Inference for a binomial proportion in the presence of ties

We suppose a case is to be compared with controls on the basis of a test that gives a single discrete score. The score of the case may tie with the scores of one or more controls. However, scores relate to an underlying quantity of interest that is continuous and so an observed score can be treated as the rounded value of an underlying continuous score. This makes it reasonable to break ties. This paper addresses the problem of forming a confidence interval for the proportion of controls that have a lower underlying score than the case. In the absence of ties, this is the standard task of making inferences about a binomial proportion and many methods for forming confidence intervals have been proposed. We give a general procedure to extend these methods to handle ties, under the assumption that ties may be broken at random. Properties of the procedure are given and an example examines its performance when it is used to extend several methods. A real example shows that an estimated confidence interval can be much too small if the uncertainty associated with ties is not taken into account. Software implementing the procedure is freely available.     

Sir Godfrey Thomson: a statistical pioneer

Summary.  Godfrey Thomson (1881–1955) was a leading figure in intelligence testing who made his name in that field first at Armstrong College, Newcastle, and then at the University of Edinburgh. In the course of his practical work he identified many theoretical problems which were essentially statistical in character. In particular, he used maximum likelihood estimation as early as 1919 and his statistical work largely set the course of modern factor analysis and related techniques. His statistical abilities were recognized, at different stages of his career, by both Karl Pearson and Sir Ronald Fisher. His key insight was to recognize the importance of Fisherian inference for the future of that subject.     

A Perturbation Approach to Outlier Detection in Two-Way Contingency Tables

In order to identify outliers in contingency tables, we evaluate the derivatives of the perturbation-formed surface of the Pearson goodness-of-fit statistic. The resulting diagnostics are shown to be less susceptible to masking and swamping problems than residual-based measures. A Monte Carlo study further confirms the effectiveness of the proposed diagnostics.     

The Mean, Median, Mode Inequality and Skewness for a Class of Densities

Recent work on the mean, median, mode inequality and skewness for unimodal continuous distributions is discussed with reference to the properties of totally positive kernels. These properties also give simple conditions which are sufficient for the inequality and which include the characterization of the Pearson family.     

Mean-Minimum Exact Confidence Intervals

This article introduces mean-minimum (MM) exact confidence intervals for a binomial probability. These intervals guarantee that both the mean and the minimum frequentist coverage never drop below specified values. For example, an MM 95[93]% interval has mean coverage at least 95% and minimum coverage at least 93%. In the conventional sense, such an interval can be viewed as an exact 93% interval that has mean coverage at least 95% or it can be viewed as an approximate 95% interval that has minimum coverage at least 93%. Graphical and numerical summaries of coverage and expected length suggest that the Blaker-based MM exact interval is an attractive alternative to, even an improvement over, commonly recommended approximate and exact intervals, including the Agresti–Coull approximate interval, the Clopper–Pearson (CP) exact interval, and the more recently recommended CP-, Blaker-, and Sterne-based mean-coverage-adjusted approximate intervals.     

Factors affecting stakeholder’s levels of satisfaction with community partnership association in Rayong Province,Thailand

ABSTRACT

Corporate social responsibility (CSR) studies have investigated the differences among five parameters: gender, age, education, income, and occupation; however, the findings are generally dissimilar. For instance, no comprehensive concordance has been reached on the performance and importance of the differences among those five parameters regarding stakeholder expectations and perceptions of CSR activities. Some voluminous investigations have revealed that the literature does not discuss the essential importance of the differences among the five parameters, and as a consequence, the magnitude of such differences is unexplained. This research analyses the quantitative and qualitative significances of the differences among the five parameters in stakeholder satisfaction level and perceptions of CSR activities conducted by the Community Partnership Association in Rayong Province, Thailand. Overall satisfaction levels positively correlated with education and age, indicating that intellectual background and personal experiences considerably influence the perceptions of CSR activities. This study assists policymakers and industrial sectors to launch the most practical strategies for plotting, scheming, implementing, and evaluating sustainability initiatives.     

Chi–square tests for comparing vectors of proportions for several cluster samples

Test statistics are developed for comparing vectors of proportions obtained from several independent two–stage cluster samples. It is assumed that clusters are selected with probability proportional to size for each sample. Wald's general method of constructing quadratic forms is used to obtain a large sample chi–square test. More easily evaluted chi–square tests are derived from the Dirichlet–multinnomial model. Corresponding goodness–of–fit test for the Dirichlet–multinomial model are also derived.     

Exact-and approximate bayes credibility intervals for the one-way analysis of variance model

In most hierarchical Bayes cases the posterior distributions are difficult to derive and cannot be obtained in closed form. In some special cases, however, it is possible to obtain the exact moments of the posterior distributions.

By applying these moments and Pearson curves or Cornish-Fisher expansions to real problems, good approximations of the exact posterior distributions of individual parameter values as well as linear combinations of parameter values could easily be obtained.     

Characterization of Continuous Distributions by Variance Bound and Its Implications to Reliability Modeling and Catastrophe Theory

We generalize some of the existing results on characterization of continuous distributions by lower bound on the variance and point out their equivalence to characterization of life distributions by relationship between conditional expectation and failure (reversed failure) rate. It is shown that these lower bounds are the same as, Cramer–Rao bound in the regular case and improves upon the latter in the non-regular case. Some applications to reliability modeling and catastrophe theory are pointed out.     

A Single Form for t-Distributions and Symmetric Beta Distributions

A single parametric form is given for the symmetric distributions in the Pearson system with finite variance. In effect, these are Student's t-distributions with ν > 2 and all centered symmetric beta distributions. A different parametrization allows the inclusion of the t-distributions with ν ≤2 at the expense of symmetric beta distributions with a low shape parameter.