Advanced Statistical Methods in Biometric Research.
About: This article is published in Journal of the American Statistical Association.The article was published on 1953-09-01. It has received 1532 citations till now.
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TL;DR: This chapter discusses design and analysis of single-Factor Experiments: Completely Randomized Design and Factorial Experiments in which Some of the Interactions are Confounded.
24,665 citations
TL;DR: In this paper, a method of estimating the parameters of a set of regression equations is reported which involves application of Aitken's generalized least-squares to the whole system of equations.
Abstract: In this paper a method of estimating the parameters of a set of regression equations is reported which involves application of Aitken's generalized least-squares [1] to the whole system of equations. Under conditions generally encountered in practice, it is found that the regression coefficient estimators so obtained are at least asymptotically more efficient than those obtained by an equation-by-equation application of least squares. This gain in efficiency can be quite large if “independent” variables in different equations are not highly correlated and if disturbance terms in different equations are highly correlated. Further, tests of the hypothesis that all regression equation coefficient vectors are equal, based on “micro” and “macro” data, are described. If this hypothesis is accepted, there will be no aggregation bias. Finally, the estimation procedure and the “micro-test” for aggregation bias are applied in the analysis of annual investment data, 1935–1954, for two firms.
7,637 citations
TL;DR: It is suggested that if Guttman's latent-root-one lower bound estimate for the rank of a correlation matrix is accepted as a psychometric upper bound, then the rank for a sample matrix should be estimated by subtracting out the component in the latent roots which can be attributed to sampling error.
Abstract: It is suggested that if Guttman's latent-root-one lower bound estimate for the rank of a correlation matrix is accepted as a psychometric upper bound, following the proofs and arguments of Kaiser and Dickman, then the rank for a sample matrix should be estimated by subtracting out the component in the latent roots which can be attributed to sampling error, and least-squares “capitalization” on this error, in the calculation of the correlations and the roots. A procedure based on the generation of random variables is given for estimating the component which needs to be subtracted.
6,722 citations
6,456 citations
TL;DR: A method for identifying clusters of points in a multidimensional Euclidean space is described and its application to taxonomy considered and an informal indicator of the "best number" of clusters is suggested.
Abstract: A method for identifying clusters of points in a multidimensional Euclidean space is described and its application to taxonomy considered. It reconciles, in a sense, two different approaches to the investigation of the spatial relationships between the points, viz., the agglomerative and the divisive methods. A graph, the shortest dendrite of Florek etal. (1951a), is constructed on a nearest neighbour basis and then divided into clusters by applying the criterion of minimum within cluster sum of squares. This procedure ensures an effective reduction of the number of possible splits. The method may be applied to a dichotomous division, but is perfectly suitable also for a global division into any number of clusters. An informal indicator of the "best number" of clusters is suggested. It is a"variance ratio criterion" giving some insight into the structure of the points. The method is illustrated by three examples, one of which is original. The results obtained by the dendrite method are compared with those...
5,772 citations
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01 Jan 1962TL;DR: In this article, the authors introduce the principles of estimation and inference: means and variance, means and variations, and means and variance of estimators and inferors, and the analysis of factorial experiments having repeated measures on the same element.
Abstract: CHAPTER 1: Introduction to Design CHAPTER 2: Principles of Estimation and Inference: Means and Variance CHAPTER 3: Design and Analysis of Single-Factor Experiments: Completely Randomized Design CHAPTER 4: Single-Factor Experiments Having Repeated Measures on the Same Element CHAPTER 5: Design and Analysis of Factorial Experiments: Completely-Randomized Design CHAPTER 6: Factorial Experiments: Computational Procedures and Numerical Example CHAPTER 7: Multifactor Experiments Having Repeated Measures on the Same Element CHAPTER 8: Factorial Experiments in which Some of the Interactions are Confounded CHAPTER 9: Latin Squares and Related Designs CHAPTER 10: Analysis of Covariance
25,607 citations
TL;DR: It is suggested that if Guttman's latent-root-one lower bound estimate for the rank of a correlation matrix is accepted as a psychometric upper bound, then the rank for a sample matrix should be estimated by subtracting out the component in the latent roots which can be attributed to sampling error.
Abstract: It is suggested that if Guttman's latent-root-one lower bound estimate for the rank of a correlation matrix is accepted as a psychometric upper bound, following the proofs and arguments of Kaiser and Dickman, then the rank for a sample matrix should be estimated by subtracting out the component in the latent roots which can be attributed to sampling error, and least-squares “capitalization” on this error, in the calculation of the correlations and the roots. A procedure based on the generation of random variables is given for estimating the component which needs to be subtracted.
6,722 citations
6,456 citations
TL;DR: A method for identifying clusters of points in a multidimensional Euclidean space is described and its application to taxonomy considered and an informal indicator of the "best number" of clusters is suggested.
Abstract: A method for identifying clusters of points in a multidimensional Euclidean space is described and its application to taxonomy considered. It reconciles, in a sense, two different approaches to the investigation of the spatial relationships between the points, viz., the agglomerative and the divisive methods. A graph, the shortest dendrite of Florek etal. (1951a), is constructed on a nearest neighbour basis and then divided into clusters by applying the criterion of minimum within cluster sum of squares. This procedure ensures an effective reduction of the number of possible splits. The method may be applied to a dichotomous division, but is perfectly suitable also for a global division into any number of clusters. An informal indicator of the "best number" of clusters is suggested. It is a"variance ratio criterion" giving some insight into the structure of the points. The method is illustrated by three examples, one of which is original. The results obtained by the dendrite method are compared with those...
5,772 citations
TL;DR: In this article, an approximate procedure based on classical analysis of variance is presented, including an adjustment to the degrees of freedom resulting in conservative F tests, which can be applied to the case where the variance covariance matrices differ from group to group.
Abstract: This paper is concerned with methods for analyzing quantitative, non-categorical profile data, e.g., a battery of tests given to individuals in one or more groups. It is assumed that the variables have a multinormal distribution with an arbitrary variance-covariance matrix. Approximate procedures based on classical analysis of variance are presented, including an adjustment to the degrees of freedom resulting in conservativeF tests. These can be applied to the case where the variance-covariance matrices differ from group to group. In addition, exact generalized multivariate analysis methods are discussed. Examples are given illustrating both techniques.
4,638 citations