Accession Number : AD0746129

Title :   Estimating True Measurements from Fallible Measurements (Binomial Case) -- Expansion in a Series of Beta Distributions,

Corporate Author : EDUCATIONAL TESTING SERVICE PRINCETON N J

Personal Author(s) : Lord,Frederic M.

Report Date : AUG 1962

Pagination or Media Count : 31

Abstract : In mental-test theory, a useful mathematical model specifies the relation of the examinee's observed score, x, to his true score, zeta. The present paper is concerned with a model for the number-right scores on a test composed of n questions or items. This model is completely specified by the assertion that the conditional frequency distribution of x when zeta is fixed is the binomial distribution (n over x)(zeta sup x)(1-zeta)sup(n-x). The basic problem in the use of this model may be thought of as the problem of estimating the unknown frequency distribution of true scores. Once this is done, the bivariate distribution of zeta and x has also been estimated. All important properties of the test score can thus be investigated. Although it might at first seem otherwise, the model has empirically verifiable implications. (Author)

Descriptors :   (*INTELLIGENCE TESTS, STATISTICAL DISTRIBUTIONS), INTEGRAL EQUATIONS, HYPERGEOMETRIC FUNCTIONS, POLYNOMIALS, STATISTICAL TESTS, CURVE FITTING

Subject Categories : Psychology

Distribution Statement : APPROVED FOR PUBLIC RELEASE