In most school achievement research, the relationships between achievement and explanatory variables follow the Newton and Einstein concept/principle and the viewpoint of the macro-observer: Deterministic measures based on the mean value of a sufficiently large number of schools. What if the relationships between achievement and explanatory…

Grading on the curve is a common practice in higher education. While there are many critics of the practice it still finds wide spread acceptance particularly in science classes. Advocates believe that in large classes student ability is likely to be normally distributed. If test scores are also normally distributed instructors and students tend…

Describes a Windows program for checking the suitability of unidimensional logistic item response models for binary and ordered polytomous responses with respect to a given set of data. The program is based on predicting the observed test score distributions from the item characteristic curves. (SLD)

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.…

Estimation/smoothing methods that are flexible enough to fit a wide variety of test score distributions are reviewed: kernel method, strong true-score model-based method, and method that uses polynomial log-linear models. Applications of these methods include describing/comparing test score distributions, estimating norms, and estimating…

A simple scheme is proposed for smoothly approximating the ability distribution for relatively long tests, assuming that the item characteristic curves (ICCs) are known or well estimated. The scheme works for a general class of ICCs and is guaranteed to completely recover the theta distribution as the test length increases. The proposed method of…

Previous work on the mathematical and implementation details of the marginalized maximum likelihood estimation procedure is extended to encompass the marginalized Bayesian procedure for estimating item parameters of R. J. Mislevy (1986) and to communicate this procedure to users of the BILOG computer program. (SLD)

Inference is considered for the marginal distribution of "X" when ("X", "Y") has a truncated bivariate normal distribution. The "Y" variable is truncated, but only the "X" values are observed. A sample of 87 Otis test scores is shown to be well described by this model. (SLD)

Derivations of several item selection algorithms for use in fitting test items to target information functions (IFs) are described. These algorithms, which use an average growth approximation of target IFs, were tested by generating six test forms and were found to provide reliable fit. (SLD)

A model developed by G. Rasch that assumes scores on some attainment tests can be realizations of a Poisson process is explained and expanded by assuming a prior distribution, with fixed but unknown parameters, for the subject parameters. How additional between-subject and within-subject factors can be incorporated is discussed. (SLD)

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…

Three methods of estimating test score distributions that may improve on using the observed frequencies (OBFs) as estimates of a population test score distribution are considered: the kernel method (KM); the polynomial method (PM); and the four-parameter beta binomial method (FPBBM). The assumption each method makes about the smoothness of the…

Attitude measures frequently produce distributions of item scores that attenuate interitem correlations and thus also distort findings regarding the factor structure underlying the items. An actual data set involving 260 adult subjects' responses to 55 items on the Love Relationships Scale is employed to illustrate empirical methods for…

Analyzes effect sizes in tails of distribution of scores in Feingold's study of joint effects of gender differences in mean and variability on 28 cognitive-ability scales. Effect sizes are smaller than Feingold assumed. Evaluates joint effect of gender differences by number of males and females in extreme score ranges. (SLD)

Monte Carlo techniques are used to examine the power of the "B" statistic of R. L. Brennan (1972) to detect negatively discriminating items drawn from a variety of nonnormal population distributions. A simplified procedure is offered for conducting an item-discrimination analysis on typical classroom objective tests. (SLD)