Calculate a test item’s upper-minus-lower discrimination index from correct counts, or plan the minimum upper-group count for a target index. Pooled difficulty covers only the two entered groups; review bands are screening heuristics.

Upper-minus-lower group proportion, from disjoint groups defined by overall test performance. Review bands are heuristics, not automatic grading or item-removal rules.

Discrimination Index Formula

The following formula is used to calculate the Discrimination Index.

DI = U / NU - L / NL For equal group sizes N: DI = (U - L) / N

Variables:

  • DI is the Discrimination Index
  • U is the number of upper group students who answered correctly
  • L is the number of lower group students who answered correctly
  • N_U and N_L are the upper- and lower-group sizes. If both are N, the equal-size formula applies.

Divide each correct count by its own group size, then subtract the lower proportion from the upper proportion. For equal group sizes, this equals (U − L)/N. Use disjoint groups defined by overall test performance; a negative index warrants review of scoring, keying and item clarity.

What is a Discrimination Index?

A Discrimination Index is a statistical measure used in educational testing to determine the effectiveness of a particular question in differentiating between high and low scorers. It indicates how well a question can distinguish between students who have a good overall understanding of the tested subject and those who do not. A high discrimination index suggests that the question is effective at distinguishing between these groups, while a low index suggests it is not.

How to Calculate Discrimination Index?

The following steps outline how to calculate the Discrimination Index.

  1. First, determine the number of upper group students who answered correctly (U).
  2. Next, determine the number of lower group students who answered correctly (L).
  3. Next, determine the size of each group (N_U and N_L).
  4. Use DI = U/N_U − L/N_L, or (U − L)/N when the group sizes are equal.
  5. Finally, calculate the Discrimination Index.
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

U: number of upper group students who answered correctly = 45

L: number of lower group students who answered correctly = 30

N: total number of students in each group = 100. Thus DI = 45/100 − 30/100 = 0.15. Minimum-count planning uses max(0, ceiling[(target DI + lower proportion) × upper size]); the attainable index may exceed the target after rounding. This statistic alone does not establish item validity.