Data-analysis in agricultural experimentation .1. Contrasts of interest

An experiment has its origin in the need to find answers to stated questions. From the start great care is given to its correct conduct (e.g. the application of treatments and the method of recording) as well as to statistical design, always with the original questions in mind. The analysis of its data is the climax of a long process and the questions to be answered must dominate all else. It is not enough to feed data into a computer package in the hope that it will provide an automated path to a true interpretation. Where the treatments have been chosen with care to answer specific questions, the statistical way of designating purpose is to declare 'contrasts of interest', each corresponding to a degree of freedom between treatments. They derive solely from the reasoning behind the selection of treatments. If possible the questions posed should be equal in number to the degrees of freedom and should admit of separate study because no one can give a single answer to several diverse questions. This paper shows how to define a contrast of interest and how to isolate it in the analysis of variance. Attention is given both to its contribution to the treatment sum of squares and to its variance (i.e. the precision with which it is estimated). Independence of estimation is also considered. Algebraic formulae are given for a restricted through important range of designs, which includes those that are completely randomized, in randomized blocks or in Latin squares, all treatments having the same replication. The methods can, however, be generalized to cover all designs. With these formulae it is possible both to test the existence of an interesting effect and to set confidence limits round its estimated value.