Jerzy Neyman

On the Two Different Aspects of the Representative Method: the Method of Stratified Sampling and the Method of Purposive Selection

Owing to the work of the International Statistical Institute,* and perhaps still more to personal achievements of Professor A.L. Bowley, the theory and the possibility of practical applications of the representative method has attracted the attention of many statisticians in different countries. Very probably this popularity of the representative method is also partly due to the general crisis, to the scarcity of money and to the necessity of carrying out statistical investigations connected with social life in a somewhat hasty way. The results are wanted in some few months, sometimes in a few weeks after the beginning of the work, and there is neither time nor money for an exhaustive research.

»Smooth test» for goodness of fit

Abstract Dedicated to the memory of Karl Pearson (27 March 1857—27 April 1936) who originated the problem of a test for goodness of fit and was first to advance its solution.

The testing of statistical hypotheses in relation to probabilities a priori

In a recent paper we have discussed certain general principles underlying the determination of the most efficient tests of statistical hypotheses, but the method of approach did not involve any detailed consideration of the question of a priori probability. We propose now to consider more fully the bearing of the earlier results on this question and in particular to discuss what statements of value to the statistician in reaching his final judgment can be made from an analysis of observed data, which would not be modified by any change in the probabilities a priori . In dealing with the problem of statistical estimation, R. A. Fisher has shown how, under certain conditions, what may be described as rules of behaviour can be employed which will lead to results independent of these probabilities; in this connection he has discussed the important conception of what he terms fiducial limits. But the testing of statistical hypotheses cannot be treated as a problem in estimation, and it is necessary to discuss afresh in what sense tests can be employed which are independent of a priori probability laws.

Contribution to the Theory of Sampling Human Populations

AT A CONFERENCE on Sampling Human Populations held last April A at the Department of Agriculture Graduate School in Washington, a problem was presented by Mr. Milton Friedman and Dr. Sidney Wilcox for which I could not offer a solution at the time. Since it seemed to be important and of general interest, I have considered it in some detail. The purpose of this paper is to present the results I have obtained. 2. STATEMENT OF THE PROBLEM

MOLECULAR STUDIES OF EVOLUTION: A SOURCE OF NOVEL STATISTICAL PROBLEMS*

Abstract The recently opened and rapidly developing field of evolution research, conducted on the level of molecules, is a novel source of interesting statistical and probabilistic problems. The biological studies are concerned with macromolecules which, in organisms as diverse as Man, Monkey, Carp, Whale and Yeast, perform similar functions and have similar structures. The apparently inconsequential differences among such homologous macromolecules, their sites and their frequencies, are at the base of current efforts to establish lineages linking the species studied to a common ancestor. The nature of statistical problems originating from such biological studies is illustrated on two tentative stochastic models of “inconsequential” substitutions in the macromolecules.

Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability.

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.

OUTLIER PRONENESS OF PHENOMENA AND OF RELATED DISTRIBUTIONS

Publisher Summary This chapter discusses the outliner proneness of the phenomena and of related distributions. It discusses the distinction between cases where the tendency to suspect and to eliminate outlier observations may be justifiable and those in which it is not. The chapter discusses three concepts: (1) the concept of a k-outlier, (2) the concept of families of distributions that are outlier-resistant, and (3) the concept of families that are outlier-prone. If a substantial previous experience in a particular domain of study appears sufficient for the statistician to act on the assumption that the observable variables follow an outlier-resistant distribution, then the efforts to seek out and, possibly, to eliminate the outliers are justified. In statistical practice, when applying a test, it is important to see that the theory underlying the test is not in conflict with the phenomenon studied. The customary requirements on the test of a hypothesis H are two: (i) if H is true, the use of the test should ensure the maintenance of the desired level of significance and (ii) if H is false and some contemplated alternative hypothesis H1 is true, the power with regard to H1 should be high.

In Determinism in Science and New Demands on Statisticians

Abstract The words “indeterministic study” are used to designate research aiming to determine how frequently a quantity X characterizing the phenomena considered assumes its various particular values. If the purpose of research is to establish the exact value of X as a function of other variables, then this research is “deterministic.” In the history of indeterminism in science four (overlapping) periods are discernible. a. Period of “marginal indeterminism.” This was the period, symbolized by the names of Laplace and Gauss, in which research in science was all deterministic with just one domain, that of errors of measurement, treated indeterministically. b. Period of “static indeterminism,” roughly covering the end of the nineteenth and the beginning of the twentieth centuries, is symbolized by names of Bruns, Charlier, Edgeworth, Galton and Karl Pearson. Here, the main subject of study was a “population” and efforts were made to develop systems of frequency curves to describe analytically the empirical ...

R. A. Fisher (1890—1962): An Appreciation

typifying Cambridge, the wonderful melting pot of ideas, where astronomers rub shoulders with historians, neurophysiologists with lawyers, and mathematicians with geneticists, statisticians, and others. The appraisal of Fishers scholarly activity should, then, be made from at least three points of view, the point of view of statistics, that of mathematics, and that of empirical science. As a statistician, R. A. Fisher appears to me to be a direct descendant of Karl Pearson, with side influences of G. Udny Yule and of F. Y. Edgeworth. From the point of view of mathematics, the situation is more complicated. Fishers early days at Cambridge were, roughly, on the dividing line between two epochs, the earlier epoch of manipulative skills and the subsequent period of conceptual developments. Fisher seems to have belonged to the epoch of manipulative skills, in which he was supreme. Also, I remember his declaring that the change symbolized by the names of Hardy and Littlewood was a disaster in English mathematics. Nevertheless, some of the most important writings of Fisher appear to be influenced by what was then the incipient era of conceptual mathematics. The part of Fishers work that I admire most is one that must have resulted from the general Cambridge atmosphere, from his contacts with representatives of empirical sciences, astronomers (in particular with A. S. Eddington), geologists, and biologists. Here I have in mind not only Fishers direct contributions to science, especially to population genetics, but also Fishers actual founding of an entirely novel discipline related to scientific research which I like to call the theory of experimentation. Even though Fishers

ASYMPTOTICALLY OPTIMAL TESTS OF COMPOSITE HYPOTHESES FOR RANDOMIZED EXPERIMENTS WITH NONCONTROLLED PREDICTOR VARIABLES

Abstract The paper is concerned with randomized experiments with one treatment. Two randomization schemes are considered: randomized pairs and unrestricted randomization. If effective at all, the treatment is supposed to affect the conditional distribution of the “experimental” variable Y given another variable X, called “predictor”. The distribution of X is not affected by the treatment. Using the general theory published elsewhere, the paper deduces the locally asymptotically optimal test of the hypothesis that the treatment has no effect. Apart from the usual difficulties connected with asymptotic tests (how large must N be?), the theory is easily applicable in many “live” cases even though the conditional distribution of Y given X may contain nuisance parameters and be of unusual form.