AN ANALYSIS OF TRANSFORMATIONS.
Technical rept. no. 26,
WISCONSIN UNIV MADISON
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In the analysis of data it is often assumed that observations y1, y2, . . . , y sub n are independently normally distributed with constant variance and with expectations specified by a model linear in a set of parameters theta. In this paper the less restrictive assumption is made that such a normal, homoscedastic, linear model is appropriate after some suitable transformation has been applied to the ys. Inferences about the transformation and about the parameters of the linear model are made by computing the likelihood function and the relevant posterior distribution. The contributions of normality, homoscedasticity and additivity to the transformation are separated. The relation of the present methods to earlier procedures for finding transformations is discussed. The methods are illustrated with examples. Author