Correlation, Point-Biserial

Point-Biserial Correlation Objectives

Before discussing the objectives of the point-biserial correlation, it is necessary to distinguish the point-biserial coefficient from the biserial correlation coefficient. When researchers are interested in the relationship between an artificially created dichotomous nominal variable and an interval (or ratio) variable, it is appropriate to use the biserial correlation coefficient (or rbi). For instance, some researchers have investigated the degree of relationship between passing or failing (artificially created dichotomy) a public speaking course and communication apprehension test scores (an interval variable).

Table 1 Types of Correlation Coefficients

It should be noted that the biserial correlation coefficient is used when researchers are interested in the relationship between an artificially created nominal variable (such as the pass–fail variable) and a quantitative variable, whereas the main purpose of the point-biserial correlation coefficient is to determine the relationship between a naturally occurred nominal variable (such as the gender variable) and a quantitative variable (data that can be anything from a range of salaries, years of education, scores on a test, or height and weight). Table 1 shows how the point-biserial correlation coefficient is related to other correlation coefficients.

Like all correlation coefficients (e.g., Pearson’s r, Spearman’s rho), the point-biserial correlation coefficient measures the strength of association of two variables in a single measure ranging from +1 and −1 in their values (where 1 indicates total positive association, 0 is no association, and −1 is total negative association). None of the correlation coefficients can show cause-and-effect relationships. In other words, the gender difference does not cause the difference of earned income, and age does not cause increased or decreased satisfaction with life. Researchers can use the experimental designs (instead of correlation coefficients) to find causation because all correlation coefficients are interdependency measures that examine only whether or not two variables have a relationship between each other; not if one causes the change to occur in the other variable.

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