# Somers' *d* using SPSS Statistics

## Introduction

Somers' delta (or Somers' *d*, for short), is a nonparametric measure of the strength and direction of association that exists between an ordinal dependent variable and an ordinal independent variable. Whilst it is possible to analyse the association between two ordinal variables using Goodman and Kruskal's gamma, Somers' *d* is appropriate when you want to distinguish between a dependent and independent variable (i.e., since Goodman and Kruskal's gamma does not make any distinction between the two ordinal variables).

For example, you could use Somers' *d* to understand whether there is an association between marathon running times and training volume (i.e., the ordinal dependent variable is "marathon running time", split into six groups – 2:30-2:59 hours, 3:00-3:29 hours, 3:30-3:59 hours, 4:00-4:29 hours, 4:30-4:59 hours and 5:00-5:29 hours – and the ordinal independent variable is "training volume", split into five groups: "0-4 hours per week", "5-9 hours per week", "10-14 hours per week", "15-19 hours per week" and "20-24 hours per week"). Alternately, you could use Somers' *d* to understand whether there is an association between customer satisfaction and hotel room cleanliness (i.e., the ordinal dependent variable is "customer satisfaction", measured on a five point scale from "very satisfied" to "very dissatisfied", and the ordinal independent variable is "hotel room cleanliness", measured on a three point scale from "above average" to "below average").

This "quick start" guide shows you how to carry out Somers' *d* using SPSS Statistics. We show you the main procedure to carry out Somers' *d* in the Procedure section. First, we introduce you to the assumptions that you must consider when carrying out Somers' *d*.

###### SPSS Statistics

## Assumptions

When you choose to analyse your data using Somers' *d*, part of the process involves checking to make sure that the data you want to analyse can actually be analysed using Somers' *d*. You need to do this because it is only appropriate to use Somers' *d* if your data "passes" two assumptions that are required for Somers' *d* 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:**You have**one dependent variable**and**one independent variable**and both are 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 dependent and independent variable. 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 Somers'*d*analysis.

If your data fail to meet 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 Somers' *d* assuming that no assumptions have been violated. First, we set out the example we use to explain the Somers' *d* procedure in SPSS Statistics.