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

Abstract

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.

Principes d'Experimentation.

“…En particulier, les résidus d'une analyse de la variance peuventêtre traités comme des résultats d'expériences d'uniformité ( § 3.5, 3.6 et 6.4) [Hatheway et Williams, 1958 ;Koch et Rigney, 1951]. L'étude approfondie des résidus peutêtre considérée comme constituant une réelle autopsie 33 de l'expérience, et peut contribuer notamment aux prises de décision en matière de données aberrantes [Pearce, 1976c ;Sudduth et Drummond, 2007].…”

Block Size and Orientation, and Allowance for Positional Effects, in Field Experiments

“…Similarly, many special analyses can be used to compensate for ineffective blocking, e.g. Pearce (1976Pearce ( , 1980 and Kirk (1980). The difficulty is learning when to choose designs using small blocks and when to use these special analyses.…”

The Importance of Lay-out in Determining Error Variance in Field Experiments

“…As is usual when data are analysed in a design other than that used, treatment and site variables are no longer orthogonal and the simple method of analysis appropriate to the original design cannot be used. Pearce (1976) presented an iterative method of estimating the error variance that would have been expected had the blocking been changed. Here, the analysis is obtained by fitting a linear statistical model to the data by least squares.…”