A note on the effect of logarithmic transformation on the probability of misclassification
John J. Beauchamp, J.E. Folkert, D. S. Robson · Communication in Statistics- Theory and Methods · 1980
The probability of misclassifying an observation as coming from one of two populations, using the discriminant function, is evaluated for the case when it is known that the original observed random variables are lognormally distributed. The misclassification probabilities are evaluated under the incorrect assumption that the observed random variables are normally distributed and also evaluated after applying the appropriate log transformation. The difference between the corresponding probabilities of misclassification is used as a measure of the effectiveness of the transformation. Different combinations of the underlying population parameters are considered to allow for comparisons in terms of population separation and relative population abundance. The results are presented in graphical form and vividly show the effect of the correct use of a data transfomation.