A promising model for the relation between true score, ζ , and ob¬served score, x , asserts that the conditional distribution of observed score when true score is fixed is a binomial with parameters ζ and n , where n is the number of items in the test;also that the distribution of ζ in the group tested is a four-parameter beta distribution. It was found that this model successfully fitted most observed-score distribu¬tions, as judged by a chi-square test, except for those with more than 100,000 examinees.nThe 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.
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