The Logarithmic Transformation

Abstract

IN a recent communication, Dr. H. V. Musham¹ directs attention to the fact that a logarithmic transformation of a variable may not only make the distribution more normal but will often stabilize the standard deviation, that is, make it more or less independent of the mean in those cases where the standard deviation of the original variable is roughly proportional to the mean. He is, perhaps, mistaken when he suggests that the latter effect has not previously been appreciated. In cases where the logarithmic transformation is used as a preparatory step to an analysis of variance, its main purpose is to ensure that the standard deviation, as calculated from a residual sum of squares, shall be applicable to the various ‘treatment’ means, even when these differ considerably from each other. The lack of normality of the distribution of the residual error is not in itself of any great practical consequence.