Item Deletions Based on Difficulty Values and Discriminating Values

Background: Deletion of items from MCQ tests or Likert type scales may be necessary due to various reasons. Methods: Considering entire data the paper gives new measures of difficulty and discriminating value of items as well as test along with their relationships including relationship with test reliability (. Discriminating value of test () and item ( are expressed as coefficient of variation (CV) of test scores and item scores respectively. Results: Non-linear relationship between and   derived. As number of persons giving correct answer to an item increases,   curve increases and  curve decreases and intersect at a point (say. Items lying outside the interval [  where SD is standard deviation of or  can be deleted. Choosing acceptance region as [] may result in discarding too few items. For Likert scale, items with high values of CV may be deleted. Relationship of reliability and discriminating values helps to find effect of such deletions. Conclusions: Proposed method of item deletions based on difficulty values and discriminating values offers significant benefits and is recommended. However, the approach may be compared with deletion of items by “alpha if the item is deleted”. Future studies suggested.