Showing papers in "Journal of the American Statistical Association in 1950"
TL;DR: In this paper, a line is fitted by least squares, minimizing the sum of the squared residuals of the dependent uncontrolled variate, regardless of whether the independent variate has been measured without error as v or with error as y.
Abstract: If, in sampling from an existent population, we wish to know the regression of u on v, a line is fitted by least squares, minimizing the sum of the squared residuals of v (or y). If there is no error in measuring the independent variate u, regardless of whether the dependent variate has been measured without error as v or with error as y, the regression is an estimate of the true regression. If, however, the independent variate is measured with error in x, the regression obtained is a biassed one. The bias will characterize the fitted line, and will be present whether the sample is a random one of the entire population or has been taken at preassigned selected values of x. If, however, the experiment is one in which one of the variates is a controlled observation, it differs from sampling from an existent population in that, 1), the line estimated by least squares, minimizing the sum of the squared residuals of the dependent uncontrolled variate, is the same, whether x or y is the controlled vari...
450 citations
422 citations
328 citations
TL;DR: A sampling technique is defined as introducing control into the selection of n out of N sampling units when it increases the probabilities of selection for preferred combinations of units (and decreases the probabilities for non-preferred combinations) Methods used in the past have by no means exhausted the possibilities of controlled selection as discussed by the authors.
Abstract: A sampling technique is defined as introducing control into the selection of n out of N sampling units when it increases the probabilities of selection for preferred combinations of units (and decreases the probabilities for non-preferred combinations) Methods used in the past have by no means exhausted the possibilities of controlled selection, however Procedures are developed by which the probabilities of selection for preferred combinations are sharply increased and the theoretical basis for the methods is stated The methods are applied to a specific problem and the procedures are described in detail It it found that as a result the variances of estimates for several important items are reduced as compared with the corresponding variances for stratified random sampling * Presented at the 108th Annual Meeting of the American Statistical Association, Cleveland, December 29, 1948
139 citations
TL;DR: In this article, a table and method for computing the maximum likelihood solution which converges more rapidly than the standard probit method is presented, and a procedure is presented for obtaining more accurate initial approximations, and the problem of the bias of the estimation in small samples is considered.
Abstract: The estimation of the parameters of dosage response curves by the standard probit method is an iterative process beginning with approximations to the parameters and using one or more cycles of computations to “improve” these estimates until they converge. The present paper gives a table and method for computing the maximum likelihood solution which converges more rapidly than the standard probit method. A procedure is presented for obtaining more accurate initial approximations, and the problem of the bias of the maximum likelihood estimates in small samples is considered.
138 citations
113 citations
TL;DR: In this article, the authors described the technique suggested by H. B. Mann and A. W. Wald for selecting the number and width of class intervals for the chi-square test of goodness of fit when the null hypothesis distribution is continuous and completely specified.
Abstract: This article describes in non-mathematical fashion the technique suggested by H. B. Mann and A. Wald for selecting the number and width of class intervals for the chi-square test of goodness of fit when the null hypothesis distribution is continuous and completely specified. The number of classes is selected by means of a formula depending upon the sample size and the level of significance and the class limits are chosen such that each class contains the same number of items under the null hypothesis. Finally it is suggested that the number of classes as given by the formula may be halved for practical purposes. * This article is based on a Master's Essay written at Columbia University under Professor T. W. Anderson, Jr.
82 citations
TL;DR: This paper reviewed the development of demography, and especially of population forecasting, and discussed the current demographic situation, the merits and limitations of several methods of making population predictions, and errors in demographic thinking are examined.
Abstract: This paper reviews the development of demography, and especially of population forecasting, and discusses the current demographic situation. The merits and limitations of several methods of making population predictions, and errors in demographic thinking are examined. The complexity of the problem of making forecasts either for short periods or long-time trends with the techniques now available is pointed out. * Revision of a paper presented before a joint meeting of the American Statistical Association and the Population Association of America in New York City on December 30, 1949.
75 citations
TL;DR: In this article, it was shown that the results in the theory of sampling from finite populations can be obtained very easily by working in terms of k's, and that the k's have very simple general properties as regards sampling from one or more finite populations, and may be easily computed numerically.
Abstract: Results in the theory of sampling from finite populations can be obtained very easily by working in terms of k's. The single subscript k's were introduced by R. A. Fisher [2], while the multiple subscript ones seem to be new. The k's have very simple general properties as regards sampling from one or more finite populations, and may be easily computed numerically. Applications are made here mostly to known results, while further applications to obtain new results will be made elsewhere. * Fellow of the John Simon Guggenheim Foundation.
