摘要:

Pvalues (or significance probabilities) have been used in place of hypothesis tests as a means of giving more information about the relationship between the data and the hypothesis than does a simple reject/do not reject decision. Virtually all elementary statistics texts cover the calculation ofPvalues for one-sided and point-null hypotheses concerning the mean of a sample from a normal distribution. There is, however, a third case that is intermediate to the one-sided and point-null cases, namely the interval hypothesis, that receives no coverage in elementary texts. We show thatPvalues are continuous functions of the hypothesis for fixed data. This allows a unified treatment of all three types of hypothesis testing problems. It also leads to the discovery that a common informal use ofPvalues as measures of support or evidence for hypotheses has serious logical flaws.

ISSN:0003-1305    

DOI:10.1080/00031305.1996.10474380

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Missing at random (MAR) and missing completely at random (MCAR) are ignorability conditions—when they hold, they guarantee that certain kinds of inferences may be made without recourse to complicated missing-data modeling. In this article we review the definitions of MAR, MCAR, and their recent generalizations. We apply the definitions in three common incomplete-data examples, demonstrating by simulation the consequences of departures from ignorability. We argue that practitioners who face potentially non-ignorable incomplete data must consider both the mode of inference and the nature of the conditioning when deciding which ignorability condition to invoke.

ISSN:0003-1305    

DOI:10.1080/00031305.1996.10474381

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Classical maximum likelihood (ML) as well as the uniformly minimum variance unbiased (UMVU) estimators of multinomial cell probabilities are given by the observed relative frequencies. Bayes estimators corresponding to symmetric Dirichlet prior distribution for p are the inflated observed relative cell frequencies of the type (ni+k) (M+kt)−1. These estimators, which are more reasonable when the observedni's are 0 or very small, are justified classically by Johnson and are also reported without proof in Good. We give here a proof of Johnson's results that perhaps is easier to understand.

ISSN:0003-1305    

DOI:10.1080/00031305.1996.10474382

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

In this departmentThe American Statisticianpublishes articles, reviews, and notes of interest to teachers of the first mathematical statistics course and of applied statistics courses. The department includes the Accent on Teaching Materials section; suitable contents for the section are described under the section heading. Articles and notes for the department, but not intended specifically for the section, should be useful to a substantial number of teachers of the indicated types of courses or should have the potential for fundamentally affecting the way in which a course is taught.

ISSN:0003-1305    

DOI:10.1080/00031305.1996.10474383

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

ISSN:0003-1305    

DOI:10.1080/00031305.1996.10474384

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A method of displaying the relationships between the various factors in experimental designs is described. Emphasis is placed on identifying crossed and nested factors and the experimental units for each factor. The resulting factor relationship diagram (FRD) is useful in establishing the correct model, such as analysis of variance (ANOVA), for analysis. The method is illustrated with a randomized block design and two split-plot designs. Some common pitfalls of these designs are discussed.

ISSN:0003-1305    

DOI:10.1080/00031305.1996.10474385

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Numerical experiments on a personal computer are used to illustrate the degrees of freedom concept. Random errors from a known distribution are added to a known model, for example,y(x) = α + β ·x, and the least squares fit to the model + error data is computed. The least squares fit produces a new model,y(x) =a+b · x. By definition the sum of squared deviations between the least squares fit model and the data is always less than the sum of squared deviations between the original model and the data. When this process is repeated thousands of times on the computer, using different random errors each time, a pattern emerges. On average the difference between the two sums of squared deviations approaches an integer multiple of the error distribution variance. Furthermore, this integer equals the number of regression parameters in the model. For instance, this is the origin of the two degrees of freedom associated with a linear model. Using the computer it is easy to verify this property for regression models with more than two parameters and for different error distributions. The previous degree of freedom property depends only on the variance of the error distribution and use of the least squares method; it does not depend on the detailed shape of the distribution. However, when the normal error distribution with mean = 0 and variance = 1 is used, a connection to another use of the degrees of freedom terminology is found. For a model withMparameters, the normalized frequency distribution of the difference between the two sets of squared deviations is calculated, using 2,000 computer trials, and shown to match the chi-square distribution withMdegrees of freedom.

ISSN:0003-1305    

DOI:10.1080/00031305.1996.10474386

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Instructors for introductory courses with large enrollments must routinely work to curb cheating during exams. A method used for such purposes is described here. Perhaps more interesting than the method's effectiveness is the inherited ability to draw inference on unknown parameters of interest, including the proportion of students who cheat (as opposed to guess) when faced with not knowing how to obtain the solution to a multiple-choice exam question. For estimation we consider the method of maximum likelihood.

ISSN:0003-1305    

DOI:10.1080/00031305.1996.10474387

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The quadratic formula technique used to find confidence limits for various distributions, such as the binomial, provides limits that are congruent with the fiducial philosophy. Specifically, the quadratic limits are the values of Θ that could have produced Θ with the specified probability 1 – α.

ISSN:0003-1305    

DOI:10.1080/00031305.1996.10474388

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

This article proves the Wishart distribution of the sample covariance matrix by induction on the sample size. The proof is elementary and is easy for adaptation in introductory multivariate statistics courses.

ISSN:0003-1305    

DOI:10.1080/00031305.1996.10474389

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor