What are the cognitive mechanisms underlying subjective valuations formed on the basis of sequential experiences of an option's possible outcomes? Ashby and Rakow (2014) have proposed a sliding window model (SWIM), according to which people's valuations represent the average of a limited sample of recent experiences (the size of which is estimated…

This paper presents and tests a general model to predict emergent exchange patterns and power differences in reciprocal exchange networks when individual actors follow the norm of reciprocity. With an interesting qualification, the experimental results reported here support the power-dependence approach (Emerson 1972a, b): those who acquire the…

The current study investigated the effects of different external representational formats on learning combinatorics and probability theory in an inquiry based learning environment. Five conditions were compared in a pre-test post-test design: three conditions each using a single external representational format (Diagram, Arithmetic, or Text), and…

In the nineteenth century many people tried to seek a value for the most famous irrational number, [pi], by means of an experiment known as Buffon's needle, consisting of throwing randomly a needle onto a surface ruled with straight parallel lines. Here we propose to extend this experiment in order to evaluate other irrational numbers, such as…

This paper focuses on the different ways in which students in lower secondary school (14-16 year olds) experience compound random events, presented to them in the form of combined junctions. A carefully designed ICT environment was developed enabling the students to interact with different representations of such structures. Data for the analysis…

Assuming errors of measurement are distributed binomially, this article reviews various procedures for constructing an interval for an individual's true number-correct score; presents two general interval estimation procedures for an individual's true scale score (i.e., normal approximation and endpoints conversion methods); compares various…

A probability distribution was developed for the Andrews-Pregibon (AP) statistic. The statistic, developed by D. F. Andrews and D. Pregibon (1978), identifies multivariate outliers. It is a ratio of the determinant of the data matrix with an observation deleted to the determinant of the entire data matrix. Although the AP statistic has been used…

This study was designed to derive the distribution of a test statistic based on normal probability plots. The first purpose was to provide an empirical derivation of the critical values for the Line Test (LT) with an extensive computer simulation. The goal was to develop a test that is sensitive to a wide range of alternative distributions,…

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 complete enumeration method and a Monte Carlo method are presented to calculate the probability distribution of arbitrary statistics of adjacency matrices when these matrices have the uniform distribution conditional on given row and column sums, and possibly on a given set of structural zeros. (SLD)

The challenge of multiple comparisons is to maximize the power for answering specific research questions, while still maintaining control over the rate of Type I error. Several multiple comparison procedures have been suggested to meet this challenge. The stagewise protected procedure (SPP) of A. J. Klockars and G. R. Hancock tests null hypotheses…

This Monte Carlo study examines whether, given various numbers of variables, treatments, and sample sizes, in a one-way multivariate analysis of variance, Type I error rates of the test approximations provided by the BMDP program, the Statistical Analysis System (SAS), and the Statistical Package for the Social Sciences (SPSS) for Roy's largest…

Modifications are proposed to the recently developed method of comparing one-step M-estimators of location corresponding to two independent groups that provides good control over the probability of Type I error even for unequal sample size, unequal variances, and different shaped distributions. Simulation results reveal cautions required. (SLD)

Previous work on the effects of dimensionality on parameter estimation was extended from dichotomous models to the polytomous graded response (GR) model. A multidimensional GR model was developed to generate data in one-, two-, and three-dimensions, with two- and three-dimensional conditions varying in their interdimensional associations. Test…

Inference is considered for the marginal distribution of "X" when ("X", "Y") has a truncated bivariate normal distribution. The "Y" variable is truncated, but only the "X" values are observed. A sample of 87 Otis test scores is shown to be well described by this model. (SLD)