The principles of orthogonality and confounding in replicated experiments. (With Seven Text-figures.)

Abstract

The principle of orthogonality in replicated experiments is discussed and the dangers of non-orthogonality emphasised. The modifications necessary in the ordinary procedure of the analysis of variance when applied to non-orthogonal data are developed, attention being paid to the shorter methods, applicable in certain cases, by which the heavy labour of computation necessary in the general method of fitting constants may be avoided.Certain modifications in the design of replicated experiments, usually designated by the term confounding, are explained. The different types of confounding are discussed, together with their uses, and the appropriate methods of analysis are set out. The methods are applied to the analysis of an experiment on sugar beet (where a previous incorrect analysis is corrected) and an experiment on potatoes.