After collecting the data, it was analyzed using both a t-test for independence and regression analysis.
The first statistical analysis divided our sample into two groups: Group One, which had a class size of 50 or below, and Group Two, which had a class size of 100 or above. As we were only interested in the largest and smallest classes, class sizes of 51 – 99 were overlooked for this analysis. The mean of Group One was 77.82%, over 5% higher than the mean of Group Two, which was 72.26% (Table 2). The t-test that was performed returned a t-value of 5.406. Because we obtained a t-statistic that was higher than the t* multiplier of 1.699 that correspond to our significance level and sample’s degree of freedom, we rejected the null hypothesis. As expected, there turned out to be a statistical difference between the two groups’ parameters (class average).
One important observation found in Table 1 confirms Bandiera, Larcinese, and Rasul’s (2010) previous findings that the impact of class size on academic performance only becomes significant at the two ends of extreme. Our data shows that many classes with less than 20 students achieve some of the highest averages sampled in high 80’s and low 90’s. On the contrary, only 1 class out of 30 with more than 100 students achieved an average above 80%. The rest are all 60’s and 70’s.
The regression analysis was performed on the entire sample, without dividing into two groups or discarding any data. It implies that there is a negative correlation between the class size and average student score (Table 3). When the data for our entire sample is plotted, the trend becomes even more evident (Graph 4). The line of best fit has a slope of -0.055 and a negligible p-value. The average of residuals is very close to 0 (Graph 5). As a result, we failed to reject the alternative hypothesis and instead, we rejected the null hypothesis, which states that there is no relationship between the class size and academic performance. This means the our result confirms Becker and Powers’s (2001) findings that a negative correlation between class enrollment and students’ academic performance.
Regression analysis also reveals some interesting characteristics to the data. A regression analysis of only Group One (50 and under) and Group Two (100 and over) shows that the slope observed in the entire sample exists in Group One, but is heavily reduced in Group Two (Graph 6). Tightening the criteria of Group Two to 120+ students increases the slope, but this suggests that either the relationship between class size and average score is less linear at higher class sizes, or that our metrics for determining large and small class size need to be revised.
In terms of faculties, scatterplots of the sample (Graph 4) show that a definite trend exists. However, each faculty deviates from the trendline by differing amounts, with Science showing the most uniform distribution and Music having the most diverse (Graph 7). Moreover, the class size distributions of the faculties also differ significantly, with the Music faculty in particular being largely composed of small classes (Table 1). This is natural, of course, as the Music faculty is the smallest faculty and possesses a number of unorthodox courses. This suggests that although the negative correlation between class size and average grade is representative of the university as a whole, the specific slope found in our sample may not apply to all faculties equally due to natural variations in course structures.