The Vanishing 2×2 Table: Linking the Hypergeometric,Binomial and Poisson

A simple procedure for establishing minimum sample size in X ² goodness-of-fit tests is presented. Samples of this size will automatically satisfy Yarnold's criterion.     

Group-testing,halving procedures,and binary search ∗

Group-testing procedures for minimizing the expected number of tests needed to classify N units as either good or bad are described, The units are assumed to have come independently from a binomial population with common probability p of being defective and q = 1-p of being good, Special consideration is given to comparing certain halving procedures with the correspending optimal procedures for the problem of finding one defective if it exists, and the problem of finding all the defectives.     

No Satisfaction? But We Try,and We Try,and We Try!

ABSTRACT

When Old Dominion University Libraries conducted the LibQUAL+ survey in 2015, results indicated a lack of satisfaction in effectively discovering and using our electronic resources. This article is based on a presentation from the 2017 North Carolina Serials Conference describing how Old Dominion University Libraries used data from the LibQUAL+ survey results to help our users connect more effectively with information resources, resulting in an improved user experience and an increased level of satisfaction.     

Lévy Processes,Phase-Type Distributions,and Martingales

Lévy processes are defined as processes with stationary independent increments and have become increasingly popular as models in queueing, finance, etc.; apart from Brownian motion and compound Poisson processes, some popular examples are stable processes, variance gamma processes, CGMY Lévy processes (tempered stable processes), NIG (normal inverse Gaussian) Lévy processes, and hyperbolic Lévy processes. We consider here a dense class of Lévy processes, compound Poisson processes with phase-type jumps in both directions and an added Brownian component. Within this class, we survey how to explicitly compute a number of quantities that are traditionally studied in the area of Lévy processes, in particular two-sided exit probabilities and associated Laplace transforms, the closely related scale function, one-sided exit probabilities and associated Laplace transforms coming up in queueing problems, and similar quantities for a Lévy process with reflection in 0. The solutions are in terms of roots to polynomials, and the basic equations are derived by purely probabilistic arguments using martingale optional stopping; a particularly useful martingale is the so-called Kella-Whitt martingale. Also, the relation to fluid models with a Brownian component is discussed.     

Robustness and power of parametric, nonparametric, robustified and adaptive tests—The multi-sample location problem

This paper deals with a survey of different types of tests, parametric, nonparametric, robustified and adaptive ones, and with an application to the two-sided c-sample location problem. Some concepts of robustness are discussed, such as breakdown point, influence function, gross-error sensitivity and especially α- and β-robustness. A robustness study on level α in the case of heteroscedasticity and nonnormal distributions is carried out via Monte Carlo methods and also a power comparison of all the tests considered. It turns out that robustified versions of the F-test and Welch-test where the original observations are replaced by its ranks behave well over a broad class of distributions, symmetric ones with different tail weight and asymmetric ones, but, on the whole, an adaptive test is to prefer.     

Cultural Anthropology and Open Access—Interview With Dominic Boyer,Cymene Howe,and Marcel LaFlamme

Abstract

In this installment of “Conversations,” Dominic Boyer, Cymene Howe, and Marcel LaFlamme, of the Cultural Anthropology editorial team, discuss the ins and outs of publishing a gold open access journal in the field of anthropology. Highlights of the discussion include Cultural Anthropology’s move to open access, the ethics of open access, the growth of international readership, ongoing publishing challenges in open access, and the role libraries can play with open access publishing.     

Mixed models and unbalanced data: wherefrom,whereat and whereto?

A brief history of the early years (1820-1947) of random effects models and the estimation of variance components is followed by a personal evaluation of M.L, REML and MINQUE estimation. A method is suggested for combining ML estimator obtained from subsets of a large data set, and comments are made on the need for simulation studies to assess the degree of approximation in using asymptotic properties of ML-type estimators as if they were exact for finite-sized unbalanced data sets.     

Minimum Variance and VOQL Chain Sampling Plans–ChSP-4(c 1, c 2)

In this article the outgoing quality and the total inspection for the chain sampling plan ChSP-4(c ₁, c ₂) are introduced as well-defined random variables. The probability distributions of outgoing quality and total inspection are stated based on total rectification of non conforming units. The variances of these random variables are studied. The aim of this article is to develop procedures for minimum variance ChSP-4(c ₁, c ₂) sampling plans and their determination. In addition to minimum variance sampling plans, a procedure is developed for designing plans with a designated maximum variance, a VOQL (Variance of Outgoing Quality Limit) plan. The VOQL concept is analogous to the AOQL (Average Outgoing Quality Limit) except in the VOQL plan, it is the maximum variance which is established instead of the usual maximum AOQ.     

