Effect of group heterogeneity on item parameters

Most indexes of item validity and difficulty vary systematically with changes in the mean and variance of the group. Formulas are presented showing how certain item parameters will vary with these alterations in group mean and variance. Item parameters are also suggested which should remain invariant under such changes. These parameters are developed under two different assumptions: first, the assumption that thetotal distribution of the item ability variable is normal, and, second, that the distribution of the item ability variablefor each array of the explicit selection variable is normal. The writer wishes to acknowledge helpful discussions of this paper with Paul Horst and Herbert S. Sichel who have worked on various aspects of the problem of invariant item parameters.