55 citations
52 citations
TL;DR: This volume contains papers in the Physical Sciences and Engineering, presented at the Fifth Berkeley Symposium on Mathematical Statistics and Probability, held at the Statistical Laboratory of the University of California, Berkeley, during the period 21 June through 18 July 1965 and 27 Dec 1965 through 7 Jan 1966.
Abstract: Abstract : The volume contains papers in the Physical Sciences and Engineering, presented at the Fifth Berkeley Symposium on Mathematical Statistics and Probability, held at the Statistical Laboratory of the University of California, Berkeley, during the period 21 June through 18 July 1965 and 27 Dec 1965 through 7 Jan 1966. Papers in Astronomy were presented by E. M. Burbridge, G. R. Burbridge, W. H. McCrea, T. Page, B. Lynds, and W. C. Livingston. Papers in Physics were presented by R. L. Dobrushin, J. M. Hammersley and H. Solomon. Papers in Spectral Analysis were presented by M. S. Bartlett and B. Mandelbrot. Papers in Control Processes were presented by J. Bather, H. Chernoff, R. Bellman and P. Whittle. Papers in Reliability were presented by R. E. Barlow, A. W. Marshall, Yu. K. Belyaev, B. V. Gnedenko, A. D. Soloviev, Z. W. Birnbaum, J. D. Esary, F. Proschan and R. Pyke.
TL;DR: A model is proposed in the present paper to measure certain factors which influence the probability of acquiring syphilis simultaneously and can be estimated by multiple regression and tested for statistical significance.
Abstract: In interpreting rates of syphilis incidence, it is worthwhile to evaluate certain factors which influence the probability of acquiring syphilis. In the past, these factors have been estimated separately either by graphical or by elementary numerical methods. A model is proposed in the present paper to measure these factors simultaneously. The parameters in the model can be estimated by multiple regression and tested for statistical significance. * The statistical investigation was made possible by the grant of an assistantship from the Institute of Statistics. The syphilis studies are supported jointly by grants from the International Health Division of the Rockefeller Foundation and the North Carolina State Board of Health.
TL;DR: In this paper, a rational selection of sample size when it is desired to estimate the standard deviation is discussed, and it is shown that changing the permissible error of the estimate from an absolute to a relative one is acceptable in many cases.
Abstract: One frequently encounters the need of a rational selection of sample size when it is desired to estimate the standard deviation. Changing the permissible error of the estimate from an absolute to a relative one is acceptable in many cases and permits an exact, a priori solution to the problem of sample size without involving any previous estimates.
TL;DR: In this article, the spacing and effectiveness functions of a quality control chart used either alone or in sets of two or more are derived for production at a constant level and for erratic production.
Abstract: The spacing and effectiveness functions of a quality control chart used either alone or in sets of two or more are derived for production at a constant level and for erratic production. The spacing of decision points is considered from a general point of view. The theory developed is fundamental in deciding which of two different decision techniques in quality control, each using the same spacing function, is the more effective. * Many of the results given herewith were obtained independently by the two authors.
TL;DR: The demographic development of the population of the world is divided into the three regions of Incipient Decline, Transitional Growth, and High Growth Potential as mentioned in this paper, and the factors of changing birth rates, death rates, and family size are considered in their relation to the changes taking place in the social structure and national economy of the countries included in each region.
Abstract: The demographic development of the population of the world is divided into the three regions of Incipient Decline, Transitional Growth, and High Growth Potential. For each of these, the factors of changing birth rates, death rates, and family size are considered in their relation to the changes taking place in the social structure and national economy of the countries included in each region.
TL;DR: In this article, the authors describe a population estimating technique which is designed to facilitate the study of population trends during postcensal periods, by using current vital statistics, population estimates for groupings of area are obtained which are sufficiently accurate to permit inferences to be made concerning growth or decline since the last census.
Abstract: This article describes a population estimating technique which is designed to facilitate the study of population trends during postcensal periods. By using current vital statistics, population estimates for groupings of area are obtained which are sufficiently accurate to permit inferences to be made concerning growth or decline since the last census.
TL;DR: In this article, a technique for the treatment of errors introduced into sampling surveys due to the nonavailability of respondents is presented, where the expected cost and variance of the sample survey are expressed as functions of sample size and of the number of call-backs made on the non-availables.
Abstract: A technique is presented for the treatment of errors introduced into sampling surveys due to the non-availability of respondents. The expected cost and variance of the sample survey are expressed as functions of sample size and of the number of call-backs made on the non-availables. A method is then presented which optimizes precision for a given cost by playing sampling error against the bias resulting from non-availables. * Research under the sponsorship of the Office of Naval Research. Presented to the Institute of Mathematical Statistics, November 27, 1948.
TL;DR: In this article, the authors employed the method of moments to estimate the mean and standard deviation of a Pearson Type III population when α3 is known and when only the form of the distribution is known in advance.
