A Statistical Procedure for Assessing Test Dimensionality.

An important problem in psychological test theory is the development of a sound method for determining whether a test which purports to measure the level of a certain ability is, in reality, significantly contaminated by one or more other abilities displayed by persons taking the test. Because of the large number of private and governmental organizations routinely using tests to screen people for the levels of various abilities, this problem of assessing the dimensionality of a test is of great importance. The solution will be useful in settings other than psychological testing, since the problem is one of general interest and should, hence, be an important addition to statistical methodology literature. Described in this paper is an approach to the problem of finding a theoretically sound and useful procedure for making inferences about the dimensionality of the ability parameter, or more precisely, the dimensionality of the distribution of the ability parameter.