Spearman Correlation

[Lindsay Platter, PhD, Data Analyst II.]  

What is a Spearman correlation? A Spearman correlation is used to determine the strength and direction of a relationship of the rankings of two ordinal or continuous variables. It's a bit more of a mouthful. We've got different things going on. You can use ordinal data or continuous data. Importantly, the Spearman correlation is a non-parametric test; it means it does not assume normality, the data do not have to meet that standard bell-shaped curve shape. And I've left you some other resources on the slide if you're trying to run this on your own and you're looking for a little more help [the SPSS LibGuide, a Laerd statistics guide, and the formal SPSS documentation]. 

What are our assumptions for the Spearman correlation? We have three of them.  

The first is you need two ordinal, interval, or ratio variables (i.e., you need ordinal data or continuous data). You can have some categories here, or you can use continuous data.  

Our second assumption here, is you must have paired observations. So, for example, if I'm a participant in the study, I need something at timepoint 1 and timepoint 2. For example, I need to be measured twice; you can't match me with my best friend, it has to be me and me. 

And our third assumption is there should be a monotonic relationship between variables (fancy way of saying the data roughly needs to be increasing or decreasing, not both). We'll cover these on the next few slides, let's go!  

[Slide contains a screenshot of a table in SPSS within Data View. The table’s column headers are as follows: Gender, Fake_Data1, Fake_Data2, Fake_Data3, Fake_Data4 Colour, and Group.]  

So checking our assumptions, again, we're going to use Fake_Data1 and Fake_Data2.  

[Fake_Data1 and Fake_Data2 columns are highlighted.] 

We've already determined it's got some decimal points, it's got a range of values, this data is continuous. We have passed this assumption.  

[Column headers Gender, Fake_Data1, and Fake_Data2 are highlighted with the associated data in the first row.] 

Our second assumption is we need to have paired observations. If we look across the rows, this looks like one person. This person identifies as male. We've got a Fake_Data1 and a Fake_Data2 variable for this person. So we say that this variable or this assumption also passes. 

[SPSS scatter plot displaying the relationship between Fake_Data1 (Y-axis) and Fake_Data2 (X-axis). The plot title reads "Scatterplot of Fake_Data1 by Fake_Data2." Red data points are scattered across the graph.] 

And I'm going to shorthand our third thing a little bit, our monotonic relationship assumption. We've already made this plot by doing the Pearson correlation, so I'm just going to give you the plot and we want to look at this plot critically and say, does it look like it's only increasing? Does it look like it's only decreasing? Or does it look like maybe it's increasing and decreasing? Does it have switchbacks? If I was to draw a line trying to touch as many of these points as possible, does it look like it's only going in one direction, or does it look like it's moving around?  

And if we look at this [graph], it looks like it might actually be decreasing for the first bid and then increasing for the second bit, which would mean this might not be considered a monotonic relationship. So we may or may not have passed this assumption, which is a reminder you always want to check your assumptions to say what can we do and what can we not do. What is statistically appropriate, what is not statistically appropriate.  

Step 1 

[Table is now open in Data View with the Analyze menu open and Correlate selected. From the Correlate sub-menu Bivariate is highlighted.] 

Alright, to actually run the Spearman correlation, these steps should look familiar if you've just done the Pearson correlation, you click Analyze > Correlate > Bivariate.  

If you have passed all assumptions, you can move on to conducting the Spearman correlation. If you failed an assumption, the Spearman correlation might not be appropriate or the result of the test might not be valid.  

If you're looking to run this on your own: Analyze > Correlate > Bivariate.  

Steps 2-4 

[SPSS Bivariate Correlations dialog box displaying selected variables "Fake data: =85 + 5*rand()" and "Fake data: =90 + 5*rand()" for correlation analysis. The left panel lists other available variables. The Correlation Coefficients section offers options for Pearson, Kendall’s tau-b, and Spearman, with Spearman selected. The Test of Significance section allows for Two-tailed or One-tailed tests, with Two-tailed selected. Additional options at the bottom include flagging significant correlations, showing only the lower triangle, and displaying the diagonal.] 

We take our two continuous or ordinal variables from the left side. We click the blue arrow and put them in the box that says “Variables:”, and then we want to make sure where it says “Correlation Coefficients” we have checked the box that says Spearman.  
This will run a Spearman correlation. And then we click OK.  

[SPSS Nonparametric Correlations output in the Statistics Viewer window. The left panel displays the Output Navigator, showing a hierarchy under " Nonparametric Correlations" with sections for Title, Notes, and Correlations. The right panel presents the Spearman’s rho correlation results for two datasets. The table has three rows: Correlation Coefficient, Sig. (2-tailed), and N.] 

If you have followed these steps, it will give you just one piece in your output. Again, you want to make sure if you're running this appropriately, you've got a much longer output; you've got all of your assumption checking, and then the Spearman correlation at the bottom. 

So with our Spearman correlation, it gives us three main pieces in the output. It gives us our correlation coefficient, which for Spearman is called Spearman's rho. This tells you the strength and direction of the relationship. If it's a positive number, it means it's a positive relationship (as one thing is increasing, the other thing is increasing); if it's got a negative in front, it means it's a negative relationship (as one thing is increasing, the other thing is decreasing). A value closer to 1 is a strong relationship; a value closer to 0 is a weak relationship. Here, we have a weak positive Spearman's rho [the value is .019].   

Our significance [Sig.] column, our significance row here is our p-value. A p-value less than (<) .05 indicates a significant relationship between these two variables. A p-value greater than (>) .05, we can't say whether there's a relationship between these variables.   

And as always, our “N” tells us about the number of observations we have used to calculate this. In this case, we've got 30.  

So again, we've got a weak positive, non-significant relationship and we've done this using a Spearman's correlation.  

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