Field experiments of factorial design

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Abstract
A recent paper by A. E. Brandt (1937) goes into the details of a type of design in field experimental procedure, where two or more factors are under examination, which has been much elaborated since 1928, when the first 2 × 2 × 2 experiment, involving two levels of each of three factors, nitrogen, potash and phosphate, was carried out at Woburn (Rothamst. Rep. 1927–8) with four-fold replication. Similar experiments, of the 3 × 2 × 2 type, had in fact been conducted at Rothamsted (Rep. 1925–6) two years earlier, but there was here the further complication that no differentiation was possible for two of the factors at one level (no manure) of the third. Details have been given by Fisher (1937) and Yates (1937) of, among others, experiments of the 2n and 3 × 2n types, and it may be said that the recent work has been in the direction of systematizing the lay-out and analysis of such experiments. Further features have been the device of confounding, which dates back to 1927 (Rothamst. Rep. 1927–8), i.e. it is almost contemporaneous with the first introduction by Fisher of randomized blocks and Latin square experiments, and the suggestion that replication may even be dispensed with entirely, a much more recent innovation. Confounding is a method of enlarging the number of blocks between which elimination of soil heterogeneity is possible by sacrificing information on certain of the higher-order interactions, which are considered unlikely to be real effects; with absence of replication an estimate of the experimental error is found by grouping together a number of these higher-order interactions.

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