Analysis of variance and regression. Design of experiments

The engineer is often faced with a question of considerable practical importance: "Does this or that factor influence the measurement result? More precisely, such questions might be: "Does such-and-such an impurity affect the mechanical characteristics of such-and-such a material?" or: "Do all operators operating such-and-such a large piece of equipment in shift work actually achieve the same result, the same quality?" or: "Does such-and-such a parameter, which we have good physical reasons for believing to be important, actually influence the measurement results?".

The preferred tool for this type of study is analysis of variance.

We'll look first at single-entry lavariance analysis (§ 2 and 3 ), where we're trying to determine the influence of a single factor, then at double-entry lavariance analysis (§ 4 and 5