Class notes MATH 3450 Principles of Biostatistics Chapter 10

This document explores the mathematical framework for multinomial experiments, which extend the concept of binomial trials to variables with more than two categories. It details three primary types of chi-square ($chi^2$) tests used to analyze categorical data: the goodness of fit test to compare observed data against a theoretical model, the test of independence to evaluate potential relationships between two variables, and the test of homogeneity to determine if different populations share the same distribution. Through various examples—ranging from voter preferences to medical outcomes—the text illustrates how to calculate degrees of freedom, determine expected counts, and interpret p-values to make statistical decisions. Ultimately, the source serves as a practical guide for using tools like the TI-84 calculator and R programming to perform these complex analyses of count data accurately.