Given a Masters partial credit item with n known step difficulties, conditions are stated for the existence of a set of (locally) independent Rasch binary items such that their raw score and the partial credit raw score have identical probability density functions. (Author/SLD)

Four indexes of agreement between ratings of a person that correct for chance and are interpretable as intraclass correlation coefficients for different analysis of variance models are investigated. Relationships among the estimators are established for finite samples, and the equivalence of these estimators in large samples is demonstrated. (SLD)

Recounts a teacher's experiences with a small group of elementary school students as they explore different forms of the combinatorics problem of choosing two out of five objects. Describes how students examine the connections between the problems and a proof of the relationship. (MDH)

The ability of the NORMIX algorithm to recover overlapping population structures was compared to the OVERCLUS procedure and another clustering procedure in a Monte Carlo study. NORMIX is found to be more accurate than other procedures in recovering overlapping population structure when appropriate implementation options are specified. (SLD)

Presents a problem for students in grades 1-6 concerning the concept of probability. Discusses the student problem-solving process, and provides some responses to the problem published in the January 1998 issue of this journal. (ASK)

Illustrates how the Academy Awards can provide an excellent motivational tool in teaching probability and statistics and presents related activities. (ASK)

Describes ways of thinking about probability and some common student misconceptions. Suggests ways of addressing students' misconceptions and illustrates these ideas with an example. (ASK)

Proves price index (proportion of references within the last five years of literature) is not a pure function of the mean or median reference age, but a well-defined relation in the form of a typical cloud of points. Compares models for analyzing price index (decreasing exponential and lognormal aging) and explains cloud using results from…

Creates graphs to see how the relative frequency of an event tends to approach the probability of that event as the number of trials increases. Uses a simulation of a poker machine to provide context for this subject. (ASK)

Describes and analyzes a learning episode in which two children in year 4 interact with each other and their teacher while playing a probability game involving chocolate M&Ms. Children developed key ideas in probability from a game that was designed to produce cognitive conflict. (ASK)

Presents a problem that has been well received by students in undergraduate mathematical statistics courses. The problem is presented as a game in which students are asked to choose between two alternatives, as if they were betting. (ASK)

Presents an activity in which students develop a handy strategy for exploring probability as applied in the life sciences by learning to use the Punnett square, an effective tool that helps students visualize sample spaces and determine the likelihood of events. (ASK)

Observes the application of probability theory to a game between two players. Shows how basic techniques such as tree diagrams can be used to demonstrate optimum strategies, how the art of bluffing can be quantified, and how this might be applied to a game of poker. (Author/ASK)

Investigates whether state course graduation requirements affect high-school dropout decisions, using aggregate data on dropout rates, individual data from two time periods, and aggregate data on high-school completion rates over 15 years. Results strongly suggest that state-mandated minimum course requirements cause students to drop out.…

In general, if a variable can be expressed as a function of its own maximum value, that function may be called a discount function. Delay discounting and probability discounting are commonly studied in psychology, but memory, matching, and economic utility also may be viewed as discounting processes. When they are so viewed, the discount function…