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# Chapter 10: Chi-Square

Difficulty Level: Advanced Created by: CK-12

## Introduction

In previous chapters, we learned that there are several different tests that we can use to analyze data and test hypotheses. The type of test that we choose depends on the data available and what question we are trying to answer. We analyze simple descriptive statistics, such as the mean, median, mode, and standard deviation to give us an idea of the distribution and to remove outliers, if necessary. We calculate probabilities to determine the likelihood of something happening. Finally, we use regression analysis to examine the relationship between two or more continuous variables. We performed hypothesis tests on proportions, means, and for correlation.

In this chapter, you will learn about a very useful distribution - the χ2\begin{align*}\chi^2\end{align*} (chi-squared) distribution. This distribution is useful because it allows us to test theories about categorical data, for which the normal and Student's t distributions do not apply. The chi-squared distribution also provides us with a method to test for the variance, or standard deviation, of a normal distribution, which we have not yet learned how to do.

## Summary

In this chapter, students will learn about the χ2\begin{align*}\chi^2\end{align*} distribution. They will learn how to use the goodness-of-fit, independence and homogeneity tests on categorical data using contingency test. Finally, students will learn how to test a hypothesis about a variance, or standard deviation using the chi-squared distribution.

Sep 26, 2013