Search

The assumption of approximate normality of a pivotal used for constructing confidence intervals or tests often is violated by a substantial correlation between the point estimator at hand and the estimator of its variance. This can be caused by underlying skewness of data, generating both bias and skewness of the pivotal and leading to, for example, confidence intervals with poorer coverage properties, especially for one-sided intervals. We present in a general setting a simple, yet effective procedure that takes into account this correlation and leads to alternative adjusted intervals with more appealing coverage properties. We provide examples, including a simulation study. [ABSTRACT FROM AUTHOR]

Statistical experiments, more commonly referred to as Monte Carlo or simulation studies, are used to study the behavior of statistical methods and measures under controlled situations. Whereas recent computing and methodological advances have permitted increased efficiency in the simulation process, known as variance reduction, such experiments remain limited by their finite nature and hence are subject to uncertainty; when a simulation is run more than once, different results are obtained. However, virtually no emphasis has been placed on reporting the uncertainty, referred to here as Monte Carlo error, associated with simulation results in the published literature, or on justifying the number of replications used. These deserve broader consideration. Here we present a series of simple and practical methods for estimating Monte Carlo error as well as determining the number of replications required to achieve a desired level of accuracy. The issues and methods are demonstrated with two simple examples, one evaluating operating characteristics of the maximum likelihood estimator for the parameters in logistic regression and the other in the context of using the bootstrap to obtain 95% confidence intervals. The results suggest that in many settings, Monte Carlo error may be more substantial than traditionally thought. [ABSTRACT FROM AUTHOR]

The use of equivalence testing in scientific research is increasing beyond its traditional role in the drug approval process. Largely due to its ease of use and recommendations from the U.S. Food and Drug Administration guidance, the most common statistical method for testing equivalence is the two one- sided tests (TOST) procedure. Like classical point-null hypothesis testing, TOST is subject to multiplicity concerns as more comparisons are made. Here we give a condition that bounds the familywise error rate (FWER) using TOST and leads to a simple solution for controlling the FWER. Specifically, we demonstrate that if all pairwise comparisons of k independent groups are being evaluated for equivalence, then simply scaling the nominal type I error rate down by (k - 1) is sufficient to maintain the FWER at the desired value or less. The resulting rule is much less conservative than the equally simple Bonferroni correction. An example of equivalence testing in a non- drug development setting is given. [ABSTRACT FROM AUTHOR]

This article reviews literature on confidence intervals for p, assuming (Bernoulli) single, double, and multistage sampling. Methods used to produce approximate single-sampling confidence intervals extend to double sampling as well. A new Wilson approximate confidence interval procedure for double sampling is compared with existing procedures in terms of general interval properties, such as interval invariance, and performance (in terms of actual coverage probability and expected length) for double-sampling plans from the literature. [ABSTRACT FROM AUTHOR]

In this article, we consider the problem of constructing confidence intervals for a population median when the underlying population is discrete. We describe seven methods of assigning confidence levels to order statistic based confidence intervals, all of which are easy to implement. A simulation study shows that, with discrete populations, it is possible to obtain consistently more accurate confidence levels and shorter intervals compared to the ones reported by the classical method which is implemented in commercial software. More precisely, the best results are obtained by inverting a two-tailed sign test that properly takes into account tied observations. Some real data examples illustrate the use of these confidence intervals. [ABSTRACT FROM AUTHOR]

This article revisits the problem of determining sample size for interval estimation of a binomial proportion. It is motivated by the author's experience as an expert witness in a legal case. The legal case involves a class action suit against a large service provider for alleged over-collection of special service fees. We discuss how: (1) focusing on relative error of the binomial outcome instead of absolute error of the Bernoulli probability p can have a dramatic effect on sample size recommendations, and (2) a year-by-year analysis may differ from a single-year analysis. We also discuss the challenges in presenting such statistical results to nonstatisticians, and propose simplifications to enhance communicability. [ABSTRACT FROM AUTHOR]

Simple random sampling is the foundation for almost every method taught in introductory statistics classes. Many students, however, have difficulty understanding the difference between simple random sampling and cluster sampling and determining whether the assumption of simple random sampling is met, We can find evidence of this difficulty in research articles reporting statistical findings: many analyze the data using simple random sampling assumptions even though a cluster sample was actually taken. We review several statistics texts' treatment of sampling assumptions for confidence intervals and hypothesis tests. We then propose activities that could be used in the classroom to help students gain a better understanding of the concepts of simple random sampling and confidence intervals. [ABSTRACT FROM AUTHOR]

When comparing two variables with nonnormal distributions, application of the Wilcoxon-Mann-Whitney test (WMW) is a common choice. However, it is only valid to test the null hypothesis stating equality of the distributions. Sometimes the hypothesis of interest is H0: P(X < Y) = P(X > Y) against P(X < Y) ≠ P(X > Y), called stochastic equality and in- equality. Here we propose a bootstrap test for this problem. Results of an extensive simulation study based on empirical distributions suggest that the new test is valid for a wide range of problems in parasitology and psychology, and the loss of power as compared to WMW is rather small in those cases when both tests are applicable. [ABSTRACT FROM AUTHOR]

Confidence intervals for discrete distributions are often evaluated only by coverage and expected length. We discuss two additional criteria, p-confidence and p-bias. The choice of these criteria is motivated by the interpretation of a confidence interval as being the set of parameter values not rejected by a hypothesis test. Using these additional criteria we compare a number of equal-tailed confidence intervals for the binomial distribution. It is shown that methods that produce superior intervals, as measured by coverage and length, need not perform well in terms of p-confidence and p-bias. Cox's measuring device example is discussed to motivate the need for criteria beyond coverage and length. [ABSTRACT FROM AUTHOR]

A common experimental design for the problem of comparing two means from a normal distribution assumes knowledge of the ratio of the population variances. The optimal sampling ratio is proportional to the square root of this quantity. This article demonstrates that a misspecification of the ratio of the population variances can cause a substantial loss in power of the corresponding tests. As a robust alternative, a maximin approach is used to construct designs, which are efficient, whenever the experimenter is able to specify a specific region for the ratio of the population variances. The advantages of the robust designs for inference in the Behrens-Fisher problem are illustrated in a simulation study and an application to the design of experiment for bioassay is presented. [ABSTRACT FROM AUTHOR]

This article presents a novel and simple way to assess the exceptionality of a new record. We illustrate the use of this measure in two examples, one from archaeology and the other from athletics. [ABSTRACT FROM AUTHOR]

Presents a data set suitable for demonstrating the X2 test with a rejection region in the low tail. Chi-square test; Random sampling.

Examines the effect of sample size on the meaning of significance tests. Relevance of the Neyman-Pearson theory of hypothesis testing in choosing between statistical hypothesis H[sub 0] and H[sub 1]; Importance of significance test for measuring the strength of evidence against H[sub 0]; Influence of interpretations of D. Bakan on the study.