IRT 능력 분포 모수 추정량의 표준오차 추정

초록

In item response theory (IRT), the normal and nonparametric methods have been used to estimate the ability distribution of an examinee population. The purpose of this study is to examine the characteristics of the formulas for the standard errors of the estimators of IRT ability distribution parameters (mean and standard deviation) through simulations. The simulation factors considered were test length (25 and 50), population distribution type (normal, positively-skewed and negatively-skewed distributions), sample size (500 and 2000), and number and range of ability points to be used for estimation (5 points and [-2, 2], 10 points and [-3, 3], and 20 points and [-4, 4]). Main results were as follows. First, when the population distributions were normal, the normal method tended to estimate not only the distribution parameters but also the standard errors of the parameter estimates more accurately as the number of ability points increased. Second, when the population distributions were positively or negatively skewed, the nonparametric method estimated the distribution parameters more accurately as the number of ability points increased, but the standard errors of the parameter estimates were severely overestimated in the 20 points conditions due to the enormous increase in the standard errors of probability estimates. Third, it was shown that such an overestimation problem in the nonparametric method might be resolved properly when the standard error formulas of the normal method were used instead.

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