TRUE SCORE THEORY--THE FOUR-PARAMETER BETA MODEL WITH BINOMIAL ERRORS,
Abstract
A promising model for the relation between true score, Z, and observed score, x, asserts that the conditional distribution of observed score when true score is fixed is a binomial with parameters Z and n, where n is the number of items in the test; also that the distribution of Z in the group tested is a four-parameter beta distribution. It was found that this model successfully fitted most observed-score distributions, as judged by a chi-square test, except for those with more than 100,000 examinees. The model is also capable of predicting the frequencies in the scatterplot between two tests of the same trait, using only the information given by the two marginal frequency distributions. When such predictions were tried out for six different scatterplots, the fits seemed visually good. However, five of six chi-squares were significant at the 5 percent level. Examination of the discrepancies between observed scatterplots and predicted scatterplots showed a simple pattern. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1964
- Accession Number
- AD0431062
Entities
People
- Frederic M. Lord
Organizations
- Educational Testing Service