Journal ArticleDOI
Multiple range and multiple f tests
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This article is published in Biometrics.The article was published on 1955-03-01. It has received 22988 citations till now. The article focuses on the topics: Range (statistics).read more
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Statistical Principles in Experimental Design
TL;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.
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Statistical Principles in Experimental Design
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.
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Extension of multiple range tests to group means with unequal numbers of replications
Abstract: In many fields of research, one is faced with the task of comparing the effects of treatments which have been replicated unequally. This happens for a number of reasons. In an experiment on animals, some may get sick and have to be removed from the experiment. In some experiments, the amount of material available for certain treatments may not be as much as for other treatments. If the experimenter has specified orthogonal contrasts that he is interested in before he runs the experiment, one can test the various treatment effects by an F-test after the treatment sum of squares has been partitioned into individual degrees of freedom for each orthogonal contrast. If the experimenter has not specified orthogonal contrasts, one is faced with the problem of deciding which treatments are significantly different. Several writers, including Duncan, Keuls, Newman, and Tukey, have developed multiple range tests to show differences among treatments that have been replicated the same number of times and when nothing was specified concerning the treatments. Duncan [1] compares the above methods and gives citations. This extension to unequal numbers of replications will be exemplified with reference to Duncan's "New Multiple Range Test," but is applicable to any of the above writers' tests; all one has to do is use their tabled ranges. In Duncan's test for an equal number of replications, the difference between any two ranked means is significant if the difference exceeds a shortest significant range. This shortest significant range is designated by R, and is obtained by multiplying the standard error of a mean, s,, by a given value, zn2, obtained from a table of significant studentized ranges which Duncan has tabled for both the 5% and 1% test. In Duncan's terminology, n2 is the degrees of freedom of the error mean square and p = 1, 2, * *, t is the number of means concerned. Consider an experiment with five treatments, A, B. C, D, and E, each replicated n times. Suppose on ranking the means from low to high one obtains
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A Cluster Analysis Method for Grouping Means in the Analysis of Variance
A. J. Scott,M. Knott +1 more
TL;DR: In this paper, the authors used the techniques of cluster analysis to split the treatments into reasonably homogeneous groups and developed a likelihood ratio test for judging the significance of differences among the resulting groups.
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Antioxidant activity of various tea extracts in relation to their antimutagenicity
Gow-Chin Yen,Hui-Yin Chen +1 more
TL;DR: The relationship between antioxidant activity and antimutagenicity of various tea extracts (green tea, pouchong tea, oolong tea and black tea) was investigated in this article, which showed that all tea extracts exhibited markedly antioxidant activity.
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Journal ArticleDOI
Comparing individual means in the analysis of variance.
TL;DR: A simple and definite procedure is proposed for dividing treatments into distinguishable groups, and for determining that the treatments within some of these groups are different, although there is not enough evidence to say "which is which."
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The use of the „studentized range” in connection with an analysis of variance
TL;DR: The method indicated in this article diverges from those discussed by Newman andTukey and is I suppose the more plausible.