Goodman and Kruskal's gamma using SPSS Statistics

Introduction

Goodman and Kruskal's γ (G or γ) is also referred to as Goodman and Kruskal's gamma. It is a nonparametric measure of the strength and direction of association that exists between two variables measured on an ordinal scale (Goodman & Kruskal, 1954). While 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 (Siegel & Castellan, 1988).

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 are five possible star ratings – 1 star (*), 2 star (**), 3 star (***), 4 star (****) and 5 star (*****) – and price bracket is 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 has three categories – low, moderate and high – and exam duration is 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 section: SPSS Statistics procedure to carry out a Goodman and Kruskal's gamma analysis. First, we introduce you to the assumptions that you must consider when carrying out Goodman and Kruskal's gamma.

SPSS Statistics

Assumptions of Goodman and Kruskal's gamma

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 items (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 quite difficult to check this assumption when running a Goodman and Kruskal's gamma analysis.
  
  While monotonicity is not actually an assumption of Goodman and Kruskal's gamma, you would not normally want to use Goodman and Kruskal's gamma to determine the strength and direction of a monotonic relationship if you already knew that the relationship between your two variables is not monotonic. Instead, the relationship between your two variables might be better described by another statistical measure of association. For this reason, it is good practice to try to determine whether the relationship between your two variables is monotonic, such that Goodman and Kruskal's gamma is the best choice as a measure of association, or whether another measure would be better.

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, SPSS Statistics procedure to carry out a Goodman and Kruskal's gamma analysis, 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.