Estimating True Measurements from Fallible Measurements (Binomial Case) -- Expansion in a Series of Beta Distributions,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1962
- Accession Number
- AD0746129
Entities
People
- Frederic M. Lord
Organizations
- Educational Testing Service