ON THE DISTRIBUTIONS OF ORDER STATISTICS1

Approximations to the distributions of order statistics based on x²t are obtained. These are easy to compute and provide reasonably accurate values for the percentage points and probability integrals of the distributions.     

THE THEORY OF COMPETING RISKS1

The theory of competing risks is motivated, certain aspects are reviewed critically, and some extensions are indicated. A unified formulation of the theory is given covering dependent as well as independent risks. The relations between various functions useful in the theory are made explicit. In a historical note a valuable early result is put into modern notation. The currently controversial subject of identifiability when risks are dependent is discussed and it is indicated under what conditions some of the difficulties raised can be overcome. Consequences of assuming proportional hazard rates are set out. New conditions are provided under which this assumption holds and it is shown how the assumption may be tested. Some concluding remarks deal with limitations of the theory and point out areas needing further work.     

ON THE BEHRENS–FISHER PROBLEM1

In this article the Behrens-Fisher problem is reformulated in terms of a structural model of inference. For this version of the problem a solution is obtained which is valid for arbitrary absolutely continuous error distributions. These results are further discussed for the standard normal distribution and for some other special cases with not normally distributed populations.     

A NOTE ON THE DISTRIBUTION OF THE DOUBLY NON-CENTRAL F DISTRIBUTION1

A three-moment central-F approximation is examined for its usefulness in giving accurate values of the probability integral of the doubly non-central F distribution.     

ON POINT MULTISERIAL CORRELATION1

Abstract
We present a simple form for the estimator of the point multiserial correlation coefficient between a quantitative variate X and a qualitative variate 7. Given a bivariate sample grouped in the form of an r × c contingency table the estimator is based on finding the optimum Y -scores which maximize the correlation coefficient. The resulting estimator is equivalent to Das Gupta's (1960) for ungrouped X -values, with the advantage of simplicity in its calculation. Under the assumption of conditional normality, the significance of point multiserial correlation may be studied by an F -test.     

THE EFFECT OF SAMPLE STRUCTURE ON ANALYTICAL SURVEYS1,2

The core of this paper is a dialogue between "Harry", an experienced survey statistician and "Fred", a young mathematical statistician. They have contrasting approaches to the problem of estimating a regression relationship from a stratified sample, but after one or two red herrings are dragged out, both realize that the situation is not as simple as they had supposed. The role played by the probabilities of selection is a central issue. Estimation sampling for means, totals, and ratios is also considered, and seen to be a special case of the general analytical sampling synthesis they had already agreed upon.     

TECHNIQUES OF COVARIANCE STRUCTURAL ANALYSIS1

The paper delineates the scope and important features of covariance structural analysis in which some pattern can be postulated a priori for the covariance matrix. The coverage given also includes a brief review of the published work in this area with illustration of statistical tests based, on principles of maximum likelihood and union-intersection. Few results on the computational ease under the assumption of particular covariance structures are reported. A few unsolved problems in the area of structural analysis are briefly mentioned.     

INTERACTION MODELS FOR THE LATIN SQUARE1

This paper presents a general method for testing if a particular type of interaction is present in latin square models with one observation per cell. Computing instructions are given along with a detailed numerical example. A data analysis approach is explained where an experimenter can use various models to determine whether interaction is present. If there is interaction, then a procedure is given for examining a number of models to decide what factors (row, column, treatment) are interacting. In addition, a number of sets of latin square data from the literature are reanalysed to determine if they contain interaction.     

THE LIMITING FORM OF THE NON-CENTRAL WISHART DISTRIBUTION1,2

Let S (p×p) have a Wishart distribution -with v degrees of freedom and non-centrality matrix θ= [θ_jK] (p×p). Define θ₀= min {| θ_jk |}, let θ₀→∞, and suppose that | θ_jK | = 0(θ_o). Then the limiting form of the standardized non-central distribution, as θ while n? remains fixed, is a multivariate Gaussian distribution. This result in turn is used to obtain known asymptotic properties of multivariate chi-square and Rayleigh distributions under somewhat weaker conditions.     

A NOTE ON SAMPLING OVER TWO OCCASIONS1

Using simple random sampling without replacement (SRSWOR) on both occasions, a new scheme of selecting the unmatched part of the sample on second occasion is presented. The proposed estimate of the population mean has been shown to be more efficient than the estimate of Pathak and Rao (1967) for the same expected cost. Kulldorff's estimate as considered by Rao and Ghangurde (1969), however, remains superior to the proposed estimate.