Structural properties of UMPU-tests for 2×2 tables and some applications

The paper is concerned with structural properties of the acceptance regions of uniformly most powerful unbiased tests (UMPU-tests) for one- and two-sided hypotheses for 2×2 tables as, for instance, the comparison of two proportions or testing for association. These tests can be considered as randomized versions of Fisher's exact tests. A series of monotonicity and unimodality properties will be proved. These properties are equivalent to a symmetry and convexity condition often required for powerful unconditional tests. Knowledge of such properties allows a fast and in some sense recursive calculation of the critical values of the UMPU-tests which is important if a repeated calculation of all critical values for different sample sizes or different levels is required. This is, for example, the case if the unconditional power has to be controlled over a certain subset of the alternative, or, if one is interested in powerful unconditional non-randomized tests generated by a UMPU-test. Our results also imply some useful properties of the two-dimensional unconditional power function. On the other hand, we found some less nice properties of the UMPU-tests, too.     

Median split, k-group split, and optimality in continuous populations

Continuous populations are grouped in many social, economic, medical, or technical fields of research. However, by grouping them, a lot of information provided by the continuous population is lost. Especially the median split, which is still adopted by many researchers, and its generalization to an equiprobable k-group split lead to a high efficiency loss. Here, this loss of information is investigated by analytical and numerical analyses for some typical symmetric and skew population distributions often found in applications. Various distribution parameters, numbers of groups, and split methods are taken from theoretical considerations and real data sets. Losses sometimes in excess of 50% can be reduced by optimal grouping.     

An extended Birnbaum–Saunders distribution: Theory,estimation, and applications

Abstract

Birnbaum and Saunders (1969a Birnbaum, Z.W., Saunders, S.C. (1969a). A new family of life distributions. J. Appl. Probab. 6:319–327.[Crossref], [Web of Science ®] , [Google Scholar]) pioneered a lifetime model which is commonly used in reliability studies. Based on this distribution, a new model called the gamma Birnbaum–Saunders distribution is proposed for describing fatigue life data. Several properties of the new distribution including explicit expressions for the ordinary and incomplete moments, generating and quantile functions, mean deviations, density function of the order statistics, and their moments are derived. We discuss the method of maximum likelihood and a Bayesian approach to estimate the model parameters. The superiority of the new model is illustrated by means of three failure real data sets. We also propose a new extended regression model based on the logarithm of the new distribution. The last model can be very useful to the analysis of real data and provide more realistic fits than other special regression models.     

Chance-Corrected Measures of Reliability and Validity in 2 × 2 Tables

It is customary to use two groups of indices to evaluate a diagnostic method with a binary outcome: validity indices with a standard rater (sensitivity, specificity, and positive or negative predictive values) and reliability indices (positive, negative and overall agreements) without a standard rater. However neither of these classic indices is chance-corrected, and this may distort the analysis of the problem (especially in comparative studies). One way of chance-correcting these indices is by using the Delta model (an alternative to the Kappa model), but this means having to use a computer program to work out the calculations. This paper gives an asymptotic version of the Delta model, thus allowing simple expressions to be obtained for the estimator of each of the above-mentioned chance-corrected indices (as well as for its standard error).     

Observational studies,clinical trials,and the women’s health initiative

The complementary roles fulfilled by observational studies and randomized controlled trials in the population science research agenda is illustrated using results from the Women’s Health Initiative (WHI). Comparative and joint analyses of clinical trial and observational study data can enhance observational study design and analysis choices, and can augment randomized trial implications. These concepts are described in the context of findings from the WHI randomized trials of postmenopausal hormone therapy and of a low-fat dietary pattern, especially in relation to coronary heart disease, stroke, and breast cancer. The role of biomarkers of exposure and outcome, including high-dimensional genomic and proteomic biomarkers, in the elucidation of disease associations, will also be discussed in these same contexts.     

Many (22, 44, 14, 7, 4) — and (15, 42, 14, 5, 4)-balanced incomplete block designs

A Balanced Incomplete Block Design (BIBD) is a pair (V, B) where V is a v-set and B is a collection of b k-subsets of V, called blocks, such that every element of V occurs in exactly r of the k-subsets and every 2-subset of V occurs in exactly λ of the blocks. The number of non-isomorphic designs of a BIBD (22, 44, 14, 7, 4) whose automorphism group is divisible by 7 or 11 are investigated. From this work, results are obtained on the number of non-isomorphic BIBDs (15, 42, 14, 5, 4).