Fuzzy-set qualitative comparative analysis (fsQCA) has become one of the most prominent methods in the social sciences for capturing causal complexity, especially for scholars with small- and medium-"N" data sets. This research note explores two key assumptions in fsQCA's methodology for testing for necessary and sufficient…

The idea of test consistency is illustrated, with reference to two sets of test scores. A mathematical model is used to explain the relative consistency and relative inconsistency of measurements, and a means of indexing reliability is derived using the model. Practical aspects of estimating reliability are considered. (TJH)

Issues arising from difference scores with zero reliability that nevertheless allow a powerful test of change are discussed. Issues include the appropriateness of underlying statistical models for psychological data and the relationship between difference scores and power. Increases in reliability always increase power for a fixed effect size.…

An error in an essential equation within the article by Williams and Zimmerman is corrected, and the algebraic inequalities are translated into questions a researcher can ask about simple or residualized difference scores. Williams and Zimmerman acknowledge the error and note that main conclusions are not affected. (SLD)

A Bayesian alternative to interpretations based on classical reliability theory is presented. Procedures are detailed for calculation of a posterior score and credible interval with joint consideration of item sample and occasion error. (Author/SLD)

The formula developed by R. Levine (1955) for equating unequally reliable tests is described. The formula can be interpreted as a method of moments estimate of an equating function that results in first order equity of the equated test score under a classical congeneric model. (TJH)

D.V. Budescu and J.L. Rogers (1981) proposed a method of adjusting correlations of scales to eliminate spurious components resulting from the overlapping of scales. Three reliability correction formulas are derived in this article that are based on more tenable assumptions. (SLD)

Coefficient alpha was examined through computer simulation as an estimate of test reliability under violation of two assumptions. Coefficient alpha underestimated reliability under violation of the assumption of essential tau-equivalence of subtest scores and overestimated it under violation of the assumption of uncorrelated subtest error scores.…

To determine if the observed correlation between two variables can be "explained" by a third variable, a significance test on the partial correlation coefficient is often used. This can be misleading when the third variable is measured with error. This article shows how the problem can be partially overcome. (Author/BW)

Conditional item independence, also known as local independence, is necessary for the accurate estimation of item parameters within item response theory (IRT). Given that the condition of local independence will be violated to at least some degree when unidimensional models are used to represent multidimensional data, it is important to study the…

The internal correlation--a measure of dependency in a set of variables--is discussed and generalized. Applications of the internal correlation coefficient and its generalizations are given for several data-analytic situations. The internal correlation is illustrated and the concept is expanded to a series of additional indices. (TJH)

Use of internal correlation for statistical analysis--proposed by G. W. Joe and J. L. Mendoza (1989)--is discussed. Focus is on the "content" question (what this application can do with the information that statistics contain) and the "eloquence" question (the advantages of this means of encoding information over other means). (TJH)

The use of confirmatory factor analysis by the LISREL program is demonstrated as an assumption-testing method when computing reliability coefficients under different model assumptions. Results indicate that reliability estimates are robust against departure from the assumption of parallelism of test items. (SLD)

Designing a test using three-parameter item response theory (IRT) is discussed. A brief review of IRT is followed by a discussion of two types of test design: (1) selecting items using confidence envelopes (confidence envelope method); and (2) using item characteristic curves and their confidence intervals (test envelope method). The confidence…

Scoring of response vectors to give maximum test-retest correlation is investigated. A general method is given for finding the best scores, deriving them for the normal factor model, and showing that for a standard model for binary response it is easy to approximate the best scores. (SLD)