Empirical Verification to Stocking’s Equations in Specifying Ability Levels Matching Maximum Information for Estimating Item Parameters in Item Response Theory

Abstract

The aim of the study was to provide empirical verifications
to stocking’s equations for estimating item parameters in IRT. For the
purpose of this study, a mental ability test, which was developed in a
previous study, was used. Software’s Bilog- Mg and Excel were used
to analyze the data. The findings were as follows: 1. Stocking’s
equations were satisfied in specifying ability levels matching
maximum information for estimating item parameters for the three
logistic models. 2. Stocking’s equations were a suitable approach
in specifying ability levels for estimating item parameters. However,
the optimal ability levels specified by Stocking’s equations were
mentioned in the text. 3. The accuracy of estimating the
discrimination parameter and guessing parameter were inconsistent
with the accuracy of estimating ability parameter, whereas, estimating
difficulty parameter was consistent with the accuracy of estimating
ability parameter. 4. Ability levels specified by Stocking’s equations
contribute more than ability levels specified by equations introduced
by Hambleton and Swaminthan in term of increasing accuracy of
estimating guessing parameter for 3PL, and discrimination parameter
for 2PL ,whereas , accuracy in estimating difficulty parameter wasn't
changed.
(Key Words: IRT, Item Parameters Estimation, Item Information Function

Information Function).