Abstract: The method of moments is employed with “single” truncated random samples; (1) to estimate the mean, μ, and the standard deviation, σ, of a Pearson Type III population when α3 is known; and (2) to estimate μ, σ, and α3 when only the form of the distribution is known in advance. No information is assumed to be available about the number of variates in the omitted portion of the sample. The results obtained can be readily applied to practical problems with the aid of “Salvosa's Tables of Pearson's Type III Function.” An illustrative example is included in the paper. * Presented before a joint session of the American Statistical Association, the Institute of Mathematical Statistics, and the Econometric Society, in New York, New York, on December 29, 1949.
TL;DR: In this paper, the problems of slope estimation and linear extrapolation when the precision of the Y-measurements changes with different values of x have been discussed, and the optimal placement of x-values and the optimum distribution of the N observations for selected relationships between σ and x are discussed.
Abstract: This paper discusses the problems of slope-estimation and of linear extrapolation when the precision of the Y-measurements changes with different values of x. Tables are presented which show, for each of these problems, the optimum placement of x-values and the optimum distribution of the N observations for selected relationships between σ and x. The optimum placements are seen to be the same for the two problems, but for the latter, the optimum distributions depend on the nearness or remoteness of the extrapolation.
TL;DR: This note provides additional information concerning the plan for eliminating the need for callbacks described in the March, 1949 issue of the Journal.
Abstract: This note provides additional information concerning the plan for eliminating the need for callbacks described in the March, 1949 issue of the Journal. Attention is called to the difference in the effects of clustering in using the “nights-at-home” plan or callbacks, and an error in the calculation of the sampling error of the former is corrected.
TL;DR: In this article, a comparison of two methods of obtaining per cent completeness of birth registration by states: 1) by relating a matched set of records for the state as a whole to the total group of matched and unmatched records combined; and 2) by a cumulative technique suggested by Chandra Sekar and Deming in the March issue of the Journal.
Abstract: A nation-wide test on the completeness of birth registration was carried out in 1940 in connection with the Decennial Census of Population and Housing. The present paper discusses the comparison, based on this data, of two methods of obtaining per cent completeness of birth registration by states: 1) by relating a matched set of records for the state as a whole to the total group of matched and unmatched records combined; and 2) by a cumulative technique suggested by Chandra Sekar and Deming in the March issue of the Journal. Differences in the results by the two methods were minor except in those areas having a comparatively high degree of under-registration.
TL;DR: In this article, the authors discuss the extension of discriminatory analysis to the case where the primary data are qualitative and apply it to the problem of scoring letter grades in school subjects so as to maximize individual differences.
Abstract: This paper discusses the extension of discriminatory analysis to the case where the primary data are qualitative. The general principle in the use of the discriminant function in the case of two classes is to determine a set of adjustable coefficients so chosen as to maximize the ratio of the difference between sample means to the standard deviation within the two classes. When only a single chosen component is to be maximized relative to a set of other components, the equations are linear. In the case discussed here we have a two-way table of non-numerical observational data where the solution of equations of higher degree is required. Appropriate values are to be determined in order that the observations may be made as additive as possible. Application is made to the problem of scoring letter grades in school subjects so as to maximize individual differences.
TL;DR: A technique for computing the precision of two measuring instruments when there is a linear relation between the scales of the two instruments is presented.
Abstract: This paper presents a technique for computing the precision of two measuring instruments when there is a linear relation between the scales of the two instruments.
TL;DR: Some efforts of the Bureau of the Census to measure and evaluate response errors are described, and particular attention is devoted to the October, 1948, pretest of Census procedures.
Abstract: Some efforts of the Bureau of the Census to measure and evaluate response errors are described. Particular attention is devoted to the October, 1948, pretest of Census procedures and the measurement of response errors of the various procedures. The procedures were: (1) Self-enumeration, using a household schedule. The schedule was a single sheet of paper 18″ × 24Prime; with 10 columns of questions for the various members of the household—two columns of questions for each individual repeated five times—on one side, and a letter to the household and questions on housing on the other side. (2) Self-enumeration using a 4 page booklet, the page size being 9Prime; × 11Prime;, with Individual Enumeration Forms (9Prime; × 11Prime;) inserted for each member of the household. The questions were printed front and back in two columns on the Individual Enumeration Form. (3) Obtaining information from respondents by direct interview. (4) Obtaining basic information by direct interview and leaving schedule with...
TL;DR: In this article, the theory of games is applied to an advertising competition and functions of susceptibility and resistance to advertising are used in a mathematical model to determine the strategy and spending rates of the participants in the campaign.
Abstract: The theory of games is applied to an advertising competition. Functions of susceptibility and resistance to advertising are used in a mathematical model to determine the strategy and spending rates of the participants in the campaign.