# Hypothesis test for correlation between ordinal and continuous variable

I would like to test the relationship between an ordinal variable (stress level, a ranking from 1 'not stressful' to 5 'very stressful') and a continuous scale (academic performance, CGPA). What correlation should I use?

At least in psychology, it's common to use plain old Pearson correlation in this sort of situation, as part of the broader practice of treating ordinal rating scales as if they were interval-scaled. However, I'd recommend the Kendall correlation, which has a straightforward interpretation that only requires both variables to be on ordinal scales. As a bonus, Kendall correlation can handle nonlinearity, which poses a problem for Pearson correlation.

• +1. Any comment on Spearman vs. Kendall? – amoeba says Reinstate Monica May 30 '16 at 20:47
• I don't really see the appeal of Spearman over Kendall. It's easier to compute, and it's more readily comparable to the Pearson correlation. But it lacks the Kendall's nice interpretation as the rescaled probability of a randomly selected pair of rows being concordant or discordant. – Kodiologist May 30 '16 at 21:35