I am doing my thesis using a a non experimental descriptive correlation analysis with continuous ratio data. One of the variables is unevenly distributed. I have calculated Pearson's correlation coefficient ($-0.61$) and Spearman's correlation coefficient ($-0.48$), and I am now deciding which one to use. I have checked the distribution of each variable using The Kolmogorov-Smirnov test of normality and one of the variables is not normally distributed and the other is. Ideally, I would prefer to use Pearson's (as the correlation is stronger) but everything I have read has said to use Spearman's if unevenly distributed. Which should I use? Why is Pearson showing a stronger correlation?
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1$\begingroup$ Read topics with "Spearman Pearson" on the site. $\endgroup$– ttnphnsApr 6, 2021 at 7:27
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Pearson's and Spearman's correlation coefficients have nothing to do with normal distributions (or with uneven distributions). Pearson's correlation coefficient measures the linear relationship between two variables, so if you were to check anything, it would be this.
Draw a scatter plot of your two variables and check if the relationship looks linear, if it doesn't, then Pearson's r is not appropriate. If the relationship is not linear but is monotonous then you can use Spearman's rho.
Pearson's r is a parametric measure, and as such has higher power (more easily detects effects) compared to non-parametric measures such as Spearman's rho, meaning if the relationship is truly linear then Pearson's r will have a higher (absolute) coefficient. However, this could also be for other unrelated reasons (such as outliers), so you cannot decide on which measure to use based solely on the coefficient.
answered Apr 6, 2021 at 5:19