Point-Biserial Discrimination

Point-biserial correlation is a standard way to assess how well a dichotomous variable correlates with a separate quantitative variable.

For PlaceU™ placement tests, student performance on each question (correct or incorrect) is correlated with the overall test score. The result is a measure of how effectively each question discriminates between students who have mastered the placement test subject matter and students who have not.

In PlaceU, the point-biserial discrimination value is calculated using the following formula:

r pb = S c S i P c P i σ S
  • Sc and Si are, respectively, the mean test scores for students who answered the question correctly and incorrectly.
  • Pc and Pi are, respectively, the percentages of students who answered the question correctly and incorrectly.
  • σS is the standard deviation of all students' test scores.
Note: For analytics calculations, correctly answered questions are those for which every part was answered correctly.

Positively Correlated Questions

For positively correlated questions, the point-biserial discrimination value is between 0 and 1, with higher values indicating stronger correlation. Weakly correlated questions might be candidates for omission in future tests, as their value in separating students with mastery from those without is limited.

Negatively Correlated Questions

Negatively correlated questions are uncommon, but occur when the mean test score for students who answered the question incorrectly is higher than the mean test score for students who answered the question correctly. A point-biserial discrimination value between 0 and -1 indicates the strength of the negative correlation.