This report documents the development and validation of the National Education Longitudinal Study of 1988 (NELS:88) cognitive test battery. The cognitive test battery assesses growth between grades 8 and 12 in the content areas of reading comprehension, mathematics, science, and history/citizenship/geography. The battery was part of the NELS:88 administered to a representative sample of eighth graders in 1988 and again in 1990 and 1992. To minimize the floor and ceiling effects that typically distort gain scores, special procedures were designed into the battery. It used a two-stage multilevel procedure that attempted to tailor the difficulty of the test items to the performance level of a particular student through the administration of different test forms. Special vertical scaling procedures were used that allowed for Bayesian priors on subpopulations for both item parameters and scale scores. This report documents the test specifications for the multilevel forms and the scaling procedures, and it compares the more traditional non-Bayesian approaches to scaling longitudinal measures with the Bayesian approach. The multilevel approach was found to increase accuracy of measurement and to reduce floor and ceiling effects. (Contains 30 tables, 3 figures, 7 appendixes of supplemental information, and 42 references.) (SLD)