A Comparison of Angoff's Design I and Design II for Vertical Equating Using Traditional and IRT Methodology

Practical considerations in conducting an equating study often require a trade‐off between testing time and sample size. A counterbalanced design (Angoff's Design II) is often selected because, as each examinee is administered both test forms and therefore the errors are correlated, sample sizes can be dramatically reduced over those required by a spiraling design (Angoff's Design I), where each examinee is administered only one test form. However, the counterbalanced design may be subject to fatigue, practice, or context effects. This article investigated these two data collection designs (for a given sample size) with equipercentile and IRT equating methodology in the vertical equating of two mathematics achievement tests. Both designs and both methodologies were judged to adequately meet an equivalent expected score criterion; Design II was found to exhibit more stability over different samples.