Showing papers in "Journal of the American Statistical Association in 1951"

The Kolmogorov-Smirnov Test for Goodness of Fit

Abstract: The test is based on the maximum difference between an empirical and a hypothetical cumulative distribution. Percentage points are tabled, and a lower bound to the power function is charted. Confidence limits for a cumulative distribution are described. Examples are given. Indications that the test is superior to the chi-square test are cited.

The Theory of Statistical Decision

Abstract: (1951). The Theory of Statistical Decision. Journal of the American Statistical Association: Vol. 46, No. 253, pp. 55-67.

The Influence of Statistical Methods for Research Workers on the Development of the Science of Statistics

Abstract: (1951). The Influence of Statistical Methods for Research Workers on the Development of the Science of Statistics. Journal of the American Statistical Association: Vol. 46, No. 253, pp. 19-34.

Response Errors in Surveys

Abstract: (1951). Response Errors in Surveys. Journal of the American Statistical Association: Vol. 46, No. 254, pp. 147-190.

Estimating Parameters of Logarithmic-Normal Distributions by Maximum Likelihood

Abstract: This paper is concerned with the three-parameter logarithmic normal distribution; i.e., the general distribution in which the terminus is unknown. Maximum likelihood equations for estimating population parameters from random samples are derived, and an iterative method for their solution is outlined. Variances and covariances of these estimates are obtained from the information matrix. An illustrative example is included.

Experimental Design in Psychological Research.

Abstract: Experimental Design in Psychological Research , Experimental Design in Psychological Research , کتابخانه مرکزی دانشگاه علوم پزشکی تهران

Sampling with Probabilities Proportional to Size: Adjustment for Changes in the Probabilities

Abstract: W E CONSIDER a simplified area sample consisting of one primary sampling unit chosen from each of a number of strata; each such selected unit is to be enumerated completely. The sample "take" (i.e., the total in the sample of whatever is being surveyed) can be converted to an estimate of the population in each stratum simply by multiplying by the number of units in the stratum; and this is, for practical purposes, the only method of estimating if no information about the unsampled units other than their number is on hand. If, however, some evidence is available on the relative "sizes" of the units in a stratum one would like to incorporate this in the estimating procedure. In an application which has now become fairly common, a number of different characteristics are to be estimated by a uniform procedure from a single survey, and the measure of size related to all characteristics is the number of persons in the several units at a precedingcensus. The Canadian Labor Force sample, like that used for the Monthly Report on the Labor Force of the United States, consists of up to four successive stages;' the theory here considered is applicable to the first stage. In the first stage the entire rural territory of Canada was divided into about 500 areas constituting primary sampling units, and these were assembled into strata each containing between 5 and 10 units. There was no requirement that the units comprising a stratum were to be contiguous; but only that they be as similar as possible in respect of type of farming, density of population etc.; nor was any attempt made to assemble into one stratum those units similar in the numbers of people they contained at the preceding census. The sub-sampling within selected primary sampling units was arranged so that multiplication of the sample take by 100 furnished an unbiased estimate of the stratum total; this was accomplished, following the suggestion of Hansen and Hurwitz, by sub-sampling in a ratio which depended on which unit was selected, so as to give a fixed expected number in the sample, i.e., 0.01 of the measure of size of the stratum. The application of the theorem of this paper, however, is not affected by sub-sampling; we may think of the estimating procedure as a matter of multiplying

Mathematical Models in Psychological Scaling

Abstract: The major theme of this paper is to stress the importance to social science and psychology of the application of mathematical and statistical theory applicable to numbers which are not elements of fields.1 The greater part of statistical theory is concerned with numbers to which the operations of arithmetic can be validly applied. There is reason to believe that in social and psychological data some the axioms of arithmetic are not satisfied and, if this is the case, weaker axiomatic systems, like partially ordered sets (posets), should be used to provide the logical framework for the description and analysis of the data. The nature of some of these weaker systems, their experimental basis, and the reasons for their importance will be discussed.

The Distribution of Blocks in an Uncongested Stream of Automobile Traffic

Abstract: The time instants at which the cars in a stream of uncongested traffic pass a point on the roadway are distributed at random. To a pedestrian trying to cross the street or to a driver on a minor side-street, the traffic stream may be viewed as an alternating succession of periods which permit crossing and periods which do not. Probability distributions of the lengths of these periods are developed and discussed.

The Impact of R. A. Fisher on Statistics

Abstract: (1951). The Impact of R. A. Fisher on Statistics. Journal of the American Statistical Association: Vol. 46, No. 253, pp. 35-46.

Results of Alternative Statistical Treatments of Sample Survey Data

Abstract: A CAREFUL formulation of the probability and economic model which , underlies observations is indispensable for the choice of correct statistical procedures to be followed in drawing econometric inferences from samples. The sample design, the methods of collecting data, and underlying economic behavior will all contribute to the formulation of the model. The study of data collected in consumer surveys' has convinced us that one cannot proceed simply by the application of conventional statistical methods in the estimation of economic relationships because of the existence of some basic difficulties which we classify as follows: (1) weighting of observations, (2) heteroscedasticity, (3) nonlinearities, (4) the choice of alternative economic concepts, (5) errors of observation. In this paper, we shall describe some empirical calculations that deal with the first four difficulties. The fifth is reserved for future study. Observations may be weighted because of the use of differential sampling rates and because of differential response rates to survey questions in the different strata of the population. High rent (a correlate of high income) areas are deliberately over-sampled because they show more variability in respect to certain economic variables than other strata, and conversely low rent areas are under-sampled. The strata also have different response rates. The weights finally used are combinations of sampling and response rates which attempt to give each stratum the same relative importance in the sample that it has in the population; i.e., they are essentially inversely proportional to the net (effective) sampling rate. The heteroscedasticity which leads to the adoption of differential sampling rates must also be taken into account in the estimation of parameters in equations expressing economic behavior. In these equations, the variance of the so-called disturbances is a fundamental parameter to be estimated, and this variance is not uniform over some

Statistical Decision Functions.

Abstract: The foundations of a general theory of statistical decision functions, including the classical non-sequential case as well as the sequential case, was discussed by the author in a previous publication [3]. Several assumptions made in [3] appear, however, to be unnecessarily restrictive (see conditions 1-7, pp. 297 in [3]). These assumptions, moreover, are not always fulfilled for statistical problems in their conventional form. In this paper the main results of [3], as well as several new results, are obtained from a considerably weaker set of conditions which are fulfilled for most of the statistical problems treated in the literature. It seemed necessary to abandon most of the methods of proofs used in [3] (particularly those in section 4 of [3]) and to develop the theory from the beginning. To make the present paper self-contained, the basic definitions already given in [3] are briefly restated in section 2.1.

On Stratification and Optimum Allocations

Abstract: Useful condensations of the variance equations for estimates of the mean obtained from stratified proportional and optimum allocation samples are presented, and a criterion for deciding between semi-optimum and proportional allocation designs is derived.