Class size reduction (CSR) has been of intense debate worldwide. From a policy perspective, class size is a school resource and class size reduction policies bear important financial implications. Therefore, although class size could be easily manipulated without disturbing the school and classroom daily routine, it can be expensive. From an education perspective, the classroom where deliberate teaching and learning activities take place is a setting of the utmost importance in schools that involves teachers and students. As class size is located within the instructional dynamic, class size research is located within the scope of educational research that is worth of much attention and investigation (Ball & Forzani, 2007). In principle, CSR signals education quality and is hypothesized to enable higher quality instruction and learning. Specifically, the theoretical framework is that CSR should reduce disciplinary management, empower more effective teaching, and increase attention and individualized instruction, which subsequently would result in increased student learning and performance.

Meta-analytic reviews on class size effects have been scarce. An early meta-analytic review of 77 studies including small-scale matched designs and randomized controlled trials (RCTs) suggested some positive effects of small class size (i.e., less than 20 students in a classroom) on academic performance (Glass & Smith, 1979). A reanalysis of these studies and other studies, however, reported much smaller class size effects (Slavin, 1989). The econometric studies dating from the 1960s have generated mixed findings (Hanushek, Mayer, & Peterson, 1999). The single large-scale randomized experiment of Student Teacher Achievement Ratio (i.e., Project STAR) generated the most pronounced evidence of class size effects on student achievement and exerted a huge impact on education policy (Hedges & Schauer, 2018). In particular, findings from Project STAR suggested that students in smaller classes have on average significantly higher achievement than students in larger classes and that the effects are even long-lasting (Finn & Achilles, 1990; Nye, Hedges, & Konstantopoulos, 1999).

During the last 20 years or so, many quasi- experimental studies have been conducted via econometric methods to facilitate causality of class size effects especially in European countries (e.g., Angrist & Lavy, 1999; Hoxby, 2000; Wößmann & West, 2006). The results of these studies have not been systematically reported or analyzed in meta-analytic reviews. Thus far, to our knowledge, there are only two recent meta-analytic studies about the effects of class size on student achievement. The first study was conducted by Goldstein and colleagues (2000) who used multilevel models to analyze the data (Goldstein, Yang, Omar, Turner, & Thompson, 2000). The focus of that study however was methodological rather than on the substantive class size effect per se and therefore, it was not a comprehensive or systematic meta-analytic review. The second study analyzed samples of studies of early education program evaluations published from 1960 to 2007 targeting infants to five-years of age. The results indicated that small classes of 15 students of less had a positive effect on student achievement (Bowne, Magnuson, Schindler, Duncan, & Yoshikawa, 2017). Noticeably, the second meta-analysis study has a narrow scope due to the specific education program and age period.

This paper reports a meta-analytical systematic review of studies that used instrumental variable (IV) and regression discontinuity design (RDD) for causal class size effects. Results suggested that increasing class size has negative, significant effects with a magnitude of about 0.01 standard deviations via using IV sample data (131 effect sizes of 29 studies) and RDD sample data (33 effect sizes of 7 studies). Moderator analyses suggested that the effect is stronger for the academic outcome and possibly more pronounced in elementary grades, but weaker for national representative sample data.

To conduct the systematic review, we used electronic database searches and hand searches of core journals plus search of references in included studies. The databases include EconLit, ERIC, PsycINFO, Web of Science, and ProQuest Dissertations & Theses Global. The library database search followed these steps. First, title search was performed in each database in the time framework of three decades from January 1, 1988 to December 31, 2018 by using the following main keywords: class size*, class-size*, class size reduction, small* class*. The initial search constituted 170, 642, 277, 635, and 317 hits in these five databases respectively. We imported these citations into Endnote to get a total of 1,761 references. After deleting 841 duplicates, 930 references underwent title, abstract and full text screening. We excluded these references due to the following main reasons: (1) using pupil-teacher ratio instead of actual class size, (2) using project STAR and follow-up studies, (3) no statistical methods were applied for causal inference (e.g., HLM model, production function study, quantile regression). We retrieved 39 studies that met the inclusion and exclusion criteria. The review authors critically appraised them and 9 studies were further excluded. Thirty quasi-experimental studies constituted our final sample of studies and used instrumental variables (IV) methods or regression discontinuity designs (RDD). Because our study uses meta-analytic methods to analyze the data derived from the studies, we inspected carefully these 30 studies in our final sample in order to derive the estimated effect-size of class size in each study. Specifically, the effect size was derived using the regression coefficient of class size in the linear model used in each study for each outcome. Because outcomes vary in their measurement scales, we divided the regression coefficient by the standard deviation (SD) of the respective outcome, so that all the effect sizes across studies are in a common metric indicating that a one unit change in class size corresponds to change in outcomes in standard deviation units. The standard error (SE) of the regression coefficient was also rescaled accordingly by dividing the SE by the SD of the respective outcome. To explore the possible sources of variations, we run a meta-regression, in which we coded certain key characteristics of the studies as predictors, namely sampling framework, grade, covariates, outcomes, subjects, and research methods.

This literature search retrieved 30 studies in which there are 29 IV samples that provide 131 effect sizes and 7 RDD samples that provide 33 effect sizes. The studies varied considerably in their sample sizes ranging from 288 to 403,969 students in the IV data and from 67 to 90,434 students in the RDD data. With regard to country, twelve studies (46.7%) used data from Europe including Norway, Denmark, Italy, Sweden, France, UK, Cyprus and Greece. In addition, five studies (16.7%) used data from the U.S., four studies used data from Asia (Japan) and one in Middle East (Israel), and two from South America (Chile and Bolivia). For IV studies, the mean effect size from random-effects multilevel models using robust error variance estimation is -0.010 standard deviations (SDs), p<0.001. The homogeneity test was statistically significant, Q(130) = 356, p < .001 (I2 = 63%), indicating more variability in the observed effect sizes than would be expected from sampling error alone. The confidence interval is [-0.014, -0.005]. With regard to the RDD studies, in multilevel model, the mean effect size is -0.015 SDs, p=0.026. The homogeneity test was statistically significant, Q(32) = 78, p < .0001 (I2 = 59%), and the prediction interval is [-0.014, -0.005]. Several variables were used as predictors in the meta-regression: national sampling framework, elementary grades, student/family covariates only, academic scores, maximum class size rule as instrumental variable, and finally two dummy variables of math and reading with other subject as the reference group. Findings revealed that Achievement outcomes have significantly lower effect size estimates of class size than non-achievement outcomes (0.01 SDs) at the 0.05 level. At the 0.10 level, results suggested that effect size estimates are lower for elementary grades (-0.009 SDs), but higher for national data or national representative data (0.007 SDs).

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