Research by Huck and McLean (1975) demonstrated that the covariance-adjusted score is more powerful than the simple difference score, yet recent reviews indicate researchers are equally likely to use either score type in two-wave randomized experimental designs. A Monte Carlo simulation was conducted to examine the conditions under which the simple difference and covariance-adjusted scores were more or less powerful to detect treatment effects when relaxing certain assumptions made by Huck and McLean (1975). Four factors were manipulated in the design including sample size, normality of the pretest and posttest distributions, the correlation between pretest and posttest, and posttest variance. A 5 × 5 × 4 × 3 mostly crossed design was run with 1,000 replications per condition, resulting in 226,000 unique samples. The gain score was nearly as powerful as the covariance-adjusted score when pretest and posttest variances were equal, and as powerful in fan-spread growth conditions; thus, under certain circumstances the gain score could be used in two-wave randomized experimental designs.

This paper presents the item and test information functions of the Rank two-parameter logistic models (Rank-2PLM) for items with two (pair) and three (triplet) statements in forced-choice questionnaires. The Rank-2PLM model for pairs is the MUPP-2PLM (Multi-Unidimensional Pairwise Preference; Morillo et al., 2016), and for triplets, is the Triplet-2PLM (Fu et al., 2023a). Fisher's information and directional information are described, and the test information for Maximum Likelihood (ML), Maximum A Posterior (MAP), and Expected A Posterior (EAP) trait score estimates is distinguished. Expected item/test information indexes at various levels are proposed and plotted to provide diagnostic information on items and tests. The expected test information indexes for EAP scores may be difficult to compute due to a typical test's vast number of item response patterns. The relationships of item/test information with discrimination parameters of statements, standard error, and reliability estimates of trait score estimates are discussed and demonstrated using real data. Practical suggestions for checking the various expected item/test information indexes and plots are provided.