ESTIMATION OF THE CONCENTRATION PARAMETERS OF THE FISHER MATRIX DISTRIBUTION ON 50(3) AND THE BINGHAM DISTRIBUTION ON Sq, q≥ 2

Two procedures are considered for estimating the concentration parameters of the Fisher matrix distribution for rotations or orientations in three dimensions. The first is maximum likelihood. The use of a convenient 1-dimensional integral representation of the normalising constant, which greatly simplifies the computation, is suggested. The second approach exploits the equivalence of the Fisher distribution for rotations in three dimensions, and the Bingham distribution for axes in four dimensions. We describe a pseudo likelihood procedure which works for the Bingham distribution in any dimension. This alternative approach does not require numerical integration. Results on the asymptotic efficiency of the pseudo likelihood estimator relative to the maximum likelihood estimator are given, and the two estimators are compared in the analysis of a well-known vectorcardiography dataset.     

The ubiquitous angle

Summary.  Previously we used the geometry of n -dimensional space to derive the paired samples t -test and its p -value. In the present paper we describe the 'ubiquitous' application of these results to single degree of freedom linear model hypothesis tests. As examples, we derive the p - and t -values for the independent samples t -test, for testing a contrast in an analysis of variance and for testing the slope in a simple linear regression analysis. An angle θ in n -dimensional space is again pivotal in the development of the ideas. The relationships between p , t , θ , F and the correlation coefficient are also described by using a 'statistical triangle'.     

ASPECTS OF CORRELATION IN BIVARIATE POISSON DISTRIBUTIONS AND PROCESSES

This paper reviews some interesting but scattered results that are known about correlation in bivariate Poisson distributions and processes and presents some new results. A particular concern in both contexts is with results and examples relating to negative correlation.     

The Proportion of Gaming Revenue Derived from Problem Gamblers: Examining the Issues in a Canadian Context

The legitimacy of government-sponsored gambling and its continued expansion depends in part on the impact that gambling has on society and the extent to which gambling revenue is derived from vulnerable individuals. The purpose of the present article is to try to establish a valid estimate of the proportion of gaming revenue derived from problem gamblers in Canada. Using recent secondary data collected in eight Canadian provinces, we estimate this proportion to be 23.1%, compared to a problem gambling prevalence rate of 4.2%. This estimate must be seen as tentative, however, as self-reported expenditures are 2.1 times higher than actual provincial gaming revenues.     

Discrepancies in Perceived Organizational Control: their Incidence and Importance in Local Churches*

The effects of discrepancies between preferred and perceived control among church members are investigated in terms of amount and distribution of control. For each dimension of control, three categories of respondents are identified: those who preferred a greater amount or wider distribution of control than they perceived to exist within their churches (deficit); those whose preferred and perceived control scores were identical (balance); and those who preferred a lesser amount or more concentrated distribution of control in their churches than they perceived to exist (surplus). For both amount and distribution of control, a perceived deficit is more common than a surplus. Respondents experiencing discrepancies in either direction are more dissatisfied and alienated than those with a balance in desired and perceived organizational control. A deficit is associated with more dissatisfaction (but not necessarily more alienation) than a surplus. Subsample comparisons show these findings hold for both officers and non-officers. Regression analyses show that discrepancies regarding organizational control are important even after other aspects of control have been introduced.     

Depression and dependence upon unsustaining environments

Applying the author's person-environment incongruence model of depression, the relationship between the predisposition to independence or dependence, in both family and work environments, and the presence or absence of depression was investigated. Fifty depressed and fifty nondepressed white women between 21 and 67 were studied. A beginning case was made for the hypothesis that incongruence between a person's predisposition and the environment results in vulnerability to depression. While most depressed women were dependent and in environments that did not meet their needs, independent women in unsustaining environments were also found to be depressed. This is a major finding, since dependence alone is generally thought to typify depressed persons.