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Spearman's Rank-Order Correlation using SPSS Statistics

Introduction

The Spearman rank-order correlation coefficient (Spearman’s correlation, for short) is a nonparametric measure of the strength and direction of association that exists between two variables measured on at least an ordinal scale. It is denoted by the symbol rs (or the Greek letter ρ, pronounced rho). The test is used for either ordinal variables or for continuous data that has failed the assumptions necessary for conducting the Pearson's product-moment correlation.

For example, you could use a Spearman’s correlation to understand whether there is an association between exam performance and time spent revising; whether there is an association between depression and length of unemployment; and so forth. If you would like some more background information about this test, which does not include instructions for SPSS Statistics, see our more general statistical guide: Spearman's rank-order correlation. Possible alternative tests to Spearman's correlation are Kendall's tau-b or Goodman and Kruskal's gamma.

This "quick start" guide shows you how to carry out a Spearman’s correlation using SPSS Statistics. We show you the main procedure to carry out a Spearman’s correlation in SPSS Statistics procedure section. First, we introduce you to the assumptions that you must consider when carrying out a Spearman’s correlation.

SPSS Statistics

Assumptions of Spearman's correlation

When you choose to analyse your data using Spearman’s correlation, part of the process involves checking to make sure that the data you want to analyse can actually be analysed using a Spearman’s correlation. You need to do this because it is only appropriate to use a Spearman’s correlation if your data "passes" three assumptions that are required for Spearman’s correlation to give you a valid result. In practice, checking for these three 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 three assumptions are:

In terms of assumption #3 above, you can check this using SPSS Statistics. If your two variables do not appear to have a monotonic relationship, you might 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).

It is also worth noting that a Spearman’s correlation can be used when your two variables are not normally distributed. It is also not very sensitive to outliers, which are observations within your data that do not follow the usual pattern. Since Spearman’s correlation is not very sensitive to outliers, this means that you can still obtain a valid result from using this test when you have outliers in your data.

In the section, SPSS Statistics procedure, we set out the SPSS Statistics procedure to perform a Spearman’s correlation assuming that no assumptions have been violated. First, we set out the example we use to explain the Spearman’s correlation procedure in SPSS Statistics.

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SPSS Statistics

Example used in this guide

A teacher is interested in whether those who do better at English also do better in maths. To test whether this is the case, the teacher records the scores of her 10 students in their end-of-year examinations for both English and maths. Therefore, one variable records the English scores and the second variable records the maths scores for the 10 pupils.

SPSS Statistics

Data setup in SPSS Statistics

In SPSS Statistics, we created two variables so that we could enter our data: English_Mark (i.e., English scores) and Maths_Mark (i.e., maths scores). In our enhanced Spearman's correlation guide, we show you how to correctly enter data in SPSS Statistics to run a Spearman's correlation. You can learn about our enhanced data setup content on our Features: Data Setup page. Alternately, see our generic, "quick start" guide: Entering Data in SPSS Statistics.

SPSS Statistics

SPSS Statistics procedure to carry out a Spearman's correlation analysis

The Correlate > Bivariate... procedure below shows you how to analyse your data using Spearman’s correlation in SPSS Statistics when none of the three assumptions in the previous section, Assumptions, have been violated. At the end of these four steps, we show you how to interpret the results from this test. If you are looking for help to assess whether the relationship between your two variables is monotonic, we show you how to do this in our enhanced guide. You can learn more about our enhanced guides on our Features: Overview page.

Since some of the options in the Correlate > Bivariate... procedure changed in SPSS Statistics version 27, we show how to carry out Spearman's correlation depending on whether you have SPSS Statistics versions 27 to 29 (or the subscription version of SPSS Statistics) or version 26 or an earlier version of SPSS Statistics. The latest versions of SPSS Statistics are version 29 and the subscription version. If you are unsure which version of SPSS Statistics you are using, see our guide: Identifying your version of SPSS Statistics.

SPSS Statistics versions 27 to 29
(and the subscription version of SPSS Statistics)
  1. Click Analyze > Correlate > Bivariate... on the top menu, as shown below:
    Menu for Spearman's correlation in SPSS Statistics

    Published with written permission from SPSS Statistics, IBM Corporation.


    You will be presented with the Bivariate Correlations dialogue box, as shown below:
    'Bivariate Correlations' dialogue box for Spearman's correlation in SPSS Statistics. Variables 'English mark' & 'Maths mark' on the left

    Published with written permission from SPSS Statistics, IBM Corporation.

  2. Transfer the variables English_Mark and Maths_Mark into the Variables: box by clicking on the Right arrow button. You will end up with the following screen:
    'Bivariate Correlations' dialogue box for Spearman's correlation in SPSS. 'English mark' & 'Maths mark' transferred into 'Variables' box

    Published with written permission from SPSS Statistics, IBM Corporation.

