Date of Award


Degree Type


Degree Name

Master of Science (MS)


Mathematics and Statistics

Committee Chair(s)

John R. Stevens


John R. Stevens


Adele Cutler


Christopher D. Corcoran


The effect of air quality on public health is an important issue in need of better understanding. There are many stakeholders, especially in Utah and Cache Valley, where the poor air quality as measured by PM 2.5 levels and consequent inversions can sometimes be the very worst in the nation. This project focuses on comparing two statistical methods used to analyze an important air quality data set from the Greenville Air Quality Study, focusing on a lung function response variable. A linear mixed model, with a random factor for subject, gives slope estimates and their significance for predictor variables of interest, especially PM 2.5 levels. The method of meta-regression in this analysis is extended from looking at multiple studies to looking at multiple subjects from the single air quality study and the effect of PM 2.5 on their lung function separately, finally combining the results using a model where the slope estimates for PM 2.5 act as the response. With other predictors mean-centered, this meta-regression allows for interpretation of the model intercept as the overall mean effect size of PM 2.5 on lung function. Both statistical methods were studied in depth in order to apply them appropriately to the data set. The primary goal of applying both of these methods, aside from comparing their results, was to determine what significant role, if any, the PM 2.5 pollution levels played in the lung function of students after a 20 minute outdoor recess, therefore validating the results of previous analyses of the data.