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The Making of Tests for Indices

A. Vogt
Journal / Anthology

Universität Bern Volkswirtschäftliches Institut preprint
Year: 1991

Starting point of the present paper is the concept of "antitheses of indices" by Fisher (1922). Fisher introduced for each price index its "time antithesis" and its "factor antithesis". His famous two "great reversal tests" state that an index should be equal to its antithesis. It can be shown that his two antitheses together with the identity and the "simultaneous time and factor antithesis" form a group of four elements (Vogt 1987). In Vogt (1989) this group is enlarged to one of eight elements. Here these eight antitheses are finally completed to "Fisher's group of sixteen antitheses". This would have been hard work without a software allowing symbolic calculation like Mathematica. Using Mathematica it was easy to find out the sixteen antitheses forming a group which we call "Fisher's antitheses group". Already Fisher (1922) expressed symmetries when dealing with his reversal tests. Groups measure symmetry as numbers measure size (Armstrong 1988). Therefore it is not astonishing that a treatment of the reversal test yields to group theoretical results. It can be proved that Fisher's index which he called the "ideal" one is the only index fulfilling all the sixteen tests which are coordinated to the sixteen antitheses. Thus, we have another justification for the attribute "idea" which Fisher gave to his index.

*Business and Economics