Publication Date

Spring 2022

Advisor(s) - Committee Chair

Reagan Brown (Director), Katrina Burch, J. Farley Norman

Degree Program

Department of Psychological Sciences

Degree Type

Master of Science


Department of Psychological Sciences Western Kentucky University There are two options to estimate a range of likely values for the population mean of a continuous variable: one for when the population standard deviation is known and another for when the population standard deviation is unknown. There are seven proposed equations to calculate the confidence interval for the population mean of a dichotomous variable: normal approximation interval, Wilson interval, Jeffreys interval, Clopper-Pearson, Agresti-Coull, arcsine transformation, and logit transformation. In this study, I compared the percent effectiveness of each equation using a Monte Carlo analysis and the interval range over a range of population means to determine the accuracy of the equations. Results indicated that the Agresti-Coull equation and Clopper-Pearson equation are the most successful at locating the population proportion at least 95% of the time across the range of population proportions and that the Agresti-Coull equation has the narrower interval range.


Applied Statistics | Industrial and Organizational Psychology | Statistical Models