A probablistic approach to classification and diagnosis of erroneous rules of operations that result from misconceptions ("bugs") in a procedural domain of arithmetic is introcuced. Variability of response errors is explicitly treated through item response theory. As a concrete example, a signed-number subtraction dataset is analyzed.…

Two specific cases involving Pascal's Problem of the Points are discussed, followed by a solution in the general case. (MNS)

How probabilities change when playing the game of craps with dice having 8, 12, or 20 faces is discussed. Five challenge questions are also included. (MNS)

Relationships between both the elements and the overall characteristics of Pascal's triangle are explored. (DT)

Many research-related classes in social sciences present probability as a unified approach based upon mathematical axioms, but neglect the diversity of various probability theories and their associated philosophical assumptions. Although currently the dominant statistical and probabilistic approach is the Fisherian tradition, the use of Fisherian…

Differences in the probability of graduating were studied for freshmen and transfer students at a metropolitan university. The study was based on students who arrived at Boise State University for the fall 1989 term (n=2,459). Of this group, 1,692 were new freshmen, and 767 were new transfers. The two groups were similar in gender and ethnicity.…

J. Barnette and J. McLean (1996) proposed a method of controlling Type I error in pairwise multiple comparisons after a significant omnibus F test. This procedure, called Alpha-Max, is based on a sequential cumulative probability accounting procedure in line with Bonferroni inequality. A missing element in the discussion of Alpha-Max was the…

The Mantel Haenszel (MH; 1959) approach of Holland and Thayer (1988) is a well-established method for assessing differential item functioning (DIF). The formula for the variance of the MH DIF statistic is based on work by Phillips and Holland (1987) and Robins, Breslow, and Greenland (1986). Recent simulation studies showed that the MH variances…

The probabilities of attaining varying magnitudes of standardized effect sizes by chance and when protected by a 0.05 level statistical test were studied. Monte Carlo procedures were used to generate standardized effect sizes in a one-way analysis of variance situation with 2 through 5, 6, 8, and 10 groups with selected sample sizes from 5 to 500.…

A probability problem concerned with drawing balls of a given color from an urn is discussed. Two methods of solution result from two different views of the problem. (JP)

The purpose of this paper is to examine the optimality of the formation of biases and their effect on the optimality of subsequent information processing. (Author/RK)

Probabilities and strategies for winning at a game of fliiping a penny are analyzed. (DT)

The orderly increase in the proportion of subjects who make optional reversal shifts over an age scale that now encompasses a range from 3 to 18 is confirmed. (Authors)