Comparing distributions of item responses for two groups

If one group of examinees can be described as having generally higher ability to respond correctly to the items on an exam than some other group—where ability is defined by a unidimensional item response model—then the observable distributions of item responses must satisfy certain constraints. Standard statistical methods for discrete data may be used to test the consistency of these constraints with observed data. In an example, the observed pattern of item responses is found to be inconsistent with a difference in the distribution of a unidimensional latent variable.