Accession Number : AD0431062


Title :   TRUE SCORE THEORY--THE FOUR-PARAMETER BETA MODEL WITH BINOMIAL ERRORS,


Corporate Author : EDUCATIONAL TESTING SERVICE PRINCETON N J


Personal Author(s) : LORD,Frederic M


Report Date : Jan 1964


Pagination or Media Count : 28


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)


Descriptors :   *STATISTICAL FUNCTIONS , *PSYCHOLOGICAL TESTS , BINOMIALS , STATISTICAL PROCESSES , FUNCTIONS(MATHEMATICS)


Distribution Statement : APPROVED FOR PUBLIC RELEASE