How do I know which correlation coefficient to use?
This is a table I made for myself and an undergraduate class a few years ago.
Figure 1: Nick’s summary of which Correlation Coeffience to choose
Tetrachoric/Polychoric
I would now add for binary another good one is Tetrachoric - which assumes that the binary variable is actually just a binary measurement of an underlying continuous distribution.
There was a huge fight in the 1920s between pearson and someone else about this correlation
This is very useful intro to tetrachoric and polychoric correlations, including to the R code for them:
http://www.john-uebersax.com/stat/tetra.htm