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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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Q: What is the difference between biserial and point biserial coefficient?
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