Discovering the Point Biserial

In this article, we define one of the most commonly used statistics in educational assessment, namely the point-biserial coefficient.  

First, let's define the correlation coefficient.

Most of us are familiar with correlations. The common correlation statistic used is known as the Pearson correlation coefficient. Almost all correlation coefficients range from -1.0 to +1.0 in their values, and are used to demonstrate how two sets of numerical data are related. Numerical data can be anything from a range of salaries, years of education, or scores on a test. Here are the three basic patterns that we see in correlations.

  • Positive Correlation. When relatively high values are paired with relatively high values, and relatively low values are paired with relatively low values. A good example is salary and years of education.
  • Negative Correlation. When relatively low values are paired with relatively high values, and relatively high values are paired with relatively low values. An example of a negative correlation might be years smoking versus life expectancy.
  • Zero Correlation. When there is basically no relationship between two sets of numerical data. Your imagination can come up with good examples here.

The point biserial

A point-biserial coefficient is a special type of correlation coefficient that relates observed item responses to a total test score. In the examples above we see that both sets of data have a range of values (e.g., salary). A point-biserial coefficient is specifically used when one set of the data is dichotomous in nature. In this case, the scored multiple-choice items are the dichotomous data; i.e., they can take on values of 1 (for a correct response) and 0 (for an incorrect response). The calculation of a point-biserial coefficient is a bit simpler than that for the Pearson coefficient, but the resulting coefficients and their meaning are the same. That is, a positive point-biserial coefficient would mean that high values on the dichotomous data (i.e., correct item responses) are related to high values on the total test score. We also call this coefficient an "item-total correlation."

How is the point biserial used?

A point-biserial coefficient, computed for every multiple-choice item, is considered useful because it reflects how well an item is "discriminating." A high point-biserial coefficient means that students selecting the correct response are students with higher total scores, and students selecting incorrect responses to an item are associated with lower total scores. Given this, the item can discriminate between low-performing examinees and high-performing examinees. This is a desirable characteristic of test questions. Very low or negative point-biserial coefficients computed after field testing new items can help identify items that are flawed.

Limitations

There are limitations to using any statistic. For example, one major drawback in using a point-biserial coefficient is that it is sample-dependent; administering an item to different groups of students may result in different values.

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