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Weiss [5] and Freeman and Weiss [2] have shown how to construct sampling plans which at least approximately minimize the maximum expected sample size in the case of Bernoulli and Normal populations. In this paper we construct sequential procedures of this type for the testing of an exponential parameter. An invariance property of the stepping region is presented which simplifies the construction of the Bayes regions. Several sampling plans are given and some of their properties are obtained, [ABSTRACT FROM AUTHOR]

This paper deals with a multivariate extension of Friedman's chi[sup 2, sub tau]-test. A rank permutation distribution and the large sample properties of the criterion are studied. The asymptotic relative efficiency (A.R.E.) for a sequence of translation alternatives is studied and bounds are given for certain special cases. It is shown that, under specified conditions, the A.R.E. of this test with respect to the likelihood ratio test is largest, when the block dispersion matrices differ and can be greater than unity when the differences are large. [ABSTRACT FROM AUTHOR]

The purpose of this paper is the presentation of formulae for obtaining matrix derivatives of the second order to use in making tests for maxima and minima. The theory of such second order derivatives is presented. These formulae require the rearrangment of the parameter elements in vector form and the transformed results feature Kronecker products, which have certain desirable properties. Application is made to several types of problems. [ABSTRACT FROM AUTHOR]

In this paper the first two moments of the Statistic (treatment sum of squares)/(treatment +error sums of squares) over all possible random assignments of treatments to the experimental plots are obtained for two associate PBIB designs. They are compared with the corresponding moments of a central beta distribution to study the extent to which the normal theory test may serve as an approximation to the randomization test. It is found that the approximation is reasonable for some classes of PBIB designs. [ABSTRACT FROM AUTHOR]

This paper uses a family of bivariate extreme-value distributions to estimate the probability of a large exceedance of a random variable given that a certain other random variable not independent of the first has exceeded a certain value. A simple method of reasonably good efficiency is given for estimating a bivariate extreme-value distribution from independent bivariate samples. The method is used to analyze the performance of a spacecraft command receiver which has an indication of data quality so that commands likely to be in error can be rejected. [ABSTRACT FROM AUTHOR]

Data editing by a computer program can be regarded as a form of statistical quality control. In that perspective, costs and benefits of alternative programs can be compared to one another and, of course, to no control plan at all. This paper outlines one approach to cost-benefit comparison and utilizes a realistic example to suggest that computerized data editing is generally superior to clerical editing. It also warns against edit programs which provide for record rejections and off-line review. Most importantly, it urges that a systematic comparison of costs can assist significantly in edit planning. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to illustrate a "give and take" type of interaction between the frequentist theory of probability and statistics, on the one hand, and research in science, on the other. Invariably, research in science involves some observations x and the unknown "true" state of nature sigma. Quite often, replication of the experiments reveals considerable variation in x, indicating that no mathematical treatment of the problem is possible without the assumption that x is a sample value of a random variable X, treated in terms of frequentist theory of probability. As to the true state of nature, sigma, situations vary. Indeed, there are cases where it appears natural to consider that sigma is selected at random out of a certain known set SIGMA, with either known or unknown probability law. Section 2 lists three typical examples in which the frequentist theory of probability can "give" something to science. In each example, however, the assumption of the randomness of sigma appears extraneous. Section 3 describes another example of research in science, again with a non-random sigma, which happened to "give" something to the frequentist theory of statistics. The motivation to reduce the frequency of erroneous conclusions in the general circumstances of the biological study had led to considering the possibility that a certain derivative may fail to exist. This created a problem of testing (Section 4) which does not appear to have been considered. A solution of the problem, in the form of optimal symmetric (C alpha) tests, is given in Section 5. [ABSTRACT FROM AUTHOR]

Abstract Given a population of N units, it is required to draw a sample of n distinct units in such a way that the probability pi[sub i], (i = 1, ..., N) for the ith unit to be in the sample is proportional to its 'size' x[sub i]. One way to achieve this is as follows: The N units in the population are listed in a random order and their x[sub i] are cumulated and a systematic selection of n elements from a "random start" is then made on the cumulation. The mathematical theory associated with this procedure has been presented in [1], where with the help of asymptotic theory, compact expressions for the variance of the estimate of the population total are derived. These expressions contain probabilities P[sub ii]'(i not equal to i'; i, i' = 1, ... , N) that units i and i' both are in the sample. For n = 2, N = 3 and n = 2, N = 4, exact formulae are derived in [1], but for other n and N only approximate formulae are obtained. It is the purpose of this paper to derive an exact formula for P[sub ii]' for any values of n and N. The argument makes use of the solution given in [1] for the case n = 2 and N = 4. The new formula for n = 2 is derived in Section 1 and illustrated in Section 2 by a numerical example for N = 10. An exact formula for general n is derived in Section 3 and examplified in Section 4. [ABSTRACT FROM AUTHOR]

This paper presents a simple method for increasing the limiting Pitman efficiency of rank tests relative to the best tests for samples normal distributions without using complicated scoring systems. Our proposal is to select two numbers p and r (0 < p, r < 1) and then score, with integer weights, the data in the top p[sup th] and bottom r[sup th] fractions of the combined sample. The percentile modified tests for scale are quite effective. When p = r = 1/8 (i.e., we score only the extreme quarter of the combined sample) the A.R.E. of the test to the F test is .85. [ABSTRACT FROM AUTHOR]

A model is described which leads to an analysis of data on the sequence of sexes in human families, particular attention being given to the detection of a correlation between the sexes of adjacent sibs. Three sources of potential confounding with this correlation are discussed. The method of analysis avoids any confounding with the effects of voluntary limitation of family size, or with the effects of variation in the probability of a male from birth to birth within a family. It is more difficult to separate the effect of correlation between the sexes of adjacent sibs from the effect of variation between families in the probability that a child born to the family will be male. The problem was solved in the present investigation by using an auxiliary analysis to show that families did not, in fact, differ in this probability. If this were not so, a separation of the two factors could still have been made by an additional analysis referred to in the paper. [ABSTRACT FROM AUTHOR]

The presents comments of the author on the article "A Memorial for William N. Hurwitz." At the memorial session which was called as a tribute to William N. Hurwitz, we have had presented three papers which summarize the outstanding work that has been and is being done by the Bureau of the Census in the area of sample surveys. The work emanating from the Census Bureau has had a profound effect upon the entire field of survey methodology. The sampling philosophies and procedures that have been developed in the Bureau have been emulated by private research companies here and abroad, by university research bureaus, by state and local governments, by other federal agencies and by foreign governments. Papers we have heard this evening give us the answer from the technical point of view. One paper deals mainly with the philosophical aspects of the role of sampling and the scientific nature of the entire process. Another one traced the development of sampling at the Census from the role of theory to that of practice. We see the evolution of concern from pure sampling and statistical error to other types of errors, such as coding errors, enumerator error and response error and we have seen how the Bureau has been able to cope with these in the design of a sample survey.