# The relationship between evaluation scores and class size in lower level mathematics classes

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This study investigated to see if a relationship occurs between increased class sizes and mean evaluation scores regarding the instructors' overall effectiveness in five lower-level mathematics classes at Texas Tech University. In addition, we considered whether a relationship exists between the number of students who took the evaluation and the mean evaluation scores. The thesis looked at both of these by class and by faculty from 2005 to 2010 of the fall semesters. We first analyzed the data from a frequentist point of view. We calculated the Pearson and Spearman correlations for each of the relations in question and examined the p-values associated with it, by class and by faculty for each year. The majority of the Pearson and Spearman correlations indicated a weak relationship, and the majority of the p-values were not significant at the 0.05 level. However, we found four cases that were significant for each relation. Due to the small sample sizes available, we also used Monte Carlo simulations to find exact p-values for the Pearson and Spearman correlations, by class and by faculty for each year. These Monte Carlo simulations yielded similar results for the exact p-values, as the ones obtained by assuming that the variables involved are normally distributed. For each class, we performed linear regressions between the years and the mean evaluation scores, by using the ordinary least squares (OLS) method and least absolute deviation (LAD) method, to see if a significant coefficient of the slope occurred. These methods of regression analyzed how the mean evaluation scores for each class change over six years. With both of these methods, we examined the 95% confidence limits for the parameter slope (coefficient of year) in order to see if there is a significant coefficient of the slope. A significant negative slope, in College Algebra and (marginally for) Statistical Methods, was observed under the OLS method. Yet, under the LAD method, there were no significant coefficient for the slope in any class, based on the 95% confidence limits. Later, we evaluated the same data using Bayesian linear regression. For each regression, we used a multivariate normal-inverse gamma hierarchical model for the three parameters of the model (the intercept, the slope and the common variance of the errors). We defined a slope of a regression to be significant in the positive direction if the posterior probability of the slope being positive (given the data) was greater than 90% and a slope to be significant in the negative direction if the posterior probability of the slope being negative was less than 10%. In order to find significant positive or negative slopes for the posterior distribution of the slope parameter, we considered three different joint prior distributions. From the Bayesian linear regression, there were nine cases of significant slopes between each of the relationships of interest.