached the same conclusion for grades 4-8, and only 18% of the studies found positive effects for class size for grades 9-12. Unfortunately, students younger than grade 4 were not represented in this study. However, in the same study, Robinson (1990) found that of the studies investigating the effects of class sizes fewer than 22, 50% found positive effects for grades 4-8.

Results

Table 1

Note.

Attendance rate was calculated by subtracting only the unexcused absences from the total days possible (175). In this regard attendance rate may be thought of as a measure of motivation, or at the very least, compliance. It was felt that calculating attendance in this fashion might produce a better predictor of academic performance. As can be seen in Table 1, the average class size for grades 4 - 6 was slightly larger than for 7 - 12 graders. The minimum and maximum class sizes were equal for the two groups with class sizes for 7 - 12 graders being more variable. Another point that should be noted is that the average ITBS scores were higher for grades 7 - 12 than grades 4 - 6 for all subtests.

The next step in the analysis was to examine the bivariate correlations of all variables to determine the degree of covariance between the predictor variables.

As can be seen in Table 2, there is a large amount of shared variance for the english subtests of the ITBS. The block of interest is presented in italics and includes R1NCE, R2NCE, and L4NCE. The correlations range from .71 to .80 suggesting a high degree of colinearity among the english subtests. There was also a fairly high degree of colinearity between the mathematics subtests of the ITBS. The correlations ranged from .60 to .67. Of interest also is the degree of covariance between the english and mathematics subtests, indicating that students who do well in one area tend to do well in the other.

Table 2

Note.

R1NCE = Vocabulary NCE score
R2NCE = Reading NCE score
M1NCE = Mathematics Concepts
M2NCE = Mathematics Problem Solving
M3NCE = Mathematics Computation
L4NCE = Usage and Expressions NCE score
ATTEND = Attendance rate (total days - unexcused absences / total days)
E_SIZE = English class size
M_SIZE = Math class size

The correlation of 1.00 between English class size and math class size is due to the class sizes being equivalent for 4 - 6 graders.

A small effect for class size and student achievement was suggested by the small negative correlations between the ITBS subscores and english and math class sizes (indicated in bold). That is, smaller class sizes are associated with larger ITBS scores. The largest correlation was between class size and the M3NCE (computation) subtest of the ITBS. This may be a result of students in smaller classes getting more time to practice mathematics computation. However, any inferences should be made with caution since only four percent of the variance in M2NCE scores can be explained by class size, and even less for the other subscores. Except for the correlation between class size and mathematics computation (M3NCE) attendance rate was a better predictor of academic achievement as measured by the ITBS.

Table 3 presents the same analysis for 7 - 12 graders with the addition of course grades for math and english. The results like those in Table 2 indicate a large amount of shared variance within the english and math portions of the ITBS. There was also a significant relationship between most of the math and english subtests.

Unlike the results for the 4 - 6 graders, for grades 7 - 12 the relationship between class size and performance on the ITBS was opposite from expectation. That is, the positive correlations suggest that increasing class size also increases ITBS scores. Although many of these correlations were significant

(p < .05) this was largely due to the large sample size. With smaller sample sizes these same correlations would likely not be significantly different from zero.

Table 3

Note.

The best predictors of performance on the ITBS were course grades. The correlations associated with mathematics computation (M3) may be considered unreliable due to the small number of students in this age group taking that particular subtest (n=47). For example, the correlation between English class size and mathematics computation (M3) of -.98 is likely spurious.

In order to make the correlation tables easier to analyze, subscores were collapsed according to content areas. That is, the english score represented the mean NCE score for R1NCE, R2NCE, and L4NCE. The math score represents the mean NCE score for the mathematics subtests. This procedure was also indicated by the degree of colinearity between these subtests. The following table summarizes the results of this analysis for grades 4-6.

Table 4

Note.

It can be seen in Table 4 that the best predictor of performance on the ITBS was attendance rate. These correlations were positive indicating that increases in attendance rate are accompanied by increases in ITBS scores. The next best predictor of performance on the ITBS was class size. The negative correlations again indicate that as class sizes are reduced, ITBS scores are increased. However, these coefficients were quite small in magnitude. The largest coefficient being -.06 between english class size and the english portion of the ITBS. This correlation indicates that only 0.3 percent of the variance in the english portion of the ITBS can be explained by english class size, compared to approximately 5 percent explained by attendance rate. The correlation between the mathematics portion of the ITBS and math class size was roughly equivalent at -.05. The larger correlations found previously between mathematics computation (M3NCE) and math class size (-.19) was washed out by combining the other mathematics subtests. This suggests that the positive effects of reduced class size may be highly specific in terms of student achievement.

Results of the same analysis for grades 7 - 12 can be seen in Table 5 with the addition of math and english course grades.

Table 5

Note.

The results found in Table 5 show the best predictors of performance on the ITBS were grades in math and english. The correlation between math grades and the mathematics portion of the ITBS was .48, indicating that 23 percent of the variance in mathematics ITBS scores is explained by math grades. Again, the correlations between class size and performance on the ITBS were all positive, suggesting that as class sizes increase, ITBS scores tend to increase as well. The results of this analysis carried out on 7 - 12 graders seem counter-intuitive. One possible explanation is that slower students may be placed into smaller classes in order to maximize one-on-one time with the teacher. If these students tend to do poorly relative to other students on the ITBS this could at least partially account for the positive correlations obtained between class size and student achievement.

