# Goodman and Kruskal's gamma using SPSS Statistics

## Introduction

Goodman and Kruskal's gamma (*G* or γ) is a nonparametric measure of the strength and direction of association that exists between two variables measured on an ordinal scale. Whilst it is possible to analyse such data using Spearman's rank-order correlation or Kendall's tau-b, Goodman and Kruskal's gamma is recommended when your data has many tied ranks.

For example, you could use Goodman and Kruskal's gamma to understand whether there is an association between restaurant star rating and price bracket (i.e., where there were five possible star ratings – 1 star (*), 2 star (**), 3 star (***), 4 star (****) and 5 star (*****) – and price bracket was split into three categories: inexpensive ($), moderate ($$) and expensive ($$$)). Alternately, you could use Goodman and Kruskal's gamma to understand whether there is an association between test anxiety and exam duration (i.e., where test anxiety had three categories – low, moderate and high – and exam duration was split into four categories: 1 hour, 2 hours, 3 hours and 4 hours).

Note: Goodman and Kruskal's gamma can be used when both ordinal variables have just two categories. For example, you could use Goodman and Kruskal's gamma to understand whether there is an association between exam performance (i.e., with two categories: "pass" or "fail") and test anxiety level (i.e., with two categories: "high" or "low"). However, in such cases, another statistical test called **Yule's Q**, which is a special case of Goodman and Kruskal's gamma is typically used instead. Yule's Q can also be used to analyse the strength and direction of association between two dichotomous variables (e.g., an example of a dichotomous variable would be "gender", which has two categories: "males" and "females").

This "quick start" guide shows you how to carry out Goodman and Kruskal's gamma using SPSS Statistics. We show you the **Crosstabs...** procedure to carry out Goodman and Kruskal's gamma using SPSS Statistics in the Procedure section. First, we introduce you to the assumptions that you must consider when carrying out Goodman and Kruskal's gamma.

###### SPSS Statistics

## Assumptions

When you choose to analyse your data using Goodman and Kruskal's gamma, part of the process involves checking to make sure that the data you want to analyse can actually be analysed using Goodman and Kruskal's gamma. You need to do this because it is only appropriate to use Goodman and Kruskal's gamma if your data "passes" two assumptions that are required for Goodman and Kruskal's gamma to give you a valid result. In practice, checking for these two assumptions just adds a little bit more time to your analysis, requiring you to click of few more buttons in SPSS Statistics when performing your analysis, as well as think a little bit more about your data, but it is not a difficult task. These two assumptions are:

**Assumption #1:**Your**two variables**should be measured on an**ordinal**scale. Examples of**ordinal variables**include Likert scales (e.g., a 7-point scale from "strongly agree" through to "strongly disagree"), amongst other ways of ranking categories (e.g., a 5-point scale explaining how much a customer liked a product, ranging from "Not very much" to "Yes, a lot"). You can learn more about ordinal variables in our article: Types of Variable.**Assumption #2:**There needs to be a**monotonic relationship**between the two variables. A monotonic relationship exists when either the variables increase in value together, or as one variable value increases, the other variable value decreases. It is typically not possible to check this assumption when running a Goodman and Kruskal's gamma analysis.

If your data fails these assumptions, you should consider using a different statistical test, which we show you how to do in our Statistical Test Selector (N.B., this is part of our enhanced content).

In the section, Test Procedure in SPSS Statistics, we illustrate the SPSS Statistics procedure to perform Goodman and Kruskal's gamma assuming that no assumptions have been violated. First, we set out the example we use to explain the Goodman and Kruskal's gamma procedure in SPSS Statistics.