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Type: Journal article
Title: Interaction: additivity plus nonlinearity?
Author: Hutchinson, T.
Citation: International Journal of Mathematical Education in Science and Technology (online), 2004; 35(4):531-537
Publisher: Taylor & Francis Ltd.
Issue Date: 2004
ISSN: 1464-5211
Statement of
T.P. Hutchinson
Abstract: Whether or not there is an interaction between two factors in their effects on a dependent variable is often a central question. This paper proposes a general mechanism by which an interaction may arise: (a) the two factors are the same thing — or, at least, have a dimension in common — in the sense that it is meaningful to add (or subtract) them; (b) the sum of them (or the difference between them) is what determines the dependent variable; and (c) the relation between the sum (or difference) and the dependent variable is nonlinear. For example, if several factors contribute to arousal in an additive manner, and the relationship of performance score to arousal is inverted-U, the factors will appear to interact in their joint effect on performance. Psychological, medical, and other scientists are likely to be unfamiliar with the (nonlinear) equations used to express this type of theory. Consequently, the task of promoting and interpreting such ideas will fall to the mathematician and statistician.
Keywords: Nonlinear theories; mathematical analysis; mathematical physics; calculus mathematics; evolution equations; nonlinear
Description: © Taylor & Francis
RMID: 0020065337
DOI: 10.1080/00207390410001703256
Appears in Collections:Centre for Automotive Safety Research publications

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