Data are presented from two magnitude estimation experiments in which the geographical areas of Brazilian states were judged. In Experiment 1 observers estimated the areas of the states in three conditions: in the presence of a map (perceived area), using memory following study of a map (remembered area), and using only general knowledge of Brazilian geography (inferred area). The results showed that the psychophysical power law describes well the inferred, remembered, and perceived magnitude estimates of areas of states. As had been found previously for areas of states, the remembered exponent approximated the square of the perceived exponent. Experiment 2 examined the correlations of the power functions exponents for observers who estimated areas of states on two sessions separated by an interval of 1 month. As in Experiment 1, observers estimated the areas from inference, from memory following study of a map, or in the presence of a map. Again, comparison of remembered and perceived psychophysical functions showed that for both sessions the remembered exponent was equal to the square of the perceived exponent. Since the correlations between Sessions 1 and 2 were fairly high and positive, the results also showed that all modes of judgments manifest temporal stability for an interval of at least 1 month between sessions. Stable individual differences can be shown for the exponent of the psychophysical power function for magnitude estimates of inferred, remembered, and perceived area. Although the exponent varies from one individual to another, the power function accurately describes the data of all observers in all conditions.
Three separate groups of observers made magnitude estimates of intercity distance in two sessions separated by an interval of 1 month. The first group of observers estimated intercity distance from memory, using just general knowledge of Brazilian geography (inferred distance). The second group estimated intercity distance from memory after studying a map for a period of7 min (remembered distance). The third group made the estimates while viewing a map (perceived distance). It was found that (1) although the exponent varied from one individual to another, the psychophysical power law described well the inferred, remembered, and perceived magnitude estimates of intercity distance; (2) the following ordinal relationship occurred between the sizes of the mean exponents: perceived > remembered > inferred; (3) the correlations between observers' exponents for the first and second sessions for all types of estimate were fairly high and positive; and (4) the individual differences observed in the exponents of the psychophysical power law for magnitude estimates of inferred, remembered, and perceived intercity distance were stable, at least for an interval of 1 month between sessions.The development of direct estimation methods by S. S. Stevens and collaborators (e.g., S. S. Stevens, 1975) was followed by an interest in the variability of individual power functions . In fact, many experiments have reported considerable individual differences in the exponent of Jones & Marcus, 1961;Ramsay , 1979;Rule , 1966;Rule & Markley, 1971;Schneider, 1980;J. C. Stevens & Guirao, 1964) . The outcomes of these experiments have raised the question of whether the variability observed in the exponents reflects genuine perceptual differences or some type of cognitive factor, such as a response bias , that affects observers' responses to stimulus intensities in a scaling task. To attack this question experimentally, Duda (1975) considered three models proposed to interpret power functions . These models also specify how sensory, stimulus, and response variables determine observers' judgmental behavior in a scaling task. A correlational analysis on individual differences in exponents was undertaken to test the predictions derived from each model. The results showed that response variables are important determinants ofjudgmental behavior in psychophysical scaling . These findings led Duda to suggest that observers' responses to stimulus magnitudes in a scaling task are largely cognitive.Correlational studies of stability of individual psychophysical power function exponents have produced inconclusive and sometimes contradictory results, even when the same sensory or perceptual attribute-for example, area or length-has been used. Jones and Woskow (1962) and Ekman et al. (1968) reported low but significant correlations between exponents for two stimulus continua when the same response cont inuum was used . In addition, Ekman et al. reported high correlations when there was no change in either stimulus or response continuum. Rule (1966) found...
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