Estimation of true scores, true score variance, reliability and tests of parallelism /

Abstract

Under classical test theory the paper presents a methodto 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 varianceand 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 (𝑋𝑔and𝑋ℎ)which can be done by testing (i) equality of regression line of observed score 𝑋on𝑋𝑔and 𝑋on𝑋ℎ(ii)equality of correlations between 𝑋and 𝑋𝑔and𝑋and 𝑋ℎ, (iii) Normality of (𝑋𝑔−𝑋ℎ)or (iv) Cosine similarity (without assuming normal distribution of 𝑋𝑔and𝑋ℎ). Reporting of theoretically defined reliability along with SD of true score/error score is recommended for a test.