  3. Deselect the Pearson checkbox and select the Spearman checkbox in the –Correlation Coefficients– area, as shown below:
    'Bivariate Correlations' dialogue box for Spearman's correlation. 'Spearman' selected in 'Correlation Coefficients' area

    Published with written permission from SPSS Statistics, IBM Corporation.

  4. Select the Show only the lower triangle checkbox and then deselect the Show diagonal checkbox, as shown below:
    'Bivariate Correlations' dialogue box for Spearman's correlation. 'Only lower triangle' selected in 'Correlation Coefficients' area

    Published with written permission from SPSS Statistics, IBM Corporation.

  5. Click on the OK button.

Now that you have run the Correlate > Bivariate... procedure to carry out Spearman's correlation, go to the Interpreting Results section. You can ignore the section below, which shows you how to carry out Spearman's correlation if you have SPSS Statistics version 26 or an earlier version of SPSS Statistics.

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SPSS Statistics version 26
and earlier versions of SPSS Statistics
  1. Click Analyze > Correlate > Bivariate... on the main menu as shown below:
    Menu for Spearman's rank-order correlation in SPSS Statistics

    Published with written permission from SPSS Statistics, IBM Corporation.


    You will be presented with the following Bivariate Correlations dialogue box:
    'Bivariate Correlations' dialogue box for Spearman's rank-order correlation in SPSS Statistics. Variables on the left

    Published with written permission from SPSS Statistics, IBM Corporation.

  2. Transfer the variables English_Mark and Maths_Mark into the Variables: box by dragging-and-dropping the variables or by clicking each variable and then clicking on the Right arrow button. You will end up with a screen similar to the one below:
    'Bivariate Correlations' dialogue box for Spearman's rank-order correlation in SPSS. Variables transferred on the right

    Published with written permission from SPSS Statistics, IBM Corporation.

  3. Make sure that you uncheck the Pearson checkbox (it is selected by default in SPSS Statistics) and select the Spearman checkbox in the –Correlation Coefficients– area. You will end up with a screen similar to below:
    'Bivariate Correlations' dialogue box for Spearman's rank-order correlation in SPSS Statistics. 'Spearman' option selected

    Published with written permission from SPSS Statistics, IBM Corporation.

  4. Click on the OK button. This will generate the results.
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SPSS Statistics

Interpreting the results of a Spearman's correlation analysis

SPSS Statistics generates a single table following the Spearman’s correlation procedure that you ran in the previous section. If your data passed assumption #3 (i.e., there is a monotonic relationship between your two variables), you will only need to interpret this one table. However, since you should have tested your data for monotonicity, you will also need to interpret the SPSS Statistics output that was produced when you tested for it (i.e., your scatterplot results). If you do not know how to do this, we show you in our enhanced Spearman’s correlation guide. If you have tested your data for these assumptions, we provide a complete explanation of the output you will have to interpret in our enhanced Spearman’s guide. Remember that if your data failed this assumption, the output that you get from the Spearman’s correlation procedure (i.e., the table we discuss below), might be misleading.

However, in this "quick start" guide, we focus on the results from the Spearman’s correlation procedure only. Therefore, after running the Spearman’s correlation procedure, you will be presented with the Correlations table, as shown below:

'Correlations' table for Spearman's rank-order correlation in SPSS. Shows 'Correlation Coefficient', 'Sig (2-tailed)' & 'N'

Published with written permission from SPSS Statistics, IBM Corporation.

Note: If you ran the Spearman's correlation procedure using SPSS Statistics version 26 or an earlier version of SPSS Statistics, the Correlations table will look like the one below:

'Correlations' table for Spearman's rank-order correlation in SPSS version 26 and earlier versions

The results in this table are identical to those produced in versions 27 to 29 (and the subscription version of SPSS Statistics), but are simply displayed using a different layout (i.e., the results are displayed in a matrix where the correlations are duplicated).

The Correlations table presents Spearman's correlation, its significance value (i.e., p-value) and the sample size that the calculation was based on.

In this example, the sample size, N, is 10, Spearman's correlation coefficient, rs, is 0.669, which is statistically significant (p = .035), as highlighted below:

'Correlations' table for Spearman's rank-order correlation in SPSS. Shows 'Correlation Coefficient', 'Sig (2-tailed)' & 'N'

Published with written permission from SPSS Statistics, IBM Corporation.

SPSS Statistics

Reporting the results of a Spearman's correlation analysis

In our example, you might present the results as follows:

A Spearman's rank-order correlation was run to determine the relationship between 10 students' English and maths exam marks. There was a strong, positive correlation between English and maths marks, which was statistically significant (rs(8) = .669, p = .035).

In our enhanced Spearman’s correlation guide, we also show you how to write up the results from your assumptions test and Spearman’s correlation output if you need to report this in a dissertation, thesis, assignment or research report. We do this using the Harvard and APA styles. You can learn more about our enhanced content on our Features: Overview page.

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