Effects of Response Method on Error and Cyclical Bias in Proportion Judgments

Abstract

The cyclical power model accounts for multi-cycle patterns of bias commonly observed in proportion judgments by proposing the use of intermediate reference points (Hollands & Dyre, 2000). We were interested in the effect of response method on the choice of reference points (fewer points lead to greater judgment error). Participants made estimates of proportions displayed in pie charts using one of three response methods: rotation of a dial, marker placement on a horizontal line, or a numerical estimate. Fitting the model indicated a two-cycle pattern for line and numeric conditions, but a four-cycle pattern for the dial, leading to reduced error. Response method did not affect the estimated value of the Stevens exponent (0.83 on average). Competing explanations of stimulus-response compatibility and response method are considered. Implications for the design of display and control systems are discussed.