interpretation of the point-biserial correlation coefficient in the context of a school examination

Abstract

When creating an examination for educational purposes, one must make sure that the entire curriculum is covered. However, it can be difficult to do so without requiring a large number of questions. Also, it is desirable for those questions to be capable of accurately discriminating students who understand from those who do not, without being too difficult or easy. A practical way of identifying questions that fit these criteria is to study the point-biserial correlation ($r_{pb}$) between the success on a question and the number of questions correctly answered. This tutorial explains what the $r_{pb}$ is and how to use it through the interpretation of effect sizes and significance testing applied to real data. It also presents the corrected point-biserial correlation ($r_{pb}^*$), which is more suited for significance testing when one of the variables is partially determined by the other.

Keywords

• Tutorial
• Examination
• Assessment
• Point-Biserial Correlation
• Corrected Point-Biserial Correlation