Principles of Managerial Statistics and Data Science

16Nonparametric Testing

16.1 Introduction

Most of the hypothesis tests performed in this book use ‐tests, ‐tests, or ‐tests. These tests rely on either the population being normally distributed or the sample mean following approximately a normal distribution. These assumptions are sometimes far from reality, and researchers are less willing to make such assumptions when the sample size is small. Furthermore, occasionally it is not reasonable to infer on the population mean (i.e. when there is support for the population having a highly skewed distribution), or it might be necessary to test the probability distribution assumption that has been made. ‐tests, ‐tests, and ‐tests all fall into the category of parametric tests, which rely on a parametric probability distribution for the population or main estimator. Nonparametric tests, also known as distribution‐free tests, either drop the probability ...