We are all familiar with the idea of a correlation. In the broadest sense of the word, a correlation can refer to any kind of dependence between two variables. There are three widely used tests for correlation:
- Spearman’s r: Used to measure a linear relationship between two variables. Requires linear dependence and each marginal distribution to be normal.
- Pearson’s ρ: Used to measure rank correlations. Requires the dependence structure to be described by a monotonic relationship
- Kendall’s 𝛕: Used to measure ordinal association between variables.
While these three measures give us plenty of options to work with, they do not work in all cases. Take for example the following variables, Y1 and Y2. These might be two variables that vary in a concerted manner.
Perhaps we suspect that a state change in Y1 leads to a state change in Y2 or vice versa and we want to measure the association between these variables. Using the three measures of correlation, we get the following results:
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