Abstract
Consider the following experimental demonstration: when undergraduate volunteers judged the pleasantness of winning small amounts of money (from 1 to 30 cents per trial), their successive ratings reflected the position of each winning in the frequency distribution of their other winnings (Parducci, 1968). Table Table11 shows how the different distributions were skewed. Ratings of individual payoffs are not shown, for the present interest centers on the overall mean rating for each of the distributions. The overall mean rating on a 7-point scale was more than one category higher for the negatively skewed distribution (in which the higher winnings were more frequent), although the mean winning was 14 cents for each distribution). More generally, negatively skewed distributions always yield higher overall mean judgments. This is entailed by my range–frequency theory of judgment and supported by experiments on various kinds of hedonic and psychophysical judgments (Parducci, 1995). Table 1 Frequency distribution of winnings.
Highlights
The overall mean rating on a 7-point scale was more than one category higher for the negatively skewed distribution, the mean winning was 14 cents for each distribution)
Range–Frequency Theory The basic notion of the theory is that each dimensional judgment represents the place of what is being judged in a context of similar events that affect the judgment. This is represented as a compromise or weighted average: Jic = wRic + (1 − w)Fic where Jic represents the internal judgment of Stimulus i in Context c, Ric is the proportion of the contextual range below i, Fic is the cumulative proportion of contextual representations below i in the same context, and w is the weighting constant, assumed here to be
It follows algebraically that the mean of the judgments of all contextual values is proportional to the skewing of the contextual distribution. When applied to this experimental demonstration, the mean of all judgments is predicted to be 0.58 for the negatively skewed distribution, 0.42 for the positively skewed distribution. This effect of the skewing of the contextual distribution has been demonstrated for other hedonic dimensions, e.g., pleasantness of lemonades of varying sweetness, melodies of varying loudness, photographs of an actress simulating varying degrees of friendliness, and for a variety of non-hedonic dimensions, e.g., size of squares, heaviness of lifted weights, largeness of abstract numerals
Summary
Negatively skewed distributions always yield higher overall mean judgments. It follows algebraically that the mean of the judgments of all contextual values (winnings in this case) is proportional to the skewing of the contextual distribution. When applied to this experimental demonstration, the mean of all judgments (ratings transformed linearly to a 0-to-1 scale) is predicted to be 0.58 for the negatively skewed distribution, 0.42 for the positively skewed distribution (both within 0.005 of the empirically obtained overall mean judgments).
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