Showing papers in "Journal of the American Statistical Association in 1957"
TL;DR: In this paper, the authors give an approach to derive maximum likelihood estimates of parameters of multivariate normal distributions in cases where some observations are missing (Edgett [2] and Lord [3], [4]).
Abstract: S EVERAL authors recently have derived maximum likelihood estimates of parameters of multivariate normal distributions in cases where some observations are missing (Edgett [2] and Lord [3], [4]). The purpose of this note is to give an approach to these problems that indicates the estimates with a minimum of mathematical manipulation; this approach can easily be applied to other cases. (The technique bears some resemblance to that of Cochran and Bliss in a dierent problem [1].) The method will be indicated by treating the simplest case involving a bivariate normal distribution. Suppose x and y have a bivariate normal distribution with means P, and m,u variances ,2 and UY2 and correlation coefficient p. We shall indicate the density by n(x, y|,ux, p,u; 2 a2; p). Suppose n observations are made on the pair (x, y) and N-n observations are made on x; that is, N-n observations on y are missing. The data are
563 citations
TL;DR: In this paper, the use of dummy variables requires the imposition of additional constraints on the parameters of regression equations if determinate estimates are to be obtained, and among the possible constraints the most useful are (a) to set the constant term of the equation to zero, or (b) to omit one of the dummy variables from the equation.
Abstract: The use of dummy variables requires the imposition of additional constraints on the parameters of regression equations if determinate estimates are to be obtained. Among the possible constraints the most useful are (a) to set the constant term of the equation to zero, or (b) to omit one of the dummy variables from the equation. In working with a single system of classes either constraint can be used, and results from the application of one are readily derived from those obtained from the other. If several systems of classes are involved the best procedure is to delete one dummy variable from each system.
499 citations
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TL;DR: In this paper, it is shown that it is required to condense observations of a variate into a small number of groups, the grouping intervals to be chosen to retain as much information as possible.
Abstract: Suppose that it is required to condense observations of a variate into a small number of groups, the grouping intervals to be chosen to retain as much information as possible. One way of formulating this requirement mathematically is given and numerical recommendations are made for use when the variate is normally distributed.
355 citations
TL;DR: This edition of Kate L. Turabian's "Manual for Writers" reflects the way students work today, taking into account the role of personal computers in the preparation and presentation of their papers.
Abstract: This book is a manual for writers of term papers, thesis and dissertations is designed as a guide to suitable style in the typewritten presentation of formal papers both in scientific and nonscientific fields
305 citations
TL;DR: The multivariate polykays, or multipart k-statistics, were obtained as a slight extension of results given by Tukey [4] for the univariate poly-kays.
Abstract: The multivariate polykays, or multipart k-statistics, are obtained as a slight extension of results given by Tukey [4] for the univariate polykays. The relationship between this system and the system of multivariate symmetric means is indicated and multiplication formulas are given. An application of these results to the construction of unbiased ratio-type estimators and variance estimates for finite populations is given as a further illustration of the usefulness of polykays.
201 citations
TL;DR: Because graduate students in statistics are given little preparation for actual consulting, they are prone, particularly in their early years, to commit errors of the third kind, many of which could be avoided if the students were properly trained.
Abstract: Because graduate students in statistics are given little, if any, preparation for actual consulting, they are prone, particularly in their early years, to commit errors of the third kind, many of which could be avoided if the students were properly trained. Errors of the third kind are defined and are illustrated with actual examples from consulting experience. The cases used represent types of error which result from different situations that arise frequently in practice. Some discussion is included of possible remedies for this problem that are suggested by the experience of educators in other fields.
189 citations
178 citations
TL;DR: In this article, historical notes on the Wilcoxon unpaired two-sample test are given, along with a discussion of its application in the two-stage two-sampling test.
Abstract: (1957). Historical Notes on the Wilcoxon Unpaired Two-Sample Test. Journal of the American Statistical Association: Vol. 52, No. 279, pp. 356-360.
177 citations
165 citations
TL;DR: In this paper, it is shown that a unique solution is obtained when one assumes a certain set of inequalities and then requires the intervals to be as short as possible, and tables of intervals for 90 and 95 per cent confidence levels are presented based on reasonable sets of inequalities, and a Poisson approximation to the binomial.
Abstract: Many more-or-less reasonable solutions to the problem of statistical estimation of the product P 1 P 2 of two binomial parameters by confidence intervals can be given. After specializing to the case where P 1 and P 2 are much less than 1 and to estimation by “one-sided” intervals it is shown that a unique solution is obtained when one assumes a certain set of inequalities and then requires the intervals to be as short as possible. Tables of intervals for 90 and 95 per cent confidence levels are presented based on reasonable sets of inequalities and on a Poisson approximation to the binomial. * I wish to thank Mr. J. M. Wiesen for suggesting this problem.
