On bias in magnitude scaling and some conjectures of Stevens

Bias in magnitude scaling can be viewed as involving deviations of judgments from proportionality. A model of bias is shown to provide a theoretical basis for Stevens's conjecture about geometrically averaging magnitude estimation and magnitude production exponents in order to obtain an estimate of the psychophysical exponent. An overlooked result is that one can also obtain an estimate of the magnitude of the bias. Examples from several well-known studies are presented. The bias is also shown to vary in response to experimental manipulation of the stimulus range. Aspects of predicting exponents across experiments are clarified, and a new prediction is examined. The model of bias fills some theoretical gaps in magnitude scaling and clarifies underlying assumptions and predictions.