One of the assumptions for Spearman correlation is that there is a monotonic relationship between the two variables. I've created a scatterplot for two Likert item variables, but it seems impossible to get the desired monotonic plot. Must the monotonicity assumption be met for me to calculate the Spearman correlation?

My second question is, can I correlate respondent's score (scale) with a Likert item or any one variable that is nominal. In this case should I rank the score first in SPSS by creating a new column for rank score or will SPSS do it for me?


1 Answer 1


Spearman's rank correlation only captures monotonic relationships. If the relationship between your two variables is not monotonic, then rank correlation is inappropriate. If the variables were continuous, there are things you could do such as transform the variables or look at splines, but that seems wrong with 5 point scales. It might be best to go to a non-ordinal measure of relationship, such as chi-square.

For your second question, if it's just about how to do something in SPSS it is off topic here. However, if score is a scale variable then you shouldn't need to rank it at all.

Note that, as @NickCox points out in a comment below, that a monotonic relation is not an assumption of either Pearson's or Spearman's correlation; however, as I say above, if you are trying to capture a non-monotonic relationship, correlation is not the right tool.

  • $\begingroup$ Why "non-ordinal" measures? What about Kendall's tau? Somer's D? (But maybe I'm missing something here) $\endgroup$ Commented Dec 22, 2014 at 12:15
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    $\begingroup$ @gottfried For a non-monotonic relationship, the use of concordant / discordant pairs in Kendall's Tau is flawed for precisely the same reasons as taking rank correlation is. That's not to say you physically can't do it -the software won't stop you - just that it won't be appropriate for capturing the relationship. $\endgroup$
    – Silverfish
    Commented Dec 22, 2014 at 12:21
  • $\begingroup$ I see, I missed the expectation of that the relation might as well be non-monotonic. Then, true, a nominal measure is the only possibility (if we don't have the exact functional expression for that specific case of course) for such a relation. Sorry, didn't see that in the question. $\endgroup$ Commented Dec 22, 2014 at 12:34
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    $\begingroup$ No answer or comment yet focuses on a confusion in the question: monotonic relationship is not an assumption of Spearman correlation; rather, that measure quantifies the tendency to a monotonic relationship. Spearman correlation will be low if there is a non-monotonic relationship or a weak monotonic relationship. Neither is a violation of an assumption. The correlation will be valid in such cases; disappointing perhaps, but that's a different story. $\endgroup$
    – Nick Cox
    Commented Dec 22, 2014 at 12:46
  • $\begingroup$ OK good point, @NickCox I will add that to my answer $\endgroup$
    – Peter Flom
    Commented Dec 22, 2014 at 12:55

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