Modelling the school-achievement test through sequential randomization of parameters
Luks, A.; Komenda, S.
Acta Universitatis Palackianae Olomucensis Facultatis Medicae 94: 315-334
1980
ISSN/ISBN: 0301-2514 PMID: 6231816 Document Number: 159964
School-achievement test is applied extensively as a method of testing knowledge of an individual (human) about the given subject. Properties of a probabilistic model of the school-achievement test in several previous papers were studied with the purpose of evaluating its information efficiency. The present communication is a continuation of this study. Relations between moments of random variables (the parameters of the school-achievement test) determining its probabilistic model and particularly the distribution of the random variables in a set of test realizations were derived. These variables were: number of questions in the test realizations were derived. These variables were: number of questions in the test answered incorrectly by an individual, number of questions in the test an individual does not know and the proportion of the unmastered matter. When an individual is put to several school-achievement tests from different subjects simultaneously, the relations between correlation coefficients measuring the dependence of 2 tests for each of the 3 variables under consideration were found. The empirically observable test results had lower correlation in comparison with that of the hypothetic variables parametrizing the influence of chance. The distribution of the proportion of unmastered matter is supposed to be beta. The results derived theoretically are applied in evaluation of the results of 2 school-achievement tests realized in the sample of 507 individuals put to the entrance examination of the medical faculty.