Generalizing the Sensitivity Conditions in an Overall Index of Product Quality

Abstract

The issue of the sensitivity of weighted linear composites to attribute-importance weights has attracted researchers from various disciplines, including marketing, psychology, and statistics. At issue is how sensitive a weighted scale is to a particular choice of weights. Scale sensitivity is defined by a negative correlation between two scales. By considering the general case of n attributes and using an algebraic approach, we specify the precise sufficiency conditions under which two scales will correlate negatively and thus be sensitive to the weights chosen. These sensitivity conditions are derived in the context of the computation of an overall product-quality scale, which is simply a special case of the general multiattribute problem. We illustrate these conditions for the case of two quality scales using examples from Test (from 1983), a German magazine similar to Consumer Reports , and from Places Rated Almanac (from 1987).