• Home
• Fundamentals
  Introduction What is statistics Terms connected to data Measurement levels Significance SPSS basics
• One variable
  Introduction a binary variable a nominal variable an ordinal variable a scale variable
• Two variables - unpaired
  Introduction binary vs binary binary vs ordinal binary vs scale nominal vs nominal nominal vs ordinal nominal vs scale ordinal vs ordinal ordinal vs scale scale vs scale
• Two variables - paired
  Introduction two nominal two ordinal two scale
• 3+ variables - paired
  Introduction 3+ binary 3+ ordinal 3+ scale
• Distributions
  Introduction Binomial Bivariate Normal Chi-Square (Standard) Normal Student t Wilcoxon (Signed Rank)
• Search

Multiple paired ordinal variables

Test

After we had a close look at the survey data, we would like to know what this means for our population. We could ask when we have multiple paired ordinal variables: Are there any differences between the results?

The test used to answer the question is usually a Friedman test (Friedman, 1937, 1939). This can be seen as an extension of the Wilcoxon signed rank test (although it is more an extension of the sign test). Where the Wilcoxon signed rank test is limited to two variables, the Friedmann test is an extension which will test all variables in one go.

In the example data the result of the Friedman test is a test statistic of 49.786. The chance of obtaining such a test statistic, or even bigger one if there wouldn't be any differences in the population, is given by the significance of the test, which in the example is .000. This is very low, and therefor very unlikely. The conclusion would then be that most likely in the population not all variables would have the same average ranking. The test results could than be reported as something like:

The Friedman test indicated that there are differences between the average ranks among the seven different questions about the teacher, χ²(6, N = 52) = 49.79, p < .001.

Of course we would then like to know, which variables had a different average ranking, which we'll discuss in the next section.

Note that Iman and Davenport (1980) showed that the original Friedman test is too conservative and devised an extension based on the F-distribution (Trawinski, Smetek, Telec, & Lasota, 2012, p. 871).

3+ Ordinal variables

Introduction

Impression

Visualisation

Omnibus test

Post-hoc test

Effect size

Reporting

Google adds