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…

Finding and interpreting lower bounds for reliability coefficients for tests with nonhomogenous items has been a problem for psychometricians. This paper presents a mathematical formula for finding the greatest lower bound for such a coefficient. (Author/JKS)

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 rederivation of Lord's formula for estimating variance in multiple matrix sampling is presented as well as the ways Cronbach's coefficient alpha and the Spearman-Brown prophecy formula are related in this context. (Author/JKS)

Three techniques for estimating Kuder Richardson reliability (KR20) coefficients for incomplete data are contrasted. The methods are: (1) Henderson's Method 1 (analysis of variance, or ANOVA); (2) Henderson's Method 3 (FITCO); and (3) Koch's method of symmetric sums (SYSUM). A Monte Carlo simulation was used to assess the precision of the three…

An upper-asymptote parameter was added to the three-parameter logistic item response model. This four-parameter model was compared to the three-parameter model on four data sets. The fourth parameter increased the likelihood in only two of the four sets. Ability estimates for the students were generally unchanged by the introduction of the fourth…

Results of a comparative study of F and Q tests, in a randomized block design with one replication per cell, are presented. In addition to these two procedures, a multivariate test was also considered. The model and test statistics, data generation and parameter selection, results, summary and conclusions are presented. Ten tables contain the…

Three equating methods were compared in terms of magnitude of scale drift: equipercentile equating, linear equating, and item response theory (IRT) equating. A sample of approximately 2670 cases was selected for each pairing of a form of the Scholastic Aptitude Tests (SAT) and an anchor test. Of the two conventional equating methods,…

A live tailored testing study was conducted to compare the results of using either the one-parameter logistic model or the three-parameter logistic model to measure the performance of college students on multiple choice vocabulary items. The results of the study showed the three-parameter tailored testing procedure to be superior to the…

Three types of test were compared: a completion test, a matching test, and a multiple-choice test. The completion test was more reliable than the matching test, and the matching test was more reliable than the multiple-choice test. (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)

The reliability of a criterion referenced test was defined as a measure of the degree to which the test discriminates between an individual's level of performance and a predetermined criterion level. The variances of observed and true scores were defined as the squared deviation of the score from the criterion. Based on these definitions and the…

Using the assumption of randomly parallel tests and concepts from generalizability theory, three signal/noise ratios for domain-referenced tests are developed, discussed, and compared. The three ratios have the same noise but different signals depending upon the kind of decision to be made as a result of measurement. (Author/JKS)

Generalizability theory (G-theory) and many-facet Rasch measurement (Rasch) manage the variability inherent when raters rate examinees on test items. The purpose of G-theory is to estimate test reliability in a raw score metric. Unadjusted examinee raw scores are reported as measures. A variance component is estimated for the examinee…

The adequacy of equipercentile, linear, one-parameter (Rasch), and three-parameter logistic item-response theory procedures for equating 12 forms of five tests of general educational development were compared. Results indicated the equating method adequacy depends on a variety of factors such as test characteristics, equating design, and sample…