Significance Tests which May be Applied to Samples from any Populations: III. The Analysis of Variance Test

Pitman, E. J. G.

doi:10.2307/2332008

Cited by 84 publications

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“…A justification for using the tabular F test, which dates back to the work of Pitman (1937), andWelch (1937), is that the randomization distribution of the F statistic is close to the theoretical F distribution. Collier & Baker (1963) made a limited examination of the randomization distribution of F ratios with 4 sets of data.…”

Section: Origin Of Small Samplesmentioning

confidence: 99%

The Behaviour of Some Significance Tests Under Experimental Randomization

Kempthorne

Doerfler

1969

Biometrika

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARYFor the past 40 years, there has been confusion on the differences between tests of significance and tests of hypotheses to the point where data interpretation is presented as an accept-reject process. This paper discusses the case of inference for a simple experiment, the paired design. It gives a rationale of the significance tester, and proceeds to a comparison of three tests of significance which can be viewed as competitors in the case of this design. These are the sign test, S, the Wilcoxon test, W, and the Fisher randomization test, R. The conclusion is that there is indeed an ordering of the tests, which is R preferred to W preferred to S. The S test should never be used if the others are possible. An Appendix gives a proof of monotonicity of the R test with respect to a shift alternative. I5

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Section: Origin Of Small Samplesmentioning

confidence: 99%

The Behaviour of Some Significance Tests Under Experimental Randomization

Kempthorne

Doerfler

1969

Biometrika

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“…For the randomized block design, the results of the empirical studies of Eden & Yates (1933) and Kempthorne (1952, p. 152) support the theoretical conclusions of Welch (1937) and Pitman (1937) that, if the number of blocks and treatments are not both small and the within-block variance is homogeneous from block to block, the F-distribution forms an adequate approximation to the exact randomization distribution. Numerical evidence has also been supplied by Hack (1958), who obtained randomization distributions for F-ratios on yields from two-factor completely randomized agricultural experiments.…”

Section: Introductionmentioning

confidence: 57%

The Randomization Distribution of F-Ratios for the Splitplot Design-an Empirical Investigation

Collier¹,

Baker²

1963

Biometrika

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“…Eden and Yates (1933) carried out a simulation study that supported this conclusion. Wald and Wolfowitz (1944) proved a theorem that justifies the chi-squared approximation in the simple case discussed above, whereas Welch (1937) and Pitman (1938) presented results that supported, to some extent, the use of the F distribution to approximate the randomization distribution of MST jMSE in the case of randomized complete block designs and Latin squares. The matter is not a simple one [see Davis and Speed (1988) for some related calculations], and it seems fair to say that the assertion of Fisher quoted above has been shown to be a reasonable approximation to the truth, under certain conditions, for certain designs.…”

Section: Ie T Iecmentioning

confidence: 97%

Introduction to Fisher (1926) The Arrangement of Field Experiments

Speed

1992

Springer Series in Statistics

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In 1919, the Director of Rothamsted Experimental Station, Sir John Russell, invited Ronald Aylmer Fisher, a young mathematician with interests in evolution and genetics, to join the small group of scientists at Rothamsted in order that [see Russell (1966, p. 327)] "after studying our records he should tell me whether they were suitable for proper statistical examination and might be expected to yield more information than we had extracted." Fisher accepted the invitation and in a very short time Russell realized (loc. cit.) "that he was more than a man of great ability; he was in fact a genius who must be retained." In the few years that followed, Fisher introduced the subdivision of sums of squares now known as an analysis of variance (anova) table (1923), derived the exact distribution of the (log of the) ratio of two independent chi-squared variates (1924), introduced the principles of blocking and randomization, as well as the randomized block, Latin square, and split-plot experiments, the latter with two anova tables (1925), promoted factorial experiments, and foreshadowed the notion of confounding (1926). Of course Fisher made many contributions to theoretical statistics over this same period [see Fisher (1922)], but the above relate directly to the design and analysis of field experiments, the topic of the paper that follows. It was an incredibly productive period for Fisher, with his ideas quickly transforming agricultural experimentation in Great Britain and more widely, and in major respects these ideas have remained the statistical basis of agricultural experimentation to this day. Other fields of science and technology such as horticulture, manufacturing industry, and later psychology and education also adopted Fisher's statistical principles of experimentation, and again they continue to be regarded as fundamental today. S. Kotz et al. (eds.), Breakthroughs in Statistics © Springer-Verlag New York, Inc. 1992 72 T.P. SpeedThe story of Fisher and the design and analysis of experiments has been told many times before and at greater length than is possible here; see

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Significance Tests which May be Applied to Samples from any Populations: III. The Analysis of Variance Test

Cited by 84 publications

References 0 publications

The Behaviour of Some Significance Tests Under Experimental Randomization

The Behaviour of Some Significance Tests Under Experimental Randomization

The Randomization Distribution of F-Ratios for the Splitplot Design-an Empirical Investigation

Introduction to Fisher (1926) The Arrangement of Field Experiments

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