Measurement is prescriptive in that the model required to produce the numbers from the phenomena is known in advance. Statistical theory is descriptive because the model required to explain the numbers is inferred from the numbers and any other information the researcher can bring to bear. There are well-known families of measurement models and…

When one wants to set data reliability standards for a class of scientific inquiries or when one needs to compare and select among many different kinds of data with reliabilities that are crucial to a particular research undertaking, then one needs a single reliability coefficient that is adaptable to all or most situations. Work toward this goal…

The jackknife statistic is discussed as a viable invariance procedure. Data from a study of leadership illustrates the use of the jackknife in determining the stability of canonical function coefficients following canonical correlation analysis. The jackknife procedure entails arbitrarily omitting one observation or a subset of observations at a…

The growth curve approach to the measurement of gain of D. Rogosa, D. Brandt, and M. Zimowski (1982) was more fully developed by J. B. Willet and D. Rogosa (1985). Willet later (1989) discussed some practical aspects of applying a linear growth model and reached the conclusion that reliability may not always be a useful index for the measurement…

This paper presents a detailed derivation of method of moments estimates used in computer programs for the four-parameter beta compound binomial strong true score model. A procedure is presented to deal with the case in which the usual method of moments estimates do not exist or result in invalid parameter estimates. The results presented…

The challenge of multiple comparisons is to maximize the power for answering specific research questions, while still maintaining control over the rate of Type I error. Several multiple comparison procedures have been suggested to meet this challenge. The stagewise protected procedure (SPP) of A. J. Klockars and G. R. Hancock tests null hypotheses…

The scree test and its linear regression technique are reviewed, and results of its use in factor analysis and Delphi data sets are described. The scree test was originally a visual approach for making judgments about eigenvalues, which considered the relationships of the eigenvalues to one another as well as their actual values. The graph that is…

Using computer simulation data, the effect of a single global outlier in two-group classification analysis was explored in terms of the outcome variables of change in classification results (PCHNG), change in misclassification rate (MISDIF), and change in precision of misclassification rate estimation. The precision of misclassification rate…

The capability of the DIMTEST statistical test to assess essential dimensionality of the model underlying item responses of real tests as opposed to simulated tests was investigated. A variety of real test data from difference sources was used to assess essential dimensionality. Based on DIMTEST results, some test data are assessed as fitting an…

The empirical Bayes modeling approach--latent ability random sampling in the item response theory (IRT) context--to the IRT modeling of psychological tests is described. Under the usual empirical Bayes unidimensional IRT modeling approach, the posterior distribution of examinee ability given test response is approximately normal for a long test.…

In 1955, R. Levine introduced two linear equating procedures for the common-item non-equivalent populations design. His procedures make the same assumptions about true scores; they differ in terms of the nature of the equating function used. In this paper, two parameterizations of a classical congeneric model are introduced to model the variables…

A statistical procedure is presented that is designed to test for unidirectional test bias existing simultaneously in several items of an ability test, based on the assumption that test bias is incipient within the two groups' ability differences. The proposed procedure--Simultaneous Item Bias (SIB)--is based on a multidimensional item response…

Combining student scores to form subtotals and finally a total score to determine a grade is discussed. The composite score reached by combining measures or subtotals is only valid when the scores are combined so that the actual weight of each measure or subtotal in the total score is the same as the intended weight. Three types of variability…

The extent to which standardized regression coefficients (beta values) can be used to determine the importance of a variable in an equation was explored. The beta value and the part correlation coefficient--also called the semi-partial correlation coefficient and reported in squared form as the incremental "r squared"--were compared for…

An adaptive test can usually match or exceed the measurement precision of conventional tests several times its length. This increased efficiency is not without costs, however, as the models underlying adaptive testing make strong assumptions about examinees and items. Most troublesome is the assumption that item pools are unidimensional. Truly…