This article proposes that sampling design effects have potentially huge unrecognized impacts on the results reported by large-scale district and state assessments in the United States. When design effects are unrecognized and unaccounted for they lead to underestimating the sampling error in item and test statistics. Underestimating the sampling…

Sampling errors limit the accuracy with which forms can be linked. Limitations on accuracy are especially important in testing programs in which a very large number of forms are employed. Standard inequalities in mathematical statistics may be used to establish lower bounds on the achievable inking accuracy. To illustrate results, a variety of…

Transformations or equating of raw test scores on two or more forms of the same test are made interchangeable by empirical procedures deriving the standard error of an equipercentile equating for four different situations. Some numerical results are checked by Monte Carlo methods. Numerical standard errors are computed for two sets of real data.…

This study investigates the amount of uncertainty added to National Assessment of Educational Progress (NAEP) estimates by equating error under both ideal and less than ideal circumstances. Data from past administrations are used to guide simulations of various equating designs and error due to equating is estimated empirically. The design…

Linear and equipercentile equating conversions were developed for two forms of the Graduate Record Examinations (GRE) quantitative test and the verbal-plus-quantitative test. From a very large sample of students taking the GRE in October 1981, subpopulations were selected with respect to race, sex, field of study, and level of performance (defined…

A Monte Carlo study was conducted to compare the statistical bias and standard errors of non-equivalent-groups linear test equating in small samples of examinees. One thousand samples of each size (15, 25, 50, and 100) were drawn with replacement from each of five archival data files from elementary school and secondary school teacher subject area…