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

CHAPTER 9Test for Randomness: The Runs Test

9.1    Objectives

In this chapter, you will learn the following items:

• How to use a runs test to analyze a series of events for randomness.
• How to perform a runs test using SPSS^®.

9.2    Introduction

Every investor wishes he or she could predict the behavior of a stock's performance. Is there a pattern to a stock's gain/loss cycle or are the events random? One could make a defensible argument to that question with an analysis of randomness.

The runs test (sometimes called a Wald–Wolfowitz runs test) is a statistical procedure for examining a series of events for randomness. This nonparametric test has no parametric equivalent. In this chapter, we will describe how to perform and interpret a runs test for both small samples and large samples. We will also explain how to perform the procedure using SPSS. Finally, we offer varied examples of these nonparametric statistics from the literature.

9.3    The Runs Test for Randomness

The runs test seeks to determine if a series of events occur randomly or are merely due to chance. To understand a run, consider a sequence represented by two symbols, A and B. One simple example might be several tosses of a coin where A = heads and B = tails. Another example might be whether an animal chooses to eat first or drink first. Use A = eat and B = drink.

The first steps are to list the events in sequential order and count the number of runs. A run is a sequence of the same event written one or more times. ...