Dichotomous variables can be either a
discrete/true dichotomy or a continuous/artificial one. Examples of
discrete dichotomies are male vs female, dead vs alive. There is no
underlying continuum between the groups. Continuous or artificial
dichotomies are those which we assume there to be an underlying
continuum but we assign individuals to a category based on some
arbitrary criterion. Examples of this artificial dichotomy are pass
vs fail (based on some cutoff score on a test) or short vs tall
(based on some arbitrary height). A point-biserial and biserial
correlation is used to correlate a dichotomy with an interval
scaled variable. The difference is that the point-biserial
correlation is used when the dichotomous variable is a true or
discrete dichotomy and the biserial correlation is used with an
artificial dichotomy.
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