Gertrude M. Cox

Experimental designs; a survey of types of experimental designs.

PLANNING a piece of research in any field involves a certain order of procedure. This will in general have three parts (1) a statement of the objectives, (2) a description of the experiment covering such points as the selection of experimental treatments, decision regarding accuracy of measurements, selecting the experimental units, determining the general condition under which the test shall be made and specifying the experimental design and (3) an outline of the method of the analysis of the results. Methods for increasing the accuracy of experiments may be classified into three types: (1) increasing the size of the experiment, (2) refining the technique and (3) handling the experimental material so that the effects of variability are reduced. This may be done by careful selection of the material, by taking additional measurements that provide information about the material or by skillful grouping of the experimental units into an efficient plan. Using the ideas of confounding and grouping of the experimental units as the criteria, the various types of experimental designs have been classified. The following types of designs were presented, illustrated and discussed: (1) Complete block designs including completely randomized, randomized blocks, latin square and cross-over designs. TABLE 1-ANALYSES OF FIELD EXPERIMENTS, 1942-1948. NORTH CAROLINA AGRICULTURAL EXPERIMENT STATION.

The Biometric Society, the first twenty-five years (1947-1972).

For this jubilee year of the Biometric Society, a 25-year anniversary report of its activities was requested. The object of this article is to give information about the Society, not only for historical reasons, but especially to give the younger members a brief report of the Societys activities and of the contributions to statistical literature that have been made by the papers in Biometrics. The historical and classical material contained in the 947 articles (from 1950 to and including 1971) make it desrable that every biometrician should possess a full set of the back issues of Biometrics. The Biometric Society has held 11 International Conferences and Symposia. However, the bulk of activities of the Society takes place in the Regions which hold meetings, thus enabling the influence of this Society to be worldwide. Many of the Regional meetings were co-sponsored by other statistical, biological, and scientific societies. Biometrics has become well established and recognized by 3,229 members and 2,135 other subscribers as of January 1, 1972. The Society still is in fair financial condition but with rising costs of printing and mailing, it will be necessary either to decrease the size of the Journal, or increase the number of members and subscribers, or raise the dues. The Regions and National Groups, their dates of becoming a part of the International Biometric Society, and the number of members for most of the years that records are available are given in Table 1. It is interesting to note that most of the larger regions reached a peak in 1967 to 1969 except Regiao Brasileira, Eastern North America, and the Osterreich-Schweiz Regions, which have increasing membership. It is the counteracting effect of these three regions plus the new Region and the new National Groups that enabled the membership increase of 102 from 1970 to 1971. The number of pages and number of articles per volume are given in Table 2. Volumes 6 to 27 (1950 to 1971) and the March 1972 issue have been used for this review and discussion, for it was in 1950 that the Biometric Society took over ownership of Biometrics.

The multiple factor theory in terms of common elements

With the mechanism of common elements we designed numerous sets of variates correlated with each other in a known manner and also correlated with the primary and specific factors in the same predetermined fashion. To the correlations from theoretical populations, and also from experimental samples, Thurstones centroid method of factoring was applied. The resulting centroid co-ordinates were rotated to yield the test vectors. These vectors were close approximations to the theoretical and sample correlations.

Methodology for estimating reliability

This paper sketches some of the work initiated in February, 1962 at the Research Triangle Institute to develop a methodology for estimating the reliability of complex electro-mechanical systems. As is true of many tasks in the reliability area, engineers, mathematicians, and statisticians have worked as a team to develop the methodology. Among the notable contributors has been Professor Harald Cram~r, who has participated on a part-time basis. Various disciplines have been drawn on, including mechanical, electrical, and systems engineering, the mathematics of stochastic processes, the statistical design of experiments, and general experimental statistics. The organization of this paper is as follows. Sections 2 through 5 are devoted to general concepts and methodology. The general concept of an element is introduced and possible modes of element behavior are discussed. This leads naturally to definitions of failure of an element and to the definition of reliability. Section 5 contains a discussion of how to estimate the reliability of a system, and briefly describes two studies which have been made of actual systems. One study is described in sufficient detail to bring out some of the statistical concepts involved, but none of the engineering mathematics is presented. Section 6 contains a brief summary of some of the research which has been conducted in the mathematical theory of stochastic processes. While developed in this instance in the reliability context, it will be readily recognized that these results have wide applicability. Section 7 describes the estimation of reliability from statistical distributions which are slowly changing with time.