Assessing the impact of Ordinary Level Grades on the Cumulative Grade Point Average of First Year University Students (A Factorial Design Approach)

Abstract

The purpose of this work is to model the Cumulative Grade Point Average (CGPA) of first year engineering students of a private university in southwestern Nigeria using the Ordinary level (O’ level) grades in mathematics, physics, and chemistry as factors. The choice of the three subjects was due to the fact that virtually all the courses taken in first year by engineering students require a solid background in these three subjects. Duplicate samples were randomly selected from a population stratified into all possible factor levels The O’ level grades were converted to scaled variables (as typically done in factorial design) and used as the model matrix of six levels of a three-factorial design. Three orthogonal statistical models were fitted namely; first order, interaction and response surface models using the Ordinary Least Squares (OLS) Estimators. The model of best fit was identified and used to obtain the combination of ordinary level grades that maximized and minimized first year CGPA. The results showed that the three models were statistically significant with each having p-value < 0.001. Response Surface Model provided a better fit in terms of the R^2=47.0% and the RMSE =0.320. The combination of grades that maximizes and minimizes first year CGPA were A1 in all the three subjects and A2 in mathematics, C6 in physics and chemistry, respectively. The results of this work suggested that a large percentage of extraneous factors is affecting the CGPA of first year engineering students in this university due to the relatively small values of the coefficient of determination returned by the three models