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The main purpose of this dissertation was to investigate the reliability of the test estimated with the congeneric model (rB and rconstruct co-efficiencies) and three - parameter logistic model ( and KR-20 co-efficiencies). For data gathering, 6,000 Prathomsuksa 5 students out of the 4 Chiangrai Education Services Area Offices divided into 4 population sizes: 300, 500, 1,000, and 1,500 were selected by the stratified random sampling technique. Otherwise, 30 sampling groups out of each the small-sized sample divided into 4 sizes: 30, 60,120, and 240 were all conducted with an achievement test on mathematical learning achievement designed for Prathomsuksa 5 students. The data were systematically analyzed through mean, standard deviation, the estimation of reliability, the standard error of the estimate, partiality, and Profile analysis. The findings of the study were as follows: 1. In terms of the estimation of the test’s reliability compared the psudo population with the 4 sample groups, including 300,500,1,000, and 1,500, it was stated that the reliability of the test with, PIRT rB , KR-20, and rconstruct co-efficiencies were respectively estimated; 2. In terms of the estimation of the test’s reliability of a test compared with the 4 small-sized sample groups of 30, 60, 120, and 240, it was stated that the rB , KR-20, and rconstruct co-efficiencies were respectively estimated; 3. In terms of the reliability of the test with the sample groups of 300, 500, 1,000, and 1,500 estimated with the KR-20 co-efficiency, it was stated that the rB co-efficiency and rconstruct co-efficiency was averaged at its reliability of 95%; 4. In terms of the estimation of the test’s reliability found in the standard error and partiality of the estimate with its reliability of 0≥1, it was stated that the appropriateness and quality of the test were found in the estimation of the reliability; 5. As compared the reliability of the test that was estimated with the KR-20, r B , r construct, and PIRT co-efficiencies with the medium-sized sample group, it was also stated that the unparallel.