It's hard for me to accept that Donald Rubin would ever come up with a true lemon of a technique. Yet that's my perception of the BESD [1, 2], 3]3. He and Robert Rosenthal (1982*) claimed that there was value in showing "how to recast any product-moment correlation into such a [2x2] display, whether the original data are continuous or categorical." The table below is from p. 451 of the 2nd link above:
This technique seems to overstate the magnitude of almost any effect size. Here, RSQ from the original data = .01, but when "translated" into a 2x2 crosstab, we seem to be faced with a much stronger effect. I don't deny that, when the data are recast into categorical format in this way, phi indeed = .1, but I feel something has been very distorted in the translation.
Am I missing something truly valuable here? Also, I have the impression that in the past 10 or so years the statistical community has by and large rejected this as a legitimate method; am I wrong on that?
*Rosenthal, R., & Rubin, D.B. (1982). A simple general purpose display of magnitude of experimental effect. Journal of Educational Psychology, 74, 166–169.