We present an exploratory study of Costa Rican and Spanish students' (11-16-year-olds) competence to compare probabilities in urns and compare ratios in mixture problems. A sample of 704 students in Grades 6 through to Grade 10, 292 from Costa Rica and 412 from Spain, were given one of two forms of a questionnaire with three probability comparison…

The object of research is a statistics exam that contains problem tasks. One examiner performed two exam evaluation methods to repeatedly evaluate the exam. The goal was to compare the methods for objectivity. One of the two exam evaluation methods we call a serial evaluation method. The serial evaluation method assumes evaluation of all exam…

In adaptive learning systems, various models are employed to obtain the optimal learning schedule and review for a specific learner. Models of learning are used to estimate the learner's current recall probability by incorporating features or predictors proposed by psychological theory or empirically relevant to learners' performance. Logistic…

Since 1973, the National Assessment of Educational Progress (NAEP) has gathered information about student achievement in mathematics. Results of these periodic assessments, produced in print and web-based formats, provide valuable information to a wide variety of audiences. They inform citizens about the nature of students' comprehension of the…

If classification in a limited number of categories is the purpose of testing, computerized adaptive tests (CATs) with algorithms based on sequential statistical testing perform better than estimation-based CATs (e.g., Eggen & Straetmans, 2000). In these computerized classification tests (CCTs), the Sequential Probability Ratio Test (SPRT) (Wald,…

The one-parameter logistic model with ability-based guessing (1PL-AG) has been recently developed to account for effect of ability on guessing behavior in multiple-choice items. In this study, the authors developed algorithms for computerized classification testing under the 1PL-AG and conducted a series of simulations to evaluate their…

To assess item dimensionality, the following two approaches are described and compared: hierarchical generalized linear model (HGLM) and multidimensional item response theory (MIRT) model. Two generating models are used to simulate dichotomous responses to a 17-item test: the unidimensional and compensatory two-dimensional (C2D) models. For C2D…

This paper will discuss the results of a series of computer simulations comparing the Rasch logistic model to a series of models departing to various degrees from its assumption of equal discrimination power for all items. The results have implications for test construction and test scoring, indicating how closely the conventional raw score…

Item characteristic curve (ICC) theory describes the relationship between the ability of individuals and the probability of their answering a test question correctly; it is useful in estimating test scores, equating the scores of various tests, and scoring responses during adaptive testing. A simulation study of the effectiveness of the following…

The question of whether test factor structure is indicative of the test item hierarchy was examined. Data from 1,000 subjects on two sets of five bivalued Law School Admission Test items, which were analyzed with latent trait methods of Bock and Lieberman and of Christoffersson in Psychometrika, were analyzed with an ordering-theoretic method to…

A flexilevel test is found to be inferior to a peaked conventional test for measuring examinees in the middle of the ability range, superior for examinees at the extremes. Throughout the entire range of ability, a flexilevel test is much superior to any conventional test that attempts to provide accurate measurement at both extremes. See also ED…

Procedures for determining cutting scores have been proposed by Angoff and by Nedelsky. Nedelsky's approach requires that a rater examine each distractor within a test item to determine the probability of a minimally competent examinee answering correctly; whereas Angoff uses a judgment based on the whole item, rather than each of its components.…

In order to determine if Rasch Model procedures have any utility for equating pre-existing tests, this study reanalyzed the data from the equating phase of the Anchor Test Study which used a variety of equipercentile and linear model methods. The tests involved included seven reading test batteries, each having from one to three levels and two…

This volume contains tables of item analysis results obtained by following procedures associated with the Rasch Model for those reading tests used in the Anchor Test Study. Appendix I gives the test names and their corresponding analysis code numbers. Section I (Basic Item Analyses) presents data for the item analysis of each test in a two part…