Procedures for determining the number of clusters in a data set are explored. A proposed stopping rule, the GRAPH criterion, is compared to four stopping rules currently in use. The GRAPH criterion's mathematically attractive properties and utility in solving the number-of-clusters problem are demonstrated. (SLD)

This dissertation includes three essays: one essay focuses on the effect of teacher preparation programs on teacher knowledge while the other two focus on test-takers' response times on test items. Essay One addresses the problem of how opportunities to learn in teacher preparation programs influence future elementary mathematics teachers'…

This paper examines some characteristics of the statistics associated with the sampling distribution of the proficiency level estimate when the Rasch model is used. These characteristics allow the judgment of the meaning to be given to the proficiency level estimate obtained in adaptive testing, and as a consequence, they can illustrate the…

In decisions from experience, there are 2 experimental paradigms: sampling and repeated-choice. In the sampling paradigm, participants sample between 2 options as many times as they want (i.e., the stopping point is variable), observe the outcome with no real consequences each time, and finally select 1 of the 2 options that cause them to earn or…

A split-sample replication stopping rule for hierarchical cluster analysis is compared with the internal criterion previously found superior by Milligan and Cooper (1985) in their comparison of 30 different procedures. Situations under which the methods are equivalent or not equally useful are discussed. (SLD)

A total of 520 high school students were randomly assigned to a paper-and-pencil test (PPT), a computerized standard test (CST), or a computerized adaptive test (CAT) version of the Dutch School Attitude Questionnaire (SAQ), consisting of ordinal polytomous items. The CST administered items in the same order as the PPT. The CAT administered all…

Effects of the following variables on performance of computerized adaptive testing (CAT) procedures for the partial credit model (PCM) were studied: (1) stopping rule for terminating CAT; (2) item pool size; and (3) distribution of item difficulties. Implications of findings for CAT systems based on the PCM are discussed. (SLD)

A split-sample replication criterion originally proposed by J. E. Overall and K. N. Magee (1992) as a stopping rule for hierarchical cluster analysis is applied to multiple data sets generated by sampling with replacement from an original simulated primary data set. An investigation of the validity of this bootstrap procedure was undertaken using…

Mixture modeling is a widely applied data analysis technique used to identify unobserved heterogeneity in a population. Despite mixture models' usefulness in practice, one unresolved issue in the application of mixture models is that there is not one commonly accepted statistical indicator for deciding on the number of classes in a study…

In a variable-length adaptive test with a stopping rule that relied on the asymptotic standard error of measurement of the examinee's estimated true score, M. S. Stocking (1987) discovered that it was sufficient to know the examinee's true score and the number of items administered to predict with some accuracy whether an examinee's true score was…

The level of confidence in pass/fail decisions obtained with computerized adaptive tests and paper-and-pencil tests was greater for 645 medical technology students when the computer adaptive test implemented a 90 percent confidence stopping rule than for paper-and-pencil tests of comparable length. (SLD)

General guidelines are developed to assist practitioners in devising operational computerized adaptive testing systems based on the graded response model. The effects of the following major variables were examined: item pool size; stepsize used along the trait continuum until maximum likelihood estimation could be calculated; and stopping rule…

A new computerized mastery test is described that builds on the Lewis and Sheehan procedure (sequential testlets) (1990), but uses fuzzy set decision theory to determine stopping rules and the Rasch model to calibrate items and estimate abilities. Differences between fuzzy set and Bayesian methods are illustrated through an example. (SLD)

This paper reports a method for assessing the adequacy of existing item banks for computer adaptive testing. The method takes into account content specifications, test length, and stopping rules, and can be used to determine if an existing item bank is adequate to administer a computer adaptive test efficiently across differing levels of examinee…

Discussion of expert systems and computerized adaptive tests describes two versions of EXSPRT, a new approach that combines uncertain inference in expert systems with sequential probability ratio test (SPRT) stopping rules. Results of two studies comparing EXSPRT to adaptive mastery testing based on item response theory and SPRT approaches are…