The decision making processes of children in a probabilistic environment were studied within the context of the theory of signal detection (TSD). The relationship between the age of the child and his ability to revise decision criteria was examined, as well as the appropriateness of TSD measures and methodology with children. It was hypothesized…

The analysis of fit of data to a measurement model for graded responses is described. The model is an extension of Rasch's dichotomous model to formats which provide more than two levels of response to items. The model contains one parameter for each person and one parameter for each "step" in an item. A dichotomously-scored item…

The tests for zero partial association in a multiple contingency table have gained new importance with the introduction of graphical models. It is shown how these may be performed as exact conditional tests, using as test criteria either the ordinary likelihood ratio, the standard x squared statistic, or any other appropriate statistics. A…

These worksheets suggest activities through which secondary school students may be introduced to the ideas of simulation. All can be played as games to give students a feel for the situation modeled; most use coins or dice and a few use random digits. Directions are detailed for each of the 17 worksheets, with variations suggested for many. (MMS)

THIS PAPER DEALS WITH SOME TESTS OF HYPOTHESIS FREQUENTLY ENCOUNTERED IN THE ANALYSIS OF MULTIVARIATE DATA. THE TYPE OF HYPOTHESIS CONSIDERED IS THAT WHICH THE STATISTICIAN CAN ANSWER IN THE NEGATIVE OR AFFIRMATIVE. THE DOOLITTLE METHOD MAKES IT POSSIBLE TO EVALUATE THE DETERMINANT OF A MATRIX OF HIGH ORDER, TO SOLVE A MATRIX EQUATION, OR TO…

The use of data on longitudinal student attendance patterns to determine variances, and hence confidence bounds, on student enrollment forecasts, in addition to finding the forecasts themselves, is demonstrated. The formulation of the enrollment model based on longitudinal student attendance patterns is described step by step, presenting the…

Students in general undergraduate courses in both biology and genetics seem to have great difficulty mastering the basic concepts of Mendelian Genetics and solving even simple problems. In an attempt to correct this situation, students in both courses at Rollins College were introduced to three simulation models of the genetics of the fruit…

The purpose of this paper is to lay a basis for and discuss the components of a system, called COMET, designed to objectively measure and evaluate the competency of trainees in military training enterprises. COMET is an acronym for "Computerized Objective Measurement and Evaluation of Trainees." These goals will be accomplished by: (a)…

The assumptions of the Criterion-Referenced Test (CRT) model proposed by Kriewall are compared to those of Emrick and Adam's Mastery-Learning (ML) model. Testing, in the context of instructional management, serves three general purposes: performance evaluation (achievement of objectives), placement (classification of students for instruction), and…

A Markov model for predicting performance on criterion-referenced tests is presented,. The model is expressed mathematically as a function of transition matrix, a current state vector, and a future state vector. The matrix is defined in terms of conditional probabilities, i.e., the probability of making a transition to a specific future…

A mathematical model for computer-aided instruction has been developed. The assumption is made that the course is divided into a hierarchy of levels of difficulty and that if a student is able to perform successfully at a given level of difficulty, he can also perform successfully at all levels of lesser difficulty. Furthermore, if a student…

An analytical framework is described through which voluntary attrition can be predicted. The approach incorporates Marshallian Utility Theory and a Maximum Likelihood Estimation procedure to evaluate a specific individual's propensity to attrit. The approach was tested twice at the United States Air Force Academy where it was able to correctly…

Summarizing work which is part of an Army research program on Methodological Issues in the Construction of Criterion Referenced Tests, the focus of this paper is on a Bayesian model, which gives the probability of correctly classifying an examiner as a master or as a nonmaster while taking into consideration the test length and the mastery cut-off…

An activity involving the charting of the spread of a disease is described. Arrows are used to develop models of the progression of the disease. (MNS)

Discusses the surprising result that the expected number of marbles of one color drawn from a set of marbles of two colors after two draws without replacement is the same as the expected number of that color marble after two draws with replacement. Presents mathematical models to help explain this phenomenon. (MDH)