Describing the variation in test scores between and within school districts is critical for: (1) for policy-related and descriptive work that investigates the sorting of students among districts and the differential effectiveness of those districts; and (2) for methodological work planning future experiments or interventions. Intraclass…

Similarity between pairs of scores with a common mean and variance can be expressed in terms of the absolute differences between them. The distribution of such absolute differences between pairs of normally distributed scores with a common mean and variance is discussed, with procedures for calculating moments and areas within this distribution.…

The normalized mean is developed and discussed as a descriptive measure of central location. The advantages of the normalized mean over the arithmetic mean, median, and trimmed mean are discussed. (Author)

Two methods of constucting equal-interval scales for educational achievement are discussed: Thurstone's absolute scaling method and Item Response Theory. Alternative criteria for choosing a scale are contrasted. It is argued that clearer criteria are needed for judging the appropriateness and usefulness of alternative scaling procedures.…

The functioning of two population-based Mantel-Haenszel (MH) common-odds ratios was compared. One ratio is conditioned on the observed test score, while the other is conditioned on a latent trait or true ability score. When the comparison group distributions are incongruent or nonoverlapping to some degree, the observed score represents different…

Three methods for estimating reliability are studied within the context of nonparametric item response theory. Two were proposed originally by Mokken and a third is developed in this paper. Using a Monte Carlo strategy, these three estimation methods are compared with four "classical" lower bounds to reliability. (Author/JAZ)

This study compared five density estimation techniques applied to samples from a population of 272,244 examinees' ACT English Usage and Mathematics Usage raw scores. Unsmoothed frequencies, kernel method, negative hypergeometric, four-parameter beta compound binomial, and Cureton-Tukey methods were applied to 500 replications of random samples of…

Four discrimination indices were compared, using score distributions which were normal, bimodal, and negatively skewed. The score distributions were systematically varied to represent the common circumstances of a military training situation using criterion-referenced mastery tests. Three 20-item tests were administered to 110 simulated subjects.…