Online educational technologies offer opportunities for providing individualized feedback and detailed profiles of students' skills. Yet many technologies for mathematics education assess students based only on the correctness of either their final answers or responses to individual steps. In contrast, examining the choices students make for how…

Fisher's two-group discriminant function has been generalized in two different ways for the case of three or more groups, leading to confusion in the literature. The precise functional relation between the two functions is derived, and the interpretation of the two functions is discussed. An example is provided. (Author/CTM)

Diagnostic hit rates for the Diagnostic Inventory of Personality and Symptoms were compared to diagnosis by psychiatrists of the same patients. The Probability Scale employing Bayesian concepts and base rates correctly classified 70% of the patients and was more accurate by far than the other two methods used. (Author/ABB)

A coherent system of decision making is described that may be incorporated into an instructional sequence to provide a supplement to the experience-based judgment of the classroom teacher. The elements of this decision process incorporate prior information such as a teacher's past experience, experimental results such as a test score, and…

Weber contends that the use of Rasch analysis, principal components analysis, and classical test analysis shows that an instrument designed to measure a "bilevel dimensionality" in probability achievement measures a single latent trait. That interpretation and the use of Rasch and classical analysis to establish unidimensionality are…

Effects of blind guessing on the success of passing true-false and multiple-choice tests are investigated under a stochastic binomial model. Critical values of guessing are thresholds which signify when the effect of guessing is negligible. By checking a table of critical values assembled in this paper, one can make a decision with 95% confidence…

Evaluated with 25 learning disabled (LD) and 25 non LD elementary level children was the Bayesian method to screen children for possible LD, an approach which uses the aggregation of data--objective test scores related to likelihood ratios and a known prior odds ratio. (Author/DB)

False-positive and false-negative decisions are the two possible errors committed with a mastery test; yet the estimation of the likelihood of committing these errors has not been investigated. Two methods of this type of estimation are presented and discussed. (Author/JKS)

Item mappings are widely used in educational assessment for applications such as test administration (through test form assembly and computer assisted testing) and for criterion-referenced (CR) interpretation of test scores or scale anchoring. Item mappings are also used to construct ordered item booklets in the CTB/McGraw Hill Bookmark standard…

By noting that a Rasch or two parameter logistic (2PL) item belongs to the exponential family of random variables and that the probability density function (pdf) of the correct response (X=1) and the incorrect response (X=0) are symmetric with respect to the vertical line at the item location, it is shown that the conjugate prior for ability is…

Since the primary purpose of classical testing is to rank order examinees consistently, the absolute value of the true score has been relatively unimportant. However, the major purpose of criterion referenced testing is to estimate the true capabilities of examinees to perform specific tasks. Hence, the problems of true score determination assume…

Describes a procedure, called a full Bayesian procedure, for making decisions in connection with criterion-referenced measurements. The procedure uses continuous utility functions instead of a dichotomized utility structure and combines the posterior distribution for a certain person with utility functions for "advance" and "retain" decisions…

Diagnostic testing confronts several challenges at once, among which are issues of test interpretation and immediate modification of the test itself in response to the interpretation. Several methods are available for administering and evaluating a test in real-time, towards optimizing the examiner's chances of isolating a persistent pattern of…

This paper describes two procedures for making binary classification decisions using tailored testing: the sequential probability ratio test (SPRT) and a Bayesian decision procedure. The first procedure described, the SPRT, was developed by Wald for quality control work. It has not been widely applied for testing applications because the…

Two procedures were developed to determine whether examinees in a given test center were affected by a testing irregularity on the Listening Comprehension section of the Test of English as a Foreign Language (TOEFL). One approach employed analysis of covariance (ANCOVA) on Listening Comprehension (Section 1) means using scores on Structure and…