Measuring object similarity using the method of free clustering is gaining in popularity. Instructions are usually simple and since no structure is imposed on the subject's selection, response bias is reduced. More importantly, measures of object similarity derived from the judges' clustering can be adequately analyzed by the methods of…

This is a School Mathematics Study Group (SMSG) probability text for primary school students. The main goal of the text is to introduce some basic ideas of probability. The text is written at the level of a child's intuitive knowledge of what constitutes "an equal chance" or "a better chance." The authors suggest that there are…

This is a manual for teachers using School Mathematics Study Group (SMSG) primary school text materials. The commentary is organized into three parts. The first part contains an introduction and a section on mathematical comments relating to background knowledge needed by the teacher. The second and main part consists of a chapter by chapter…

IN THIS EXPERIMENT, 186 FRESHMAN ENGINEERING STUDENTS STUDIED ELEMENTARY PROBABILITY BY THESE INSTRUCTIONAL METHODS--(1) MULTIPLE CHOICE TEACHING MACHINES, (2) FREE-RESPONSE TEACHING MACHINES IN INDIVIDUAL BOOTHS AND IN CLASSROOMS, (3) PROGRAMED TEXTS REQUIRING OVERT RESPONSES AND GIVING CORRECT ANSWERS, (4) PROGRAMED TEXTS REQUIRING NO OVERT…

A method of estimating the parameters of the Rasch Model removing the effect of ramdom guessing is presented. The procedure is an application of the ARRG (Abilities Removing Random Guessing) model recently developed for two parameter latent trait models. Under the Rasch model ARRG provides for estimation of abilities, removing the effects of…

This paper explains the concept of models, their construction, and their use. It is suggested that mathematics is a helpful tool in model construction, and that models in general are indispensable in science. Models identify variables and illustrate causal relationships among the variables. An attempt is made to classify models from the point of…

Probability and statistics have become indispensable to scientific, technical, and management progress. They serve as essential dialects of mathematics, the classical language of science, and as instruments necessary for intelligent generation and analysis of information. A prelude to probability and statistics is presented by examination of the…

College students attempted to learn the concept of binomial probability from four-lesson teaching booklets. The booklets were of two forms, one emphasizing calculation with a formula and the other stressing the meanings of component variables. Also some subjects studied only one or two parts of the booklets while others completed the booklets…

The relationship between true ability (operationally defined as the number of items for which the examinee actually knew the correct answer) and the effects of guessing upon observed test variance was investigated. Three basic hypotheses were treated mathematically: there is no functional relationship between true ability and guessing success;…

The main purpose of this study was to develop predictive expressions for community college curricula, particularly in the vocational areas, that would indicate the probable success of entering freshmen. The study, conducted at San Diego City and San Diego Mesa Colleges during 1967-68, included 2,279 students. The subjects were divided into groups…

The area investigated in the present study is the comparison of the permutation t-test with Student's t-test and the Mann-Whitney U-test. The comparison was made for small samples for three distributions, including a normal distribution, a uniform distribution, and a skewed distribution. The properties of each test compared were the probability of…

One approach to the problem of analyzing classroom interaction by use of a Markoff chain is presented. The two sections of the paper present (1) a discusion of Hoel's test of order of a Markoff chain, and a Likelihood Ratio Criterion (LRC) for a two-dependent Markoff chain is given, and (2) a discussion of possible adjustments of Darwin's LRC with…

The analysis of covariance is frequently used in observational studies to either adjust treatment comparisons for biases due to different distributions of extraneous variables or for improving the precison of the treatment comparisons. This paper discusses aspects that the researcher should keep in mind when planning such a study. In particular it…

Some applications of the theory of games to competitive situations are examined by looking at several examples, including a military problem, a political problem, and a prisoner's dilemma. (MP)

This informal survey found that the probability that a person is in the over 45 age group, and is left-handed, is significantly different from the probability in the population as a whole. (MP)