Statistical Method for Comparing Two Proportions

This publication is a technical report that details the statistical method for comparing two proportions in populations with binary outcomes, such as success or failure. It outlines the process of determining whether the proportions are statistically different by using a two-proportion test. The report begins with an introduction to the concept of comparing proportions, followed by an example involving high school students and smoking rates in two different cities. It provides the necessary calculations, including sample sizes, successes, and failures for each population. The document explains the hypotheses involved in the test, the calculation of the z statistic, and the interpretation of the results, including confidence intervals and p-values. It also discusses the pooled estimate of proportions and presents another example involving a survey on cigarette taxation. The report concludes with considerations for small sample cases and alternative testing methods, ensuring a comprehensive understanding of the statistical approach to comparing two proportions.