Table 5 also contains information on the relationship between course grades and attendance rate. The correlation between attendance rate and english grades was .37. This correlation indicates that approximately 14 percent of the variance in grades can be accounted for by attendance rate.

The final form of analysis was to run multiple stepwise regression with performance on the ITBS as the dependent variable. This procedure partials the shared variance out of the predictor variables before entering them into the equation. This allows one to analyze the unique contribution to prediction of each predictor variable. In order to at least partially correct for the possibility mentioned above of slower students being assigned to smaller classes, only class sizes above 10 were used in the current analysis. Table 6 presents a summary of a multiple regression with performance on the mathematics portion of the ITBS as the dependent variable with attendance rate and math class size as the predictor variables.

Table 6

The same analysis was again carried out on the same population, this time with the english portion of the ITBS as the dependent variable.

The results of Table 7 show essentially the same pattern of results as those of Table 6, where the dependent variable was math achievement. For english achievement the best predictor was attendance rate, with a beta weight of .223. The B weight of 1.09 indicates that a 10 percent increase in attendance rate should result in an additional 11 points on the average ITBS math score. The relationship between english class size and english achievement was essentially the same as that found for math class size and

Table 7

mathematics achievement. The multiple-R of .23 in the present analysis compared to .17 in Table 6 is largely due to the increased contribution of attendance rate in predicting english achievement.

The same multiple regression analyses were carried out on students in grades 7 - 12 with the addition of course grades. The results of the multiple regression analysis for grades 7 - 12 can be seen in Tables 7 and 8.

Table 8

As can be seen the multiple-R of .50 is more than twice as large as that obtained with forth through sixth graders. This may be due to math grades being the best predictor of math achievement, data which unfortunately was not available for forth through sixth graders. Again, the positive B weights indicate that larger class sizes are associated with greater mathematics achievement, even though class sizes less than 10 were not included in the analysis.

The same analysis was then carried out with average scores on the english portion of the ITBS as the dependent variable.

As can be seen in Tables 8, the results are quite similar to those of Table 7 where mathematics achievement was the dependent variable. The present analysis produced the same pattern of results with english grades being the best predictor of english achievement, followed be english class size, and attendance rate being the least effective predictor.

Table 9

Consistent with all previous analyses the relationship between class size and achievement was opposite from expectation for middle and high school students.

Comparison of Effects for White/Anglo Versus Minority Students

Previous research has suggested that reducing class size may have a differential impact on white/anglos versus minority students (e.g., Finn & Achilles, 1990). To investigate this possibility separate analyses were carried out on white/anglo and minority students. Following the same procedure used throughout this study a bivariate correlation matrix was produced with all variables included in the analysis. The results of this analysis can be seen in Tables 10.

As shown in Tables 10, class size appeared to have an impact on student achievement as indicated by the negative correlations between class size and all subtests of the ITBS. Although most of the coefficients were small in magnitude the correlation of -.29 between class size and mathematics computation (M3NCE) was the largest effect found for class size. Class size accounted for over 8 percent

of the variance in mathematics computation scores. The correlation between class size and mathematics computation was based on 289 students making the statistic fairly reliable. Attendance rate appeared to have less of an impact on achievement scores for white/anglos than it did for the entire population. This may be at least partially explained be the decreased variability in attendance rate for white/anglos compared to the entire population. The standard deviation of attendance rate for the entire population was 4.3 percent compared to 3.3 percent for white/anglos alone. Except for the differences just noted, the pattern and magnitude of the coefficients was quite similar to those found in the entire population.

Table 10

Note.

The next step was to compare the results of Tables 10 with those of Table 11 that analyzed white/anglo students in grades 7 - 12. The results of Table 11 show essentially the same pattern of results as those found in Tables 3 where the population consisted of both white/anglos and minorities from grades 7 - 12. Perhaps the most salient difference between Table 3 and Tables 11 involved the correlations between class size and the subtests of the ITBS. In Table 3 all coefficients were positive and significant (p < .05). In Tables 11 one can see that several coefficients were negative, but not significant (p < .05). The only coefficients that reached significance were for math class size and reading (R2), and for math class size and mathematics

concepts (M1). These correlations were positive, indicating that larger class sizes were associated with higher scores on subtests of the ITBS. The dashed lines in Tables 11 indicated that there were too few students to calculate coefficients for these variables. The remaining coefficients associated with mathematics computation are probably unstable due to the small number of students in these cells.

To stay consistent with the pre-established procedure would require presenting the correlation results for all predictor variables correlated with the combined scores of the ITBS for grades 4 - 6, and then for grades 7 - 12. However, since these tables contain little additional information beyond that found in the expanded tables they will not be presented. In addition, the prediction of the combined ITBS scores is presented in the summary tables of the multiple stepwise regression analyses.

Table 11

Note.

Tables 12 and Table 13 present summary statistics of the multiple regression analyses for predicting mathematics and english achievement of white/anglo students in grades 4 - 6, respectively. These results are consistent with those found for the entire population including white/anglos and minorities.

A comparison of Tables 12 and 13 reveal the same pattern of results. Attendance rate was the best predictor of both the mathematics and english portions of the ITBS. Class size explained approximately equal amounts of variance in both the english and mathematics portions of the ITBS. The negative B weights greater than 5 indicate that for every additional 10 students in a class one could expect a decrease of approximately 5 points on the ITBS scores.

Table 12