| Abstract: | In Sections 49 and 50 of the Design of Experiments, Fisher discusses an experiment designed to compare the effects of several types of manure on yield. Each type of manure is applied at three dosage levels: zero, single, and double doses. Fisher points out that the usual contrasts constructed for a factorial experiment are unsatisfactory in this setting. In particular, since the response curves necessarily meet at the zero dose, the usual notion of interaction as a lack of parallelism cannot apply. Fisher then gives an appropriate definition for interaction in this setting. This paper is concerned with a class of orthogonal polynomials that can be used as an aid in the detection of this modified definition of interaction. |
