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Detecting the interaction of quantity and quality: A study of Fisher's analysis
Author(s) -
Fick Gordon Hilton
Publication year - 1993
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315662
Subject(s) - factorial , mathematics , interaction , zero (linguistics) , factorial experiment , quality (philosophy) , parallelism (grammar) , class (philosophy) , statistics , exact test , fisher information , computer science , artificial intelligence , mathematical analysis , epistemology , linguistics , parallel computing , philosophy
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.