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

CHAPTER 5Comparing More Than Two Related Samples: The Friedman Test

5.1    Objectives

In this chapter, you will learn the following items:

• How to compute the Friedman test.
• How to perform contrasts to compare samples.
• How to perform the Friedman test and associated sample contrasts using SPSS^®.

5.2    Introduction

Most public school divisions take pride in the percentage of their graduates admitted to college. A large school division might want to determine if these college admission rates are changing or stagnant. The division could compare the percentages of graduates admitted to college from each of its 10 high schools over the past 5 years. Each year would constitute a group, or sample, of percentages from each school. In other words, the study would include five groups, and each group would include 10 values.

The samples in the example are dependent, or related, since each school has a percentage for each year. The Friedman test is a nonparametric statistical procedure for comparing more than two samples that are related. The parametric equivalent to this test is the repeated measures analysis of variance (ANOVA).

When the Friedman test leads to significant results, then at least one of the samples is different from the other samples. However, the Friedman test does not identify where the difference(s) occur. Moreover, it does not identify how many differences occur. In order to identify the particular differences between sample pairs, a researcher might use sample contrasts, ...