149 citations
TL;DR: In this article, the authors present a problem in life testing, which they call A Problem in Life Testing (APLTT), and propose a method to solve it, using statistical methods.
Abstract: (1957). A Problem in Life Testing. Journal of the American Statistical Association: Vol. 52, No. 279, pp. 350-355.
TL;DR: In this paper, the rank of the matrix is less than p, k < p linear combinations of the original variates are obtained by the method of principal components, which are used both for short and long range control with some simplifications when the short range procedures are to be handled by production personnel.
Abstract: There are a large number (p) of correlated variables to be controlled in a photographic process. Independent control charts for each would lead to a considerable misstatement of the Type I error for the system as a whole. The use of Hotelling's T may involve computational problems if the determinant is near zero. Since this would imply that the rank of the matrix is less than p, k < p linear combinations of the original variates are obtained by the method of principal components. These new variates are used both for short and long range control with some simplifications when the short range procedures are to be handled by production personnel.
TL;DR: In this article, a method is proposed and empirically demonstrated for extending Thurstone's law of comparative judgment so as to transform psychological qualities into an additive measurement scale, an equal unit scale with a meaningful zero point.
Abstract: A method is proposed and empirically demonstrated for extending Thurstone's law of comparative judgment so as to transform psychological qualities into an additive measurement scale. Application of the method yields results supporting the contention that subjective values can be measured on an additive scale, an equal unit scale with a meaningful zero point. * This paper reports research partially supported by the Quartermaster Food and Container Institute for the Armed Forces.
TL;DR: A brief history of the Latin square design and a generalization of the design to the case in which the rows, columns and treatments represented in the experiment are samples from populations of rows, column and treatments respectively is studied in this article.
Abstract: A brief history of the Latin square design is given. A generalization of the design to the case in which the rows, columns and treatments represented in the experiment are samples from populations of rows, columns and treatments respectively is studied. A possible frame of reference for the interpretation of the experimental results is described. The leads to what is termed a “population model,” various population parameters, means and components of variation which are of interest to the experimenter. No assumptions are made about additivity of experimental units and treatments. Results on expectations of mean squares in the analysis of variance are given in terms of quantities (denoted by [Sgrave]'s) which result in a concise description and in terms of the components of variation. Biases in the estimation of components of variation by means of the analysis of variance are discussed and assessed. Comparisons of randomized block designs and Latin square designs are given for the general case of n...
TL;DR: In this article, the problem of using all the observations in a sample of multivariate observations when for some of the observations values for certain of the characters are missing was considered and it was concluded that for purposes of prediction no use can be made of incomplete samples.
Abstract: The problem considered is that of using all of the observations in a sample of multivariate observations when for some of the observations values for certain of the characters are missing. This paper extends results obtained for estimation of the parameters in special cases to the general p-variate case and presents the solution to the problem of what use may be made of data from incomplete multivariate samples when the interest lies in the prediction of one character from a knowledge of the rest. It is concluded that for purposes of prediction no use can be made of incomplete samples. Under certain circumstances all the observations in an incomplete sample can be used to construct improved estimators. Application of the results to multivariate normal distributions truncated on one or more characters is mentioned.
TL;DR: Abstract * Research sponsored by the Office of Naval Research under Contract Nonr 1636(00) is permitted for any purpose of the United States Government.
Abstract: * Research sponsored by the Office of Naval Research under Contract Nonr 1636(00). Reproduction in whole or in part is permitted for any purpose of the United States Government.
TL;DR: In this paper, the standard errors and correlations of the residuals from regression are derived both for situations involving cumulative and independent errors, and can be used as a basis for judging which of the two types of error is predominant in a given case.
Abstract: Many situations giving rise to linear data involve measurements made at progressive stages of a physical or chemical process carried out on the same subject of experimentation. In such cases, the experimental errors include cumulative components related to the process, and the errors corresponding to different points on the line are not independent. Failure to take such cumulation of errors into account results in serious underestimation of the standard error of the estimated rate of the process. The standard errors and correlations of the residuals from regression are derived both for situations involving cumulative and independent errors. The differences between the two situations are striking and may be used as a basis for judging which of the two types of error is predominant in a given case. The procedure is illustrated by means of the data obtained in an experiment in physical optics.
TL;DR: Abstract * Revision of paper presented at a joint meeting of the American Statistical Association and the Econometric Society, session on Applications of Electronic Computers to Economic Statistics, December 27, 1955, in New York, N.Y.
Abstract: * Revision of paper presented at a joint meeting of the American Statistical Association and the Econometric Society, session on Applications of Electronic Computers to Economic Statistics, December 27, 1955, in New York, N.Y.