On Analysis of Variance Test

The technique of analysis of variance is a powerful statistical tool in tracing the sources of variation of an observed random variable to different assignable causes. But the ease of calculations and the readily available F-test have made possible its somewhat uncritical applications in some cases. As a test of significance it should, however, derive its justification from the measure of control · it might effect over errors of different types involved ; and this has to be realised all the more because this test very often precedes any detailed analysis of the results. As for example, in judging the differences between the yields of a number of varieties of any particular crop, say rice, first of all we apply a comprehensive F-test embracing all the varieties simultaneously, and only when this comes out to be significant we proceed to analyse the individual differencesi. Hence there is the need of investigating whether the commonly applied F-test takes adequate account of the individual differences and whether any alternative procedure might appear to be better in particular situations. In this article we study the differeut properties of the F-test which point out its merits and demerits f . cm the point of view of errors of the first and second kind and v. hich also wggest a useful modification of the analysis of variance procedure for certain types of problems. For this purpose we will consider throughout the following simpler formulation (i.e. canonical form) of the problem, and at the