A comparison of Van der Linden's conditional equipercentile equating method with other equating methods under the random groups design

To ensure test security and fairness, alternative forms of the same test are administered in practice. However, alternative forms of the same test generally do not have the same test difficulty level, even though alternative test forms are designed to be as parallel as possible. Equating adjusts for differences in difficulties among forms of the test. Six traditional equating methods are considered in this study: equipercentile equating without smoothing, equipercentile equating with pre-smoothing and postsmoothing, IRT true-score and observed-score equatings, and kernel equating. A common feature of all of the traditional procedures is that the end result of equating is a single transformation (or conversion table) that is used for all examinees who take the same test. Van der Linden has proposed conditional equipercentile (or local) equating (CEE) to reduce the error of equating contained in the traditional equating procedures by introducing individual level equating. Van der Linden’s CEE is conceptually closest to IRT-T in that CEE is with respect to a type of true score ( , or proficiency), but it shares similarities with to IRT-O in that CEE uses an estimated observed score distribution for each individual to equate scores using equipercentile equating. No real-data study has yet compared van der Linden’s CEE with each of the traditional equating procedures. Indeed, even for the traditional procedures, no study has compared all six of them simultaneously. In addition to van der Linden’s CEE, two additional variations of CEE are considered: CEE using maximum likelihood (CEE-MLE) and CEE using the true characteristic curve (CEE-TCC). The focus of this study is on comparing results from CEE vis-à-vis the traditional procedures, as opposed to answering a “best-procedure” question, which would require a common conception of “true” equating.