Questions and Answers

(We are attempting to inaugurate a different type of questions and answers page in this issue of the American Statistician. Our purpose is to stimulate an interest in conceptual and measurement problems which arise in the course of statistical work and which require discussion apart from purely mathematical considerations. It is hoped that our readers will find this approach of interest and value. We are inviting questions of this type.)     

Questions and Answers

I shall describe a practical classroom exercise in applied statistics, which has an impressive effect on the students who are beginning to learn statistics. This is based on a remarkable paper by Fisher (1934) on methods of ascertainment.     

Questions and Answers

This paper applies some of the current methodology and thinking of operations research to an analysis of the cumulative flow of water in the bathtub. The analysis presented herein is an extension of a paper that recently appeared in this journal, viz. Operations Research at the Kitchen Sink and Other Applications.     

Questions and Answers

In addition to his contributions to biostatistics and clinical trials, Paul Meier had a long-term interest in the legal applications of statistics. As part of this, he had extensive experience as a statistical consultant. Legal consulting can be a minefield, but as a result of his background, Paul had excellent advice to give to those starting out on how to function successfully in this environment.     

Questions & Answers

In the univariate case, the Poisson probability function can be derived as the limiting form of the binomial probability function as n →∞ such that np → m (fixed). The present note gives a similar derivation of the bivariate Poisson probability function as the limiting form of the bivariate binomial probability function.     

Questions & Answers

Several methods are available for finding minimum variance unbiased estimators for functions of distribution parameters. This paper concentrates on two which are rarely used but simple when applicable. The first, previously discussed by Davis (1951) and Tate (1959), yields estimators by differentiation when the range of nonzero probability for a continuous random variable depends on an unknown parameter. The second, which has wider applicability, permits estimators for some rather complicated functions to be found by using some well-known results from distribution theory. A number of examples are presented, many of which are suitable for classroom exercises.     

Questions & Answers: Statistical Aspects of Chronology

For discrete statistical models it is shown that any statistic induces a partition of the set of all possible distributions defined on the sample space. This partition identifies the subsets of the parameter space for which the statistic is sufficient.     

Questions & Answers: The Role of Mathematical Models in Clinical Research

Given any generalized inverse (X'X)^? appropriate to normal equations X'Xb ⁰ = X'y for the linear model y = Xb + e, a procedure is given for obtaining from it a generalized inverse appropriate to a restricted model having restrictions P'b = 0 for P'b nonestimable.     

问卷调查中情境题的应答质量及其与认知功能的关系

情境题在多个国内大型问卷调查中被用来测量受访者的主观评价标准。从设计上来说，情境题题干较长或者涉及维度较多，对受访者的认知功能要求较高，因此情境题的应答质量可能受到影响。本研究基于三个大型调查数据集（中国家庭追踪调查、中国健康与养老追踪调查、国际学生评价项目）中的10类情境题数据来评估情境题的应答质量，然后进一步分析应答质量与受访者教育水平和认知功能的相关性。研究结果显示，情境题的应答质量在不同调查的不同情境题之间有显著差异，受访者对同一情境题组内部不同情境题的打分排序与原设计意图不符的比例在2.73%到30.31%之间。进一步分析表明，情境题的应答质量与受访者的受教育水平和认知功能呈现显著的正相关性，排序不合理和应答不一致的现象更可能出现在受教育水平和认知功能偏低的人群中。因此，研究者在进行情境题的设计和分析时都应该考虑认知功能对其应答质量的影响。