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Point-biserial correlation coefficient
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<p>The point biserial correlation coefficient (<i>rpb</i>) is a <a href="/facts/Correlation_coefficient/j8Swz1R9">correlation coefficient</a> used when one variable (e.g. <i>Y</i>) is <a href="/facts/Dichotomy/mDufyfsP">dichotomous</a>; <i>Y</i> can either be "naturally" dichotomous, like whether a coin lands heads or tails, or an artificially dichotomized variable. In most situations it is not advisable to dichotomize variables artificially. When a new variable is artificially dichotomized the new dichotomous variable may be conceptualized as having an underlying continuity. If this is the case, a <a href="/facts/Biserial_correlation/yYUMLcrp">biserial correlation</a> would be the more appropriate calculation. </p><p>The point-biserial correlation is mathematically equivalent to the <a href="/facts/Pearson_correlation_coefficient/Igf0xDPc">Pearson (product moment) correlation coefficient</a>; that is, if we have one continuously measured variable <i>X</i> and a dichotomous variable <i>Y</i>, <i>rXY</i> = <i>rpb</i>. This can be shown by assigning two distinct numerical values to the dichotomous variable. </p>