Bias effects on magnitude and ratio estimation power function exponents

Abstract

A bias'model of relative judgment was used to derive a ratio estimation (HE) power function, and its effectiveness in providing estimates of exponents free of the effects of standards was eval uated. The RE bias model was compared with the simple RE power function that ignores bias. Results showed that when bias was not taken into account, estimates of exponents exhibited the usual effects of standards observed in previous research. However, the introduction of bias parameters into the RE power function virtually eliminated these effects. Exponents calculated from "equal-range segments" (e.g., low stimulus range vs. high stimulus range) judged by magnitude estimation (ME) were examined: the effects of equal-range segments on exponents were much stronger for ME than standards were for RE, using the bias model. 221The power function (S. S. Stevens, 1957), based on ratio scaling methods, appears to be firmly established as a psychophysical law. Yet context effects on the exponent of the power function are ubiquitous-depending, for example, on scaling method, range and spacing of stimuli, standard and modulus, and sequence of stimuli (Poulton, 1968(Poulton, , 1979. In addition, there are numerous reports of large individual differences in exponents for the same modality (e.g., Marks & Cain, 1972S. S. Stevens's concern with the effect of the standard on the exponent led to his adoption of the "no-standard" procedure (see S. S. Stevens, 1956, and 1975, p. 27). Marks (1974b) also sees little reason to use a standard in magnitude estimation experiments, and Cross (1982) views "current practice" among psychophysicists as imposing minimal constraints on the scaling task. This position would be more convincing if magnitude estimation without a standard were free of context effects, but such is not the case. For example, range and sequence effects are present for magnitude estimation with or without a standard (Poulton, 1968(Poulton, , 1979. R. Teghtsoonian and M. Teghtsoonian (1978) reported that, for both loudness and distance judgments, intramodal range exerts a systematic effect on the exponent, which results from magnitude estimation without a standard; and Cross (1973) reported sequential dependencies in magnitude estimation of loudness, without a standard or modulus.It is argued by many investigators, including the present authors, that an adequate theory of psychophysics must This research was supported in part by Public Health Service Grant 5ROI MH 20449-06. This paper has benefited considerably from critical suggestions by M. Teghtsoonian, as Action Editor, and two anonymous reviewers. Robert Pokorny is now at Brooks Air Force Base, AFHRL/MOD, San Antonio, TX 78235-2601. Requests for reprints should be sent to Robert Fagot, Department of Psychology, University of Oregon, Eugene, OR 97403-1227. develop models that account for, rather than ignore or average out, context effects. One example is the work of Parducci (1982), who proposes a range-frequency theory that describes well the effects of stimulus range, spa...

The range effect as a function of stimulus set, presence of a standard, and modulus

“…In studies in which stimulus location has been manipulated, results have been inconclusive. Exponents were greater at the lower than at the upper end of the continuum for judgments of sound intensity (Ahlstrom & Baird, 1989;Foley et al, 1990) and heaviness (Fagot & Pokorny, 1989). However, Marks (1988) reported no difference in exponents, whereas Fagot and Pokorny reported smaller exponents at the lower end than at the upper end of the sound intensity continuum.…”

“…In studies that have examined the effect of a modulus and a standard on the exponent, results have been inconclusive. Some have shown no effect (Fagot & Pokorny, 1989, for loudness; Wiest & Bell, 1985), whereas others have shown that exponents are greater when a standard and a modulus are present (Fagot & Pokorny, 1989, for heaviness;MacMillan, Moschetto, Bialostozky, & Engel, 1974;J. C. Stevens & Tulving, 1957;S.…”

“…Teghtsoonian & M. Teghtsoonian, 1978) for several stimulus continua, but not explained satisfactorily. The role of one factor-location of the stimulus range along the stimulus continuum-in determining the range effect has only recently received attention (Ahlstrom & Baird, 1989;Fagot & Pokorny, 1989;Foley et al, 1983;Foley, Cross, & O'Reilly, 1990;Marks, 1988). Response magnitude, a second factor that might contribute to the range effect, has not been studied systematically.…”

Reliability of Ratings for Multiple Judges: Intraclass Correlation and Metric Scales

“…To demonstrate the effect on reliability of ignoring arbitrary scale factors, the standardization procedure was used to estimate the reliability index for psychophysical data from Fagot and Pokorny (1989). Twelve raters made magnitude estimations of loudness and heaviness for nine log-spaced stimuli.…”

What are we estimating when we fit Stevens’ power law?

“…Further evidence on grouped data is reported by Macmillan, Moschetto, Bialostozky, and Engel (1974), which show that when Eδ 1 = δ 2 (their case MS) the exponent is larger than when either Eδ 1 ≪ δ 2 (their case LS) or Eδ 1 ≫ δ 2 (their case SS). The effect has also been observed in Marks (1988, p. 522), Ahlström and Baird (1989), Fagot and Pokorny (1989) and Kowal (1993, p. 558). The last reference draws an unprecedented connection between the location and the range effects, and suggests that the former may be more robust than the latter (Kowal, 1993, p. 561) and may even have a role in determining it (p. 555).…”