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# Chapter 12: Non-Parametric Statistics

Difficulty Level: Advanced Created by: CK-12

## Introduction

In previous chapters, we discussed the use of the normal distribution, Student's t\begin{align*}t\end{align*}-distribution, and the F\begin{align*}F\end{align*}-distribution in testing various hypotheses. With each of these distributions, we made certain assumptions about the populations from which our samples were drawn. Specifically, we made assumptions that the underlying populations were normally distributed and that there was homogeneity of variance within the populations. But what do we do when we have data that are not normally distributed or not homogeneous with respect to variance? In these situations, we use something called non-parametric tests.

These tests include tests such as the sign test, the sign-ranks test, the ranks-sum test, the Kruskal-Wallis test, and the runs test. While parametric tests are preferred, since they are more powerful, they are not always applicable. In this chapter, you will examine situations in which we would use non-parametric methods and the advantages and disadvantages of using these methods.

Chapter Outline

## Summary

This chapter concludes the course by introducing a series of tests that are utilized in non-parametric situations, including: the sign test, rank sum test, Kruskal Wallis test, runs test, and sign rank test.

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