Comparing Ratios: The Logarithmic Response Bias Revisited

Abstract

A ratio is often used to compare the magnitudes of two related variables and can form an important basis for judgments and decisions as in financial ratio analysis in accounting. However, in psychophysics research shows that ratio judgments of sensory stimuli can produce a logarithmic response bias wherein subjects do not respond to differences in the ratio components but to differences in the relative magnitudes of the resulting ratios. Subjects were required to predict the results of basketball matches when supplied summary information regarding each team's performance. Those subjects who received this information as ratios of wins to losses produced predictions with margins consistent with the logarithmic response bias. Each subject's awareness of or sensitivity to the logarithmic response bias was evaluated from his preferences for various methods of presenting such summary information, including the ratios used in the present study. The ratios which produced the response bias were deemed acceptable although less preferable methods, and these ratings were independent of previous experience with comparisons of such ratios. The results of this study highlight the problems associated with comparing ratios, and the lack of awareness individuals have of such problems.

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