A statistical criterion to determine the group to which an individual belongs

Abstract

In a previous note, I have discussed the logical problems involved in the classification of an individual into one of two groups to which he can possibly belong. Some observations were the same as those given by Welch in an earlier note. The solution derived above was identical with the discriminant function proposed by Fisher for this purpose. The corresponding problem when the individual has to be specified as a member of one out of many groups to which he can possibly belong does not appear to have been tackled. The following solution, which comes out as an obvious extension of the discriminant function analysis, has been derived so as to satisfy a logical set of requirements.