Cochran–Mantel–Haenszel Test for Repeated Tests of Independence: An Application in Examining Students’ Performance

Abstract

From the result of graduate of ten departments in Faculty of Science, University of Ilorin for 2011/2012 academic session, data on final cumulative grade point average (Final Grade); department (ten departments of the faculty); age at entry (below or 20 years and above 20 years) and sex (male and female) are analyzed using Cochran-Mantel-Haenszel statistics. Odds of a student graduating with Second Class Upper and above (0.5270) is about half of graduating with Second Class Lower and below. This implies that the final grade is approximately symmetrical about two groups. The first group are those with Second Class Lower and below (Low Grade) while the other is for those with Second Class Upper and above (High Grade). Breslow-Day and Tarone’s statistics show that the null hypothesis of homogeneity of odds ratio across the departments is not rejected for both age at entry and sex. This implies that the odds ratio across the ten departments (relating to age at entry & final grade and sex & final grade) are all equal. Cochran’s and Mantel-Haenszel statistics reveals the final grade of students (Low Grade or High Grade) is not associated with both sex and age students at entry. The odds in favour of a student whose age is less than 20 years graduating with Low Grade (Pass, Third Class, and Second Class Lower) is 0.865 while it is 0.670 for male students graduating with lower grade.

Keywords: Test of Independence, Students’ Performance, Cochran-Mantel-Haenszel