On the Analysis of Response Curve Data

Abstract

Experimenters often make several observations on a given experimental unit. If these observations can be associated with some continuous variable, such as t)ime or temperature, they collectively form a curve. Wishart (1938) first recommended that a general regression model be fitted to each curve and that the effects of the experimental treatments be evaluated by analyzing the coefficients in the model. Univariate (Box, 1950) and multivariate analysis of variance (Cole and Grizzle, 1966) and principal component analysis (Church, 1966) are other techniques for the analysis of response curves. A discussion of these methods is presented and a new model, which combines the univariate analysis of variance and principal component analysis, is developed. This model overcomes some of the inadequacies of the available procedures and gives results which are easy to understand and interpret. Examples are presented which compare the various methods of analysis and illustrate the usefulness of this new model.