The relationship between item exposure and test overlap in computerized adaptive testing

The purpose of this article is to present an analytical derivation for the mathematical form of an average between-test overlap index as a function of the item exposure index, for fixed-length computerized adaptive tests (CATs). This algebraic relationship is used to investigate the simultaneous control of item exposure at both the item and test levels. The results indicate that, in fixed-length CATs, control of the average between-test overlap is achieved via the mean and variance of the item exposure rates of the items that constitute the CAT item pool. The mean of the item exposure rates is easily manipulated. Control over the variance of the item exposure rates can be achieved via the maximum item exposure rate (r(max)). Therefore, item exposure control methods which implement a specification of r(max) (e.g., Sympson & Hetter 1985) provide the most direct control at both the item and test levels.