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In his answer to my question on Hamann similarity, user @ttnphns wrote

If you want a "correlation" (or quasi-correlation) measure defying marginal distributions shape - choose Hamann over Phi.

He illustrated there the effect of distributional asymmetry on both:

Crosstabulations:
        Y
X    7     1
     1     7
Phi = .75; Hamann = .75

        Y
X    4     1
     1    10
Phi = .71; Hamann = .75

I wonder under which typical circumstances I might want a "correlation defying marginal distributions shape" and choose Hamann, and under which circumstances I might want a "correlation not defying marginal distributions shape" and choose Phi?

Phi and Hamann are correlation measures for binary data. I'd like to hear, if possible, also about continuous data case: what might be a correlation coefficient for continuous data, similar to usual $r$ but not sensitive to the marginal distribution shape ($r$ can practically reach both its bounds -1 and +1 only in data with symmetric distribution).

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Hans-Peter Stricker
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  • I've added a question about continuous case as well, to make it more general and interesting. If you don't like the edit please feel free to roll back. – ttnphns Jan 18 '17 at 12:12

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