Nonparametric Statistics: A Step-by-Step Approach, 2nd Edition

CHAPTER 2Testing Data for Normality

2.1    Objectives

In this chapter, you will learn the following items:

• How to find a data sample's kurtosis and skewness and determine if the sample meets acceptable levels of normality.
• How to use SPSS^® to find a data sample's kurtosis and skewness and determine if the sample meets acceptable levels of normality.
• How to perform a Kolmogorov–Smirnov one-sample test to determine if a data sample meets acceptable levels of normality.
• How to use SPSS to perform a Kolmogorov–Smirnov one-sample test to determine if a data sample meets acceptable levels of normality.

2.2    Introduction

Parametric statistical tests, such as the t-test and one-way analysis of variance, are based on particular assumptions or parameters. The data samples meeting those parameters are randomly drawn from a normal population, based on independent observations, measured with an interval or ratio scale, possess an adequate sample size (see Chapter 1), and approximately resemble a normal distribution. Moreover, comparisons of samples or variables should have approximately equal variances. If data samples violate one or more of these assumptions, you should consider using a nonparametric test.

Examining the data gathering method, scale type, and size of a sample are fairly straightforward. However, examining a data sample's resemblance to a normal distribution, or its normality, requires a more involved analysis. Visually inspecting a graphical representation of a sample, such ...