Coefficient alpha, the most commonly used estimate of internal consistency, is often considered a lower bound estimate of reliability, though the extent of its underestimation is not typically known. Many researchers are unaware that coefficient alpha is based on the essentially tau-equivalent measurement model. It is the violation of the…

Use of the Mantel-Haenszel procedure as a test for differential item functioning under the Rasch model of item-response theory is examined. Results of the procedure cannot be generalized to the class of items for which item-response functions are monotonic and local independence holds. (TJH)

The binomial error model includes form-to-form difficulty differences as error variance and leads to Ruder-Richardson formula 21 as an estimate of reliability. If the form-to-form component is removed from the estimate of error variance, the binomial model leads to KR 20 as the reliability estimate. (Author/BW)

Single administration (beta-binomial) estimates for the raw agreement index p and the corrected-for-chance kappa index in mastery testing are compared with those based on two test administrations in terms of estimation bias and sampling variability. Bias is about 2.5 percent for p and 10 percent for kappa. (Author/RL)

One aim of criterion-referenced testing is to classify an examinee without reference to a norm group; therefore, any statements about the dependability of such classification ought to be group-independent also. A population-independent index is proposed in terms of the probability of incorrect classification near the cutoff true score. The…

Two fundamental problems in mental test theory are to estimate true score and to estimate the amount of error when testing an examinee. In this report, three probability models which characterize a single test item in terms of a population of examinees are described. How these models may be modified to characterize a single examinee in terms of an…

A method of estimating the operating characteristics of a new test item added to an established test without assuming a prior model has been proposed by the author. In this paper, the author extends this logic by proposing a different hypothesized distribution of the resulting estimate. The former method used a normal approximation; the present…

The setting of standards involves subjective value judgments. The inherent arbitrariness of specific standards has been severely criticized by Glass. His antagonists agree that standard setting is a judgmental task but they have pointed out that arbitrariness in the positive sense of serious judgmental decisions is unavoidable. Further, small…

Ways in which the Statistical Package for the Social Sciences (SPSS) can be used to perform some Rasch analyses are described in detail. It is shown how SPSS and a set of item calibrations can be used to estimate person abilities, standard errors of measurement, test characteristic curve, test information curve, classification consistency on a…

A general process for testing the feasibility of applying alternative mathematical or statistical models to the solution of a practical problem is presented and flowcharted. The system is used to develop a plan to compare models for test equating. The five alternative models to be considered for equating are: (1) anchor test equating using…

Believing that examinee-by-item interaction should be conceptualized as true score variability rather than as a result of errors of measurement, Lu proposed a modification of Hoyt's analysis of variance reliability procedure. Via a computer simulation study, it is shown that Lu's approach does not separate interaction from error. (Author/RL)

The relationship between levels of reliability and the power of two bias and differential item functioning (DIF) detection methods is examined. Both methods, the Mantel-Haenszel (MH) procedure of P. W. Holland and D. T. Thayer (1988) and the Simultaneous Item Bias (SIB) procedure of R. Shealy and W. Stout (1991), use examinees' raw scores as a…

The robustness of a partial credit (PC) model-based computerized adaptive test's (CAT's) ability estimation to items that did not fit the PC model was investigated. A CAT program was written based on the PC model. The program used maximum likelihood estimation of ability. Item selection was on the basis of information. The simulation terminated…

In order to determine the effectiveness of multidimensional scaling (MDS) in recovering the dimensionality of a set of dichotomously-scored items, data were simulated in one, two, and three dimensions for a variety of correlations with the underlying latent trait. Similarity matrices were constructed from these data using three margin-sensitive…

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…