Simpson's reversal paradox and cost allocation

Abstract

Allocation of indirect costs among products sometimes yields a paradoxical result that unit cost for each product may increase under one method of allocation and may decrease for each product under another method. The Stalcup Paper Company case illustrate such behaviour of costs at the same, time, provides an accounting example of Simpon's Reversal Paradox Simpson (1951), which Blyth (1972) discussed in the statistics literature. As with other paradoxes, this cost allocation paradox disappears upon closer scrutiny. This paper examines the properties of allocated costs in order to arrive at an intuitive understanding of the results. The relationship of the cost allocation problem to Simpson's Paradox and the implications of the analysis for cost control are briefly discussed.