Assumptions of ANOVA

The valid use of analysis of variance as a tool of statistical inference are a set of fundamental assumptions. We refer to the paper of Eisenhart. Although an experimenter must not expert to find all the assumptions met to perfection, it is important that the user of analysis variance techniques be aware of the underlying assumptions and be able to recognize when they are substanially unsatisfied.The consequences of the failure to meet the assumptions are discussed by Cochran in a companion paper to that of Eisenhart. Because experiments in which all the assumptions are perfectly met are rare, Cochran suggests that ANOVA results be considered as approximate rather than exact. These assumptions are pointed out at appropriate points in the following.
We discuss ANOVA as it is used to analyze the results of two different experimental designs, the completely randomized and the randomized complete  block design. In addition to these , the concept of a factorial experiment is given through its use in a completely randomized design. These do not exhaust the possibilities.