Criteria for prediction of multinomial responses are examined in terms of estimation bias. Logarithmic penalty and least squares are quite similar in behavior but quite different from maximum probability. The differences ultimately reflect deficiencies in the behavior of the criterion of maximum probability.

The probability integral of the multivariate normal distribution (ND) has received considerable attention since W. F. Sheppard's (1900) and K. Pearson's (1901) seminal work on the bivariate ND. This paper evaluates the formula that represents the "n x n" correlation matrix of the "chi(sub i)" and the standardized multivariate…

The use of a Bayesian approach in evaluating data from clinical trials with many treatment centers and from many studies is discussed. The main distinction between a metaanalysis and an analysis of a multicenter trial is that different studies may have very different designs, while the centers in a multicenter trial usually follow the same…

The probability of experiment-wise error is explored. Overall, the experiment-wise error rate is directly related to the test-wise error rate--the alpha level set by researchers to curtail the existence of a Type I error. A Type I error occurs when a true null hypothesis is rejected in a given study or experiment. The experiment-wise error rate is…

In an attempt to accommodate each of two perspectives (nature versus nurture) in the formulation of a developmental framework, two complementary approaches to developmental theory are presented. First, consideration is given to what is now known about the developmental process in general (thought out in terms of the question "Where is the…

SPIRIT is an Intelligent Tutoring System for tutoring probability theory which has evolved through a continuous process of experimentation and tuning. The system manages a unique flexible tutoring style. On one hand, the system may behave as a tutor who mostly observes the student without interference, intervening only when things are really going…

To determine whether the distraction effect associated with material rewards in discrimination learning can account for the superior performance of reward groups in probability learning, the performance of 144 school children (preschool, second, and fifth grades) on a two-choice successive discrimination task was compared under three reinforcement…

This teacher's guide provides background information, lists of needed equipment, suggestions for instruction, and answers to student exercises. The unit is designed for elementary school students as a supplement to other SMSG volumes; it can, however, be used in any program. It is designed to make mathematics enjoyable, promote systematic…

The studies reported here asked: (a) How does receipt of outcome knowledge affect judgment? (b) How aware are people of the effects that outcome knowledge has on their perceptions? Answers to these questions will shed light on how people do learn and might better learn from history. (Author/RK)

A Bayesian Model II approach to the estimation of proportions in m groups is extended to obtain posterior marginal distributions for the proportions. The approach is extended to allow greater use of prior information than previously and the specification of this prior information is discussed. (Author/RC)

In two experiments the probabilistic properties of an internal (skill) task were simulated in an external (chance) task. (Editor)

Four different extensions to McNemar's problem concerning the hypothesis of equal probabilities for the unlike pairs of correlated binary variables are considered, each for testing simultaneous equality of proportions of unlike pairs in c independent populations of correlated binary variables, but each under different assumptions and/or additional…