Explanatory item response models (EIRMs) have been applied to investigate the effects of person covariates, item covariates, and their interactions in the fields of reading education and psycholinguistics. In practice, it is often assumed that the relationships between the covariates and the logit transformation of item response probability are…

We present a logistic function of a monotonic polynomial with a lower asymptote, allowing additional flexibility beyond the three-parameter logistic model. We develop a maximum marginal likelihood-based approach to estimate the item parameters. The new item response model is demonstrated on math assessment data from a state, and a computationally…

An approximation procedure for determining the correct power or sample size values for Scheffe contrasts is given. (RL)

The purpose of this study was to investigate the degree to which various selected test item discrimination indices reflect a common factor. The indices used include the point-biserial, biserial, phi and tetrachoric coefficients, Flanagan's approximation of the product-moment correlation, Gulliksen's item reliability index, and Findley's difference…

Some procedures for estimating internal consistency reliability may be superior mathematically to the more commonly used methods such as Coefficient Alpha. One problem is computational difficulty; the other is the possibility of overestimation due to capitalization on chance. (Author/CTM)

A simple, usefully accurate approximation of the standard error of measurement is proposed for use by classroom teachers. An empirical comparison with Lord's approximation indicated that, though not as easy to calculate as Lord's, this approximation is more practical because it is useful at any point in the score distribution. (BW)

For tests used to make pass/fail decisions, the relevant standard error of measurement (SEM) is the SEM at the passing score. If the test is highly stratified, this SEM should be estimated by a split-halves approach. A formula and its derivation are provided. (Author)

Different indices for the internal consistency, reproducibility, or homogeneity of a test are based upon highly similar conceptual frameworks. Illustrations are presented to demonstrate how the maximum and minimum values of KR20 are influenced by test difficulty and the shape of the distribution of test scores. (Author/CTM)

The determination of acceptable performance in Thorndike's constant ratio standard of fair selection is considered. It is shown that suitable choice of acceptable performance can make any minority-majority selection disparity consistent with Thorndike's standard. A rule for determining acceptable performance which avoids the Petersen-Novick…

Procedures are described for studying the reliability of decisions based on specific passing scores with tests made up of discrete items and designed to measure continuous rather than categorical traits. These procedures are based on the estimation of the joint distribution of true scores and observed scores. (CTM)

The consistency with which students apply procedural rules for solving signed-number operations across identical items presented in different orders was examined in a study involving 161 eighth graders. Inconsistent rule application was common among students who had not mastered signed-number arithmetic operations. (TJH)