Chi-squared tests

Abstract

This article describes the range of applications of chi‐squared tests via five illustrative examples. The first of these applies chi‐squared approximations to randomization‐based nonparametric rank tests for a randomized clinical trial concerning heart disease. The second example illustrates three types of analyses for a three‐way contingency table based on a clinical trial for mastitis in dairy cows. The first analysis implements randomization model methods, while the other two analyses use chi‐squared tests pertaining to functions of proportions and related statistical models for testing linear and log‐linear hypotheses. Alternative chi‐squared tests for goodness‐of‐fit of logistic regression models via maximum likelihood methods for a quantal response animal study are illustrated in the third example. Example 4 describes the modeling of the proportion of hours women had little or no obstetric pain via weighted least squares methods and the chi‐squared tests used to assess contrasts of specific interaction effects. The final example applies Wald chi‐squared statistics and the fitting of linear models to a repeated measures observational study for two diagnostic procedures with a dichotomous outcome at two time points.