Estimation of True Scores, True score variance, Reliability and tests of parallelism

Article Type

Research Article

Publication Title

Journal of Modern Applied Statistical Methods


Under classical test theory the paper presents a method to find test reliability (rtt) as per theoretical definition from a single administration of the test, involving dichotomization of a test in parallel halves. The method helps to find point and interval estimations of test reliability, individual true score, true score variance, error variance and testing Ho: rtt = 1 Dichotomization of a test in parallel halves requires simultaneous testing of equality of mean, variance and correlation for two parallel sub-tests (Xg and Xh) which can be done by testing (i) equality of regression line of observed score X on Xg and X on Xh (ii) equality of correlations between X and Xg and X and Xh, (iii) Normality of (Xg − Xh) or (iv) or (iv) Cosine similarity (without assuming normal distribution of Xg and Xh). Reporting of theoretically defined reliability along with SD of true score/error score is recommended for a test.



Publication Date



Open Access, Bronze

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