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# Chapter 8Statistical Tests for Categorical Data

As indicated elsewhere in this book, a major part of statistical analysis is the assessment of the independence of two or more variables. The t test assesses the independence of two variables, one measured on a numerical scale and the other measured on a categorical scale that takes only two values. Analysis of variance (ANOVA) assesses the independence of two or more variables. With ANOVA, one variable is measured on a numerical scale and the others are measured on categorical scales that may take on any number of values, although typically the number of values will be limited to fewer than five or six. Regression assesses the independence of two or more variables, all of which can be measured on a numerical scale. The chi-square statistic is a statistical analysis that can be used to establish the independence of two or more variables, each of which is measured on a categorical scale.

## 8.1 Independence of Two Variables

Chapter 5 introduced the subject of independence of two variables. There it was noted that independence could be thought ...

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