Simultaneous Absolute Scaling for Several Groups

Abstract

THE METHOD of absolute scaling was developed some years ago (ref. 1) as one solu tion to the problem of a mental unit of measure ment. The method defines the psychological scale of measurement to be such that the distri butions of ability for several age groups on that scale are normal in form. A check on whether such a definition is possible for a given s e t of data is made available, and a way of determin ing the parameters of the resulting scale is pro vided. The present paper is concerned with an alternative way of determining these same par ameters. The logic of absolute scaling is not difficult. If a scale of measurement exists such that the distributions for several age groups on i t are normal, then the location of any point on that scale can be expressed very simply in terms of its position in any one of these distributions. Let the point Xi have normal deviates Z^ in age group 1, Zi2 in age group 2, etc. Then