Nonequivalent Groups: Equipercentile Methods

Equipercentile equating methods have been developed for the common-item nonequivalent groups design. These methods are similar to the equipercentile methods for random groups described in Chapter 2. Equipercentile methods with nonequivalent groups consider the distributions of total score and scores on the common items, rather than only the means, standard deviations, and covariances that were considered in Chapter 4. As has been indicated previously, equipercentile equating is an observed score equating procedure that is developed from the perspective of the observed score equating property described in Chapter 1. Thus, equipercentile equating with the common-item nonequivalent groups design requires that a synthetic population, as defined in Chapter 4, be considered. In this chapter, we present an equipercentile method that we show to be closely allied to the Tucker linear method of Chapter 4. We also describe how smoothing methods, such as those described in Chapter 3, can be used when conducting equipercentile equating with nonequivalent groups. The methods described in this chapter are illustrated using the same data that were used in Chapter 4, and the results are compared to the linear results from Chapter 4.