Test Length and Sample Size for Item-Difficulty Parameter Estimation in Item Response Theory

Abstract

The study investigated test lengths and sample sizes in the accurate and stable estimation of item-difficulty parameter in the Item Response Theory (IRT) One Parameter Logistic Model (1PLM). Real data of students that sat for the June/July 2015 Economics Multiple-Choice Examinations in Edo State was obtained from the National Examinations Council (NECO), Nigeria. The statistical population of examinees were 5,158 and the test length 60. Sample sizes of 200, 500, 1000, 2000 and 5000 were randomly drawn from the population with replacement; these samples were each paired with test lengths of 10, 20, 30 and 50.all amounting to 20 statistical conditions (5 sample sizes× 4 test lengths)The parameter estimates were generated using the eirt - Item Response Theory Assistant for Excel. The generated item-difficulty parameter using the entire population was assumed to be the true parameter value against which others were compared, using the Root Mean Square Error (RMSE) as an evaluative criteria. The acceptable RMSE was ≤ 0.33. Conclusion reached was that for an accurate item-difficulty parameter estimate in the 1PLM at least a test length of 10 and sample size of 1000 is required. Key words: Test-Length, Sample-Size, IRT, Difficulty-Parameter, Logistic Model. DOI : 10.7176/JEP/10-30-08 Publication date :October 31 st 2019