摘要:

Orthogonal regression is one of the standard linear regression methods to correct for the effects of measurement error in predictors. We argue that orthogonal regression is often misused in errors-in-variables linear regression because of a failure to account for equation errors. The typical result is to overcorrect for measurement error, that is, overestimate the slope, because equation error is ignored. The use of orthogonal regression must include a careful assessment of equation error, and not merely the usual (often informal) estimation of the ratio of measurement error variances. There are rarer instances, for example, an example from geology discussed here, where the use of orthogonal regression without proper attention to modeling may lead to either overcorrection or undercorrection, depending on the relative sizes of the variances involved. Thus our main point, which does not seem to be widely appreciated, is that orthogonal regression, just like any measurement error analysis, requires careful modeling of error.

ISSN:0003-1305    

DOI:10.1080/00031305.1996.10473533

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

In considering the inference about the unknown proportion of a Bernoulli process, it is shown that the choices involved in the frequentist approach are equivalent, from a Bayesian point of view, to the choice of a particular ignorance prior within a restrictedignorance zone.This link sheds light on the nature of both kinds of choices, and on undesirable properties that go with null variance data.

ISSN:0003-1305    

DOI:10.1080/00031305.1996.10473534

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A simple method of modifying probability to create independence counterexamples is given. This method can be used to construct counterexamples for finite collections of events and for infinite sequences of events. It is shown how to construct examples of countable collections of events where all equations in the (countable) family of “product rules” that define independence are satisfied except for one or, more generally, except for an arbitrarily specified subfamily.

ISSN:0003-1305    

DOI:10.1080/00031305.1996.10473535

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A number of examples of nonnormal bivariate distributions whose marginal distributions are normal have been described in the literature. Such examples can be extremely useful in classroom discussions of univariate and bivariate normality. The present note introduces a new, practically motivated example involving maximum and minimum daily temperatures, in which the marginal distributions appear to be normally distributed, whereas the bivariate distribution is not. Two differences exist compared to previous examples: (1) there is a practical motivation; (2) despite the apparent normality of the marginal distributions, it can be shown that such normality cannot really be valid, except in an unrealistic special case. The example illustrates a number of additional points that would be of value in a classroom discussion of univariate and bivariate distributions.

ISSN:0003-1305    

DOI:10.1080/00031305.1996.10473536

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

This article presents an analysis of the small-sample distribution of a class of approximate pivotal quantities for a normal coefficient of variation that contains the approximations of McKay, David, the “naïve” approximate interval obtained by dividing the usual confidence interval on the standard deviation by the sample mean, and a new interval closely related to McKay. For any approximation in this class, a series is given fore(t)the difference between the cdf's of the approximate pivot and the reference distribution. Let κ denote the population coefficient of variation. For McKay, David, and the “naïve” intervale(t)=O(κ2), while for the new proceduree(t)=O(κ4).

ISSN:0003-1305    

DOI:10.1080/00031305.1996.10473537

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Tournaments are popularly used in sporting events to select a champion. They are also used in experiments where paired comparison procedures are needed. Knockout tournaments are most useful when the number of treatments is too large to use the more well-known round-robin tournament. The mathematical and statistical literature does not address questions such as how one should seed teams in a tournament or which tournament structures are appropriate. For double-elimination (DE) tournaments even basic questions such as how many structures there are remain unanswered. This article addresses some fundamental questions concerning DE tournaments, including the number of DE tournaments and the probabilities of teams winning a DE tournament. Edwards gives many results about single-elimination (SE) tournaments, such as the probability of winning an SE tournament and a notation for labeling and counting them. In this article I develop similar results for the DE tournaments. The results given apply to an arbitrary number of teams, and not just four or eight, as is popular in the literature.

ISSN:0003-1305    

DOI:10.1080/00031305.1996.10473538

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Sports events and tournament competitions provide excellent opportunities for model building and using basic statistical methodology in an interesting way. In this article, National Collegiate Athletic Association (NCAA) regional basketball tournament data are used to develop simple linear regression and logistic regression models using seed position for predicting the probability of each of the 16 seeds winning the regional tournament. The accuracy of these models is assessed by comparing the empirical probabilities not only to the predicted probabilities of winning the regional tournament but also the predicted probabilities of each seed winning each contest.

ISSN:0003-1305    

DOI:10.1080/00031305.1996.10473539

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Several models for estimating the probability that a given team in an NCAA basketball tournament emerges as the regional champion were presented by Schwertman, Mc-Cready, and Howard. In this article we improve these probability models by taking advantage of external information concerning the relative strengths of the teams and the point spreads available at the start of the tournament for the first round games. The result is a collection of regional championship probabilities that are specific to a given region and tournament year. The approach is illustrated using data from the 1994 NCAA basketball tournament.

ISSN:0003-1305    

DOI:10.1080/00031305.1996.10473540

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

One-factor-at-a-time experiments and similar “common sense” design strategies continue to be prevalent in industrial experiments in spite of the strong emphasis in statistics courses that these design strategies should be avoided. In justifying the avoidance of such design strategies, technical criteria such as design efficiency and confounding are usually stressed. However, these technical criteria routinely are overlooked by experimenters in industry when the desire for rapid feedback on factor effects is given undue precedence. In this article the preference for rapid feedback over statistical considerations is discussed relative to the compelling inherent deficiencies of these designs. The practical difficulties associated with the dynamic nature of the design construction, geometric imbalance of the designs, and serious modeling inadequacies that result from the use of these design strategies are detailed.

ISSN:0003-1305    

DOI:10.1080/00031305.1996.10473541

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Traditionally, a large class in elementary statistics is taught by having the instructor lecture for the class period with little interaction from the students. This article considers an approach for teaching a large elementary statistics class that encourages student involvement. Comments and evaluations from the students who took a class using this approach are examined.

ISSN:0003-1305    

DOI:10.1080/00031305.1996.10473542

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor