Utilizing Graeco-Latin Square Design to Improve Teaching and Learning Outcomes in Secondary Education

Abstract

This study applies the Graeco–Latin square experimental design, an extension of the 
classical Latin square design, to evaluate the joint effects of multiple instructional 
factors on students’ academic performance while controlling for nuisance variability. The 
Graeco–Latin square framework enables the simultaneous investigation of four factors—
rows, columns, Latin treatments, and Greek treatments—without confounding, thereby 
ensuring orthogonality and efficient estimation of main effects within a balanced design 
structure. The empirical application focuses on six classes of students exposed to six 
subjects, taught by six different teachers employing six distinct teaching methods 
across six instructional periods. Academic performance was operationalized using 
students’ failure rates, and the dataset was analyzed using Minitab 17. Descriptive 
statistics revealed that Senior Secondary 3 (SS3) students exhibited the best 
performance, with the lowest mean failure rate (21.33%). Subjects taught by Aishatu 
(Biology and Basic Science) recorded comparatively lower failure rates (22.67%), while 
Method C (deductive teaching approach) yielded improved outcomes (21.91%). 
Additionally, the sixth instructional period (ζ) demonstrated the most favorable 
performance, with a minimum average failure rate of 19.25%. Inferential analysis using 
analysis of variance (ANOVA) indicated that the p-values associated with the four 
factors—classes (0.594), teachers (0.646), teaching methods (0.571), and instructional 
periods (0.604)—exceeded the conventional significance threshold (α = 0.05). 
Consequently, the null hypotheses were not rejected, suggesting that variations across 
these factors are statistically insignificant. The findings imply that, within the 
experimental constraints, no single factor exerts a dominant influence on student 
performance, highlighting the robustness of the instructional system under study.