摘要:

Quantitative graphics have been central to the development of science, and statistical graphics date from the earliest attempts to analyze data. Many familiar forms, including bivariate plots, statistical maps, bar charts, and coordinate paper, were used in the 18th century. Statistical graphics developed through attention to four problems: spatial organization (17th and 18th centuries), discrete comparison (18th and early 19th centuries), continuous distribution (19th century), and multivariate distribution and correlation (late 19th and early 20th centuries). Today, statistical graphics appear to be reemerging as an important analytic tool, with recent innovations exploiting computer graphics and related technologies.

ISSN:0003-1305    

DOI:10.1080/00031305.1978.10479235

出版商:Taylor & Francis Group    

年代:1978

数据来源: Taylor

摘要:

Box plots display batches of data. Five values from a set of data are conventionally used; the extremes, the upper and lower hinges (quartiles), and the median. Such plots are becoming a widely used tool in exploratory data analysis and in preparing visual summaries for statisticians and nonstatisticians alike. Three variants of the basic display, devised by the authors, are described. The first visually incorporates a measure of group size; the second incorporates an indication of rough significance of differences between medians; the third combines the features of the first two. These techniques are displayed by examples.

ISSN:0003-1305    

DOI:10.1080/00031305.1978.10479236

出版商:Taylor & Francis Group    

年代:1978

数据来源: Taylor

摘要:

In least-squares fitting it is important to understand the influence which a data y value will have on each fitted y value. A projection matrix known as the hat matrix contains this information and, together with the Studentized residuals, provides a means of identifying exceptional data points. This approach also simplifies the calculations involved in removing a data point, and it requires only simple modifications in the preferred numerical least-squares algorithms.

ISSN:0003-1305    

DOI:10.1080/00031305.1978.10479237

出版商:Taylor & Francis Group    

年代:1978

数据来源: Taylor

摘要:

In this article a natural extension of the beta-binomial distribution is developed. Forced binary choice situations are modeled such that each individual has a probabilitypof knowing the correct answer. (This probability is distributedf(p) across the population.) Hence each individual will guess at the correct answer with probability 1 –p.The observable random variableR, the total number of correct answers (both by knowing and guessing) out ofktrials has a rather complicated distribution. However, whenf(p) is distributed beta with parametersmandn, the distributionP(r; k, m, n) can be expressed in terms of the well-known Gaussian hypergeometric function. This distribution has implications for true-false tests, taste tests, and virtually every other forced binary choice situation.

ISSN:0003-1305    

DOI:10.1080/00031305.1978.10479238

出版商:Taylor & Francis Group    

年代:1978

数据来源: Taylor

摘要:

The well-known result that measurement error in an independent variable biases the least-squares estimator of that variable's regression coefficient towards zero is insufficient information to determine the effect of measurement error on the standardttest of the null hypothesis that the coefficient equals zero. This note shows that measurement error tends to lower the probability of rejecting such a null hypothesis by inducing a lower limiting value of the coefficient'ststatistic. This result holds despite an ambiguous effect of measurement error on the coefficient's estimated standard error.

ISSN:0003-1305    

DOI:10.1080/00031305.1978.10479239

出版商:Taylor & Francis Group    

年代:1978

数据来源: Taylor

摘要:

A lemma is given which simplifies the derivation of maximum likelihood estimates of the covariance matrix in the multivariate normal case.

ISSN:0003-1305    

DOI:10.1080/00031305.1978.10479240

出版商:Taylor & Francis Group    

年代:1978

数据来源: Taylor

摘要:

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.

ISSN:0003-1305    

DOI:10.1080/00031305.1978.10479241

出版商:Taylor & Francis Group    

年代:1978

数据来源: Taylor

摘要:

Several theorems are stated which are useful in establishing whether a given sequence of averages of independent but not identically distributed random variables does or does not satisfy the weak and/or strong laws of large numbers. The theorems are illustrated with two families of examples, one discrete and one continuous. In each family, by varying one parameter we obtain cases in which the strong law holds, neither the strong nor the weak law holds, and only the weak law holds.

ISSN:0003-1305    

DOI:10.1080/00031305.1978.10479242

出版商:Taylor & Francis Group    

年代:1978

数据来源: Taylor

ISSN:0003-1305    

DOI:10.1080/00031305.1978.10479243

出版商:Taylor & Francis Group    

年代:1978

数据来源: Taylor

ISSN:0003-1305    

DOI:10.1080/00031305.1978.10479244

出版商:Taylor & Francis Group    

年代:1978

数据来源: Taylor