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Given that previous findings on the social distribution of the effects of small classes have been mixed and inconclusive, in the present study I attempted to shed light on the mechanism through which small classes affect the achievement of low- and high-achieving students. I used data from a 4-year large-scale randomized experiment (project STAR) to examine the effects of small classes on the achievement gap. The sample consisted of nearly 11,000 elementary school students who participated in the experiment from kindergarten to grade 3. Meta-analysis and quantile regression methods were employed to examine the effects of small classes on the achievement gap in mathematics and reading SAT scores. The results consistently indicated that higher-achieving students benefited more from being in small classes in early grades than other students. The findings also indicated that although all types of students benefited from being in small classes, reductions in class size did not reduce the achievement gap between low and high achievers.

Multilevel models are widely used in education and social science research. However, the effects of omitting levels of the hierarchy on the variance decomposition and the clustering effects have not been well documented. This paper discusses how omitting one level in three-level models affects the variance decomposition and clustering in the resulting two-level models. Specifically, I used the ANOVA framework and provided results for simple models that do not include predictors and assumed balanced nested data (or designs). The results are useful for teacher and school effects research as well as for power analysis during the designing stage of a study. The usefulness of the methods is demonstrated using data from Project STAR. -- Variance decomposition ; nested designs ; clustering

Thus far researchers have focused on computing average differences in student achievement between smaller and larger classes. In this study, the author focus on the distribution of the small class effects at the school level and compute the inconsistency of the small class effects across schools. The author use data from Project STAR to estimate small class effects for each school on mathematics and reading scores from kindergarten through third grade. Then, all school estimates were combined to calculate an overall weighted average. The results revealed that a large proportion of the school-specific small class effects are positive, while a smaller proportion of the estimates are negative. Although students benefit considerably from being in small classes in many schools, in other schools being in small classes is either not beneficial or is a disadvantage. Small class effects were inconsistent and varied significantly across schools in all grades indicating a small class by school interaction.

In experimental designs with nested structures, entire groups (such as schools) are often assigned to treatment conditions. Key aspects of the design in these cluster-randomized experiments involve knowledge of the intraclass correlation structure, the effect size, and the sample sizes necessary to achieve adequate power to detect the treatment effect. However, the units at each level of the hierarchy have a cost associated with them and thus researchers need to decide on sample sizes given a certain budget, when designing their studies. This article provides methods for computing power within an optimal design framework that incorporates costs of units in all three levels for three-level cluster-randomized balanced designs with two levels of nesting at the second and third level. The optimal sample sizes are a function of the variances at each level and the cost of each unit. Overall, larger effect sizes, smaller intraclass correlations at the second and third level, and lower cost of Level 3 and Level 2 units result in higher estimates of power.

This study examines high school effects on the labor market success of young adults, above and beyond individual and family characteristics. We employ data from two longitudinal, nationally probability samples: the National Longitudinal Study and the High School and Beyond study and the 5th and 4th follow-up studies respectively. We employ multi-level models and adjust for selection into the labor force. Our findings reveal that there are differential, enduring school effects on future earnings for individuals attending different schools.

Previous findings from Project STAR have highlighted the benefits of being in small classes in early grades on average. Here, we examined the differential "value-added" effects of small classes across the achievement distribution. We find that once previous grade achievement and small class membership are controlled for, small class effects are by and large insignificant. Although high-achievers benefited more from small classes in third grade reading, overall, the differential small class effects were not systematic. Findings from longitudinal analyses failed to show that being in small classes for two or more years is as beneficial as being in small classes for only one year. Although the cumulative small class effects are positive, significant, and meaningful in magnitude, they do not indicate which grade (or grades) are the most important.