Exact tests for two-way symmetriccontingency tables

A two-way contingency table in which both variables have the same categories is termed a symmetric table. In many applications, because of the social processes involved, most of the observations lie on the main diagonal and the off-diagonal counts are small. For these tables, the model of independence is implausible and interest is then focussed on the off-diagonal cells and the models of quasi-independence and quasi-symmetry. For ordinal variables, a linear-by-linear association model can be used to model the interaction structure. For sparse tables, large-sample goodness-of-fit tests are often unreliable and one should use an exact test. In this paper, we review exact tests and the computing problems involved. We propose new recursive algorithms for exact goodness-of-fit tests of quasi-independence, quasi-symmetry, linear-by-linear association and some related models. We propose that all computations be carried out using symbolic computation and rational arithmetic in order to calculate the exact p-values accurately and describe how we implemented our proposals. Two examples are presented.     

Empirical bayes testing of a distribution function with d1richlet process priors

This paper considers the generalised empirical Bayes two-action (testing) and multiple action problems concerning a distribution function The Dirichiet process priors p of Ferguson have been used as the prior distributions on the space of distribution functions on the real line. The two-action component problem is considered in detail and when p is unknown partially empirical Bayes procedures {6 } which are asymptotically optimal with rates 0{jT1/2) and OCCmCn+l))     

Comparison of Some Mrpp and Standard Rank Tests for Two Unequal Samples

MRPP rank tests for two subgroups of unequal size are studied in detail. Based on the Pearson criteria, appropriate Pearson curves are suggested for their approximate distributions. On the basis ot extensive simulations, empirical powers of these tests are compared among themselves and with some standard nonparametric tests for several underlying populations.     

Empirical power comparisons of two mrpp rank tests

Simulated powers of the MRPP two-sample rank test statistic ?₁- are compared with the powers of the MRPP test statistic ?₂(the two-sided Wilcoxon-Mann-Whitney test) for large samples from several underlying populations. Powers are obtained using two approximate distributions of ?₁ involving three and four moments

respectively, The use of the fourth moment indicates that an approximation to the null distribution of ? based on four moments can perform better     

Robust tests for equality of two population means under the normal model

A robust procedure is developed for testing the equality of means in the two sample normal model. This is based on the weighted likelihood estimators of Basu et al. (1993). When the normal model is true the tests proposed have the same asymptotic power as the two sample Student's t-statistic in the equal variance case. However, when the normality assumptions are only approximately true the proposed tests can be substantially more powerful than the classical tests. In a Monte Carlo study for the equal variance case under various outlier models the proposed test using Hellinger distance based weighted likelihood estimator compared favorably with the classical test as well as the robust test proposed by Tiku (1980).     

Partitioning chi-squape in contingency tables: A teaching approach

A representation of sums and differences of the form 2n log n, the lnn function, is introduced to express likelihood-ratio chi-square test statistics in contingency table analysis. This is a concise explicit form to display when partitioning chi-square statistics in accordance with hierarchical models. The lnn representation gives students insights into the construction of test statistics, and assists in relating identical forms under differing model sets. Hierarchies are presented for independence and equi-probability in two-way tables, for symmetry in correlated square tables, for independence-and-homogeneity of two-way responses across levels of a factor, and for mutual independence in three-way tables, along with relevant partitions of chi-square.     

The performance of several statistical tests for seasonality in monthly data

The type I and II error rates of several statistical tests for seasonality in monthly data were investigated through a computer simulation study at two nominal significance levels, α=1% and α=5%. Three models were used for the variation: annual sinusoidal; semi—annual sinusoidal; and a curve which is constant in all but three consecutive months of the year, when it exhibits a constant increase (a “one—pulse” model). The statistical tests are compared in terms of the simulation results. These results may be applied to calculate either the sample size required to detect seasonal variation of fixed amplitude or the probability of detecting seasonal variation of variable amplitude with a fixed sample size. A numerical case study is given     

Self-perceived occupational stress and distress in a Scottish police force

Abstract

This paper describes an empirical study (n = 699) of occupational stress in a Scottish police force. The self-perceived stress associated with a variety of organizational and opearational stressors was examined along with the associated distress in the police officers in terms of symptoms of anxiety, somatic complaint, severe depression and social dysfunction. The analysis revealed that in spite of the potential that police work offers for exposure to adverse opeational situations such as violence or death, the highest levels of associated stress lie in relation to organizational factors such as officers' perceptions of staff shortages, inadequate resources, time pressures, lack of communication and work overload. Differential rates of perceived stress are reported accordng to gender, rank and working location. This paper further validates previsous research on stress in British police and addresses the situation from a Scottish perspective.     

Exponential family distribution with unknown truncation parameter: two sample problem

The uniformly most powerful unbiased tests are formulated for two sample problem of a given continuous distribution belonging to the exponential family with unknown scale and truncation parameters. The two-parameter exponential and Paretc distributions are considered in examples.     

An application of lomax distributions in receiver operating characteristic(roc)curve analysis

Receiver operating characteristic(ROC)curves are useful for studying the performance of diagnostic tests. ROC curves occur in many fields of applications including psychophysics, quality control and medical diagnostics. In practical situations, often the responses to a diagnostic test are classified into a number of ordered categories. Such data are referred to as ratings data. It is typically assumed that the underlying model is based on a continuous probability distribution. The ROC curve is then constructed from such data using this probability model. Properties of the ROC curve are inherited from the model. Therefore, understanding the role of different probability distributions in ROC modeling is an interesting and important area of research. In this paper the Lomax distribution is considered as a model for ratings data and the corresponding ROC curve is derived. The maximum likelihood estimation procedure for the related parameters is discussed. This procedure is then illustrated in the analysis of a neurological data example.