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Abstract:
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This research evaluates the accuracy of formulas derived from classical test theory (CTT) foundations in approximating item response theory (IRT) parameters. Monte Carlo simulations were used to obtain unidimensional data, where the item characteristic curves were normal ogives, local item independence was observed, and theta values were normally distributed. Six data files were simulated with item properties representing small (n = 100), medium (n = 500), and large (n = 1,000) sample sizes with either good (lower and upper asymptotes were set a 0 and 1.0 respectively) or poor fit (lower asymptote alternated from 0 to .25 and the upper asymptote alternated from 1.0 to .85) to the 2 parameter logistic model. Results indicate the formulas were able to roughly approximate the IRT parameters. Formulas were more accurate when items had typical statistics versus those with extreme statistics as well as in the good fit versus the poor fit condition. |
