The Basic Contrasts of an Experimental Design with Special Reference to the Analysis of Data

Pearce, S. C.; Calinski, T.; Marshall, T. F. de C.

doi:10.2307/2334726

Cited by 4 publications

(8 citation statements)

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“…The process described by equation (4) is well known in the analysis of blocked experiments, where it was introduced by Kuiper [2]. A proof that Kuiper's iteration converges is given in Pearce et al [3] and an adaptation of that proof is given in the Appendix. The convergence of equation (4) depends on the eigenvalues oi(I-F), which are required to be in modulus less thanl.…”

Section: Murgatroyd's Proceduresmentioning

confidence: 99%

“…Estimating the parameters of this model by the method of least squares yields, for p (the estimate of p) [3], or Unfortunately these equations have no ready solution because of the singularity of F already noted. A solution is provided, however, by…”

Section: A Model For Examination Marksmentioning

confidence: 99%

“…The following demonstration of the convergence of Murgatroyd's procedure is taken from the proof of the convergence of Kuiper iteration given by Pearce et al [3].…”

Section: Appendixmentioning

confidence: 99%

“…These are to be compared in Murgatroyd's method with the averages in equation(2). Murgatroyd's initial adjustments are therefore at (0) = r~iAD'k~l'Dy ->-" 8 Ay(3) where<f> = (I-D'k~aD).Applying these adjustments, the vector of adjusted marksy (0) =y+A'a (0)is obtained. The vector of second adjustments is obtained by substituting y (0) for y in equation(3): = -»• ~8 A</> y ->-~~8 A(j> A'a (0) Similarly, the third adjustments are x i2) =Q-r and so on.…”

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confidence: 99%

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A note on combining marks from several examination papers

Charlton¹

1979

International Journal of Mathematical Education in Science and

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Section: Murgatroyd's Proceduresmentioning

confidence: 99%

Section: A Model For Examination Marksmentioning

confidence: 99%

“…The following demonstration of the convergence of Murgatroyd's procedure is taken from the proof of the convergence of Kuiper iteration given by Pearce et al [3].…”

Section: Appendixmentioning

confidence: 99%

mentioning

confidence: 99%

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A note on combining marks from several examination papers

Charlton¹

1979

International Journal of Mathematical Education in Science and

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“…one with two crossing systems of blocks. The best known is, of course, the Latin square, which would have been impossible here, but many other such designs exist (Freeman, 1975;Pearce, 1963Pearce, , 1975 and could Table 4. Start of the calculations needed for the analysis of the data in Table 1 perhaps have been used.…”

Section: Use Of a Row-and-column Designmentioning

confidence: 99%

The Conduct of ‘Post-Mortems’ on Concluded Field Trials

Pearce

1976

Ex. Agric.

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The design of field trials sometimes raises queries (which often go unanswered) about alternative designs and the best ways of allowing for environmental variation in the area allotted to the experiment. It is shown how recent developments in iterative methods for working out analyses of variance make possible the determination of error for systems of blocks other than the one actually used, and also for the row-and-column case. Some suggestions are also made for judging the error to be expected if plots were made larger.An experimenter starting work on an unfamiliar crop is often at a loss in deciding the size and shape of plots, the number of replications needed and much else that relates to field technique. It is true that data from a uniformity trial would be a help, but he would not wish to divert energies from his main task to obtain some, nor could he usually delay starting till such guidance was available. Although the crop may be new to him there is probably experience of it elsewhere, but even that can be misleading if conditions are different. Moreover, a survey of errors from past experiments needs care in interpretation, because investigators adapt methods to problems. Thus, in variable conditions they tend to use a large number of small plots, but to be content with a smaller number of larger ones when environmental variation is less, so that a survey might even suggest that large plots control local differences better than small ones, which is contrary to experience. In practice the experimenter is likely to conduct his first trials in any convenient manner that seems reasonable, but with a readiness to modify his methods in the light of experience. In this paper some statistical techniques are presented that could help him since, by their use, it is possible to re-analyse data to discover what error would have been encountered had the experiment been designed differently in the first place.It should be emphasized that it is always wrong to analyse and re-analyse data until something appears that can be declared 'significant'. In the present instance it is also likely to be ineffective. If an agronomist has 25 plots, arranged five by five, and he runs his blocks north and south, his randomization of five treatments will usually be such that each block contains each treatment once. If he then enquires what would have happened if he had taken his blocks east and west, he is at the mercy of the randomization that was actually adopted, which will almost certainly give a poor design for the alternative set of blocks. However, that is to mistake the problem. In the methods to be described the intention is not the usual one of isolating the effects of treatments so that they can be studied, but of eliminating them to disclose the underlying pattern of error.

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A Conversation with Professor Tadeusz Caliński

Atkinson¹,

Bogacka²

2015

Statist. Sci.

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Tadeusz Caliński was born in Poznań, Poland in 1928. Despite the absence of formal secondary eduction for Poles during the Second World War, he entered the University of Poznań in 1948, initially studying agronomy and in later years mathematics. From 1953 to 1988 he taught statistics, biometry and experimental design at the Agricultural University of Poznań. During this period he founded and developed the Poznań inter-university school of mathematical statistics and biometry, which has become one of the most important schools of this type in Poland and beyond. He has supervised 24 Ph.D. students, many of whom are currently professors at a variety of universities. He is now Professor Emeritus. Among many awards, in 1995 Professor Caliński received the Order of Polonia Restituta for his outstanding achievements in the fields of Education and Science. In 2012 the Polish Statistical Society awarded him The Jerzy Sp lawa-Neyman Medal for his contribution to the development of research in statistics in Poland. Professor Caliński in addition has Doctoral Degrees honoris causa from the Agricultural University of Poznań and the Warsaw University of Life Sciences.His research interests include mathematical statistics and biometry, with applications to agriculture, natural sciences, biology and genetics. He has published over 140 articles in scientific journals as well as, with Sanpei Kageyama, two important books on the randomization approach to the design and analysis of experiments.He has been extremely active and successful in initiating and contributing to fruitful international research cooperation between Polish statisticians and biometricians and their colleagues in various countries, particularly in the Netherlands, France, Italy, Great Britain, Germany, Japan and Portugal. The conversations in addition cover the history of biometry and experimental design in Poland and the early influence of British statisticians.

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The Basic Contrasts of an Experimental Design with Special Reference to the Analysis of Data

Cited by 4 publications

References 4 publications

A note on combining marks from several examination papers

A note on combining marks from several examination papers

The Conduct of ‘Post-Mortems’ on Concluded Field Trials

A Conversation with Professor Tadeusz Caliński

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