Does Classroom Size Affect Academic Achievement?
A multilevel statistical analysis of Tennessee's Project STAR dataset, examining the causal effect of small class sizes on student SAT performance across kindergarten through 3rd grade.
The Tennessee Project STAR (Student/Teacher Achievement Ratio) study is a landmark four-year randomized controlled trial conducted by the Tennessee State Department of Education (1985–1990), tracking ~11,600 students across 79 public schools from Kindergarten through Grade 3. Students were randomly assigned to one of three class types: Small (13–17 students), Regular (22–25), or Regular with Aide.
Methods
Exploratory Data Analysis — Density plots and longitudinal score trends confirmed that the average SAT composite score (math, reading, listening, word skills) is more stable than any individual subject. Caterpillar plots revealed significant between-school heterogeneity, motivating a multilevel model.
Linear Mixed-Effects Model (Multilevel Model) — To account for the nested structure of students within teachers within schools, we specified a mixed-effects model with student-level fixed effects (class type, gender, race, free-lunch status) and nested random intercepts at the teacher and school levels:
\[Y_{ijk} = \beta_0 + \beta_1\text{ClassType} + \beta_2\text{Covariates} + u_i + v_{ij} + \epsilon_{ijk}\]Variance Decomposition & ICC Analysis — ~27% of total score variance was attributable to the classroom and school hierarchy (School ICC: 15.6%, combined Teacher+School: 26.7%), validating the multilevel framework.
Robustness Checks — Three nested specifications (OLS → Random Effects → Full Mixed Model) yielded consistent estimates of the small-class advantage (−5.4 to −5.7 points for regular vs. small), confirming the result is not sensitive to modeling assumptions.
Time Stability Analysis (Grades K–3) — The small-class advantage was estimated separately for each grade, revealing a “fade-out” pattern: strongest in Grade 1 (−11.4 pts), gradually declining through Grade 3 (−4.0 pts), but remaining statistically significant throughout.
Key Findings
- Small classes outperform regular classes by approximately 5 points on the composite SAT score in Kindergarten, even after controlling for teacher and school heterogeneity.
- Socioeconomic status (free lunch eligibility) is the strongest predictor of achievement (16.7 pt gap), yet the small-class advantage holds for all subgroups.
- The treatment effect is most pronounced in Grade 1 and gradually fades, consistent with the Project STAR literature.
Team: Liang-Yin Tao, Jian Lin, Elliot Weisberg, Xiaoyi Liu
Course: STA 207 · Winter 2026
Data: Harvard Dataverse — Project STAR