Open AccessSTATISTICAL THEORY FOR LOGISTIC MENTAL TEST MODELS WITH A PRIOR DISTRIBUTION OF ABILITY
Author(s) -
Birnbaum Allan
Publication year - 1967
Publication title -
ets research bulletin series
Language(s) - English
Resource type - Journals
eISSN - 2333-8504
pISSN - 0424-6144
DOI - 10.1002/j.2333-8504.1967.tb00363.x
Subject(s) - statistical inference , inference , test (biology) , statistical hypothesis testing , logistic regression , statistics , statistical theory , econometrics , distribution (mathematics) , point (geometry) , mathematics , chi square test , computer science , artificial intelligence , paleontology , mathematical analysis , geometry , biology
The logistic model of a mental test was introduced by the present writer in Chapters 17 through 20 of Lord and Novick, Statistical Theories of Mental Test Scores , where statistical inference methods were developed without assumption of a prior distribution of ability. Such a distribution is assumed in this paper, and corresponding statistical inference methods and distribution theory are developed. Results include detailed investigation of posterior distributions, given observed response patterns; point‐estimation of ability, and its mean‐squared error; and distributions of test scores and their moments. Some computational methods and detailed examples are given.