A 3x3 LATIN SQUARE COUNTERBALANCED DESIGN FOR COMPARING INSTRUCTIONAL TREATMENTS IN PHYSICS EDUCATION

Abstract

Conventional quasi-experimental designs in physics education are prone to bias due to differences in characteristics between classes, order-of-instruction effects, and the influence of prior treatments. This study introduces and demonstrates a balanced 3×3 Latin Square design as an alternative methodological framework to enhance internal validity in physics education experiments based on in Indonesia. Using a quasi-experimental rotation at SMAN 4 South Tangerang (N = 102; three 11th-grade classes), each class received three instructional treatments in rotation: (A) Problem-Based Learning (PBL) aided by Zep Quiz, (B) Zep Quiz without PBL, and (C) conventional lectures, on three subtopics of Dynamics of Motion. Students’ critical thinking skills were assessed using an instrument based on Facione’s six indicators. Data were analyzed using prerequisite tests (Shapiro-Wilk, Levene, Mauchly), Repeated-Measures ANOVA, Latin Square ANOVA, and a carryover effect test. Three main findings emerged: (1) a significant period effect (p = 0.028, η² = 0.035) indicated a gradual increase in scores over time; (2) the class factor accounted for the majority of the variance (F = 153.051, p < 0.001, η² = 0.736), far exceeding the effect of the learning method (F = 0.678, p = 0.058, η² = 0.005); and (3) the carryover effect was not significant (F = 0.000, p = 1.000), confirming the effectiveness of rotation in minimizing cross-treatment contamination. These findings establish the 3×3 Latin square design as a practical and bias-controlled framework for research on physics education in whole-class settings.