Variance difference between maximum likelihood estimation method and expected A posteriori estimation method viewed from number of test items

Abstract

The aim of this study is to determine variance difference between maximum likelihood and expected A posteriori estimation methods viewed from number of test items of aptitude test. The variance presents an accuracy generated by both maximum likelihood and Bayes estimation methods. The test consists of three subtests, each with 40 multiple-choice items of 5 alternatives. The total items are 102 and 3159 respondents which were drawn using random matrix sampling technique, thus 73 items were generated which were qualified based on classical theory and IRT. The study examines 5 hypotheses. The results are variance of the estimation method using MLE is higher than the estimation method using EAP on the test consisting of 25 items with F= 1.602, variance of the estimation method using MLE is higher than the estimation method using EAP on the test consisting of 50 items with F= 1.332, variance of estimation with the test of 50 items is higher than the test of 25 items, and variance of estimation with the test of 50 items is higher than the test of 25 items on EAP method with F=1.329. All observed F values ≥ 1.00. 5 RMSE in items 10, 15, 20, and 25 are different in both MLE and EAP, with t = 3.060, , thereby meaning that statistical null hypothesis are rejected. The study concludes that variance of MLE method is higher than EAP, and the test with 50 items has higher variance than that with 25 items, the accuracy of EAP estimate higher than that of MLE in item 10, 15, 20, and 25. Key words: Variance, RMS of estimation, maximum likelihood, expected A posteriori.