Point Biserial Correlation

What is Point Biserial Correlation?

measures the strength of association or co-occurrence between two variables.

Correlation analyses express this strength of association in a single value, the correlation coefficient.

The Point-Biserial Correlation Coefficient

a correlation measure of the strength of association between a continuous-level variable (ratio or interval data) and a binary variable.

Binary variables are variables of nominal scale with only two values. They are also called dichotomous variables or dummy variables in Regression Analysis.

When both variables are dichotomous, the resulting correlation is called a phi-coefficient.

The Point-Biserial Correlation Coefficient The Point-Biserial Correlation Coefficient is typically denoted as rpb .

Typical questions to be answered with a Point-Biserial Correlation Analysis are as follows:

Biology – Do fish react differently to red or green lighted stimulus as food signal? Is there an association between the color of the stimulus (red or green light) and the reaction time?

Medicine – Does a cancer drug prolong life? How strong is the association between administering the drug (placebo, drug) and the length of survival after treatment?

Sociology – Does gender have an influence on salary? Is there an association between gender (female, male) with the income earned?

Typical questions to be answered with a Point-Biserial Correlation Analysis are as follows:

Social psychology – Is satisfaction with life higher the older you are? Is there an association between age group (elderly, not elderly) and satisfaction with life?

Economics – Does analphabetism indicate a weaker economy? How strong is the association between literacy (literate vs. illiterate societies) and GDP?

EXAMPLE: The data in Table 2 are set up with some obvious examples to illustrate the calculation of rpbi between items on a test and total test scores. Notice that the items have been coded 1 for correct and 0 for incorrect (a natural dichotomy) and that the total scores in the last column are based on a total of 50 items

rpbi = point-biserial correlation coefficient

Mp = whole-test mean for students answering item correctly (i.e., those coded as 1s)

Mq = whole-test mean for students answering item incorrectly (i.e., those coded as 0s)

St = standard deviation for whole test

p = proportion of students answering correctly (i.e., those coded as 1s)

q = proportion of students answering incorrectly (i.e., those coded as 0s)

Computation:

Interpretation: the correlation between item 1 and the total scores is a very high .91, and this item appears to be spreading the students out in very much the same way as the total scores are. In this sense, the point-biserial correlation coefficient indicates that item 1 discriminates well among the students in this group (at least in terms of the way the overall test discriminates).

the correlation between item 2 and the total scores is a very high negative value of -.91, and this item appears to be spreading the students out opposite to the way the total scores are. In other words, the point-biserial correlation coefficient shows that item 2 discriminates in a very different way from the total scores at least for the students in this group.

the correlation between item 3 and the total scores is zero, and this item does not appear to be spreading the students out in the same way as the total scores. In other words, item 3 is not discriminating at all among the students in this particular group, in this case because there is no variation in their answers

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