Contextual Skewing and Overall Mean Judgment

Systematic manipulation of the context for category ratings of psychophysical stimuli has isolated two dominating factors: 1) the range of contextual stimuli, and 2) the relative frequencies of stimuli within this range. The effects of these two factors upon the rating or judgment of any particular stimulus can be described as a weighted average between the proportion of the contextual range and the proportion of all contextual stimuli below the stimulus, implying that the overall mean of the judgments is proportional to contextual skewing. This characterization of the effects of skewing is illustrated by an experiment in which participants rated how satisfying monitary outcomes were in different contexts. A negatively-skewed context resulted in a greater overall mean judgment in this experiment and in each of a sample of more traditional psychophysical experiments. These results are described by a physical model, the teeter-totter, which also suggests how a decision that extends the range upward can lower the overall mean judgment. When the judgment is taken as a measure of pleasantness, a basic distinction between pleasure and utility is illuminated by contextual considerations. Because psychophysical experiments permit control of the set of stimuli affecting the rating of each of the presented stimuli, such experiments have proven particularly useful for understanding the effects of the stimulus context upon category ratings. In the simplest cases, this context is constituted of just those stimuli presented in the experimental session. For example, if presented with a series of lifted weights, subjects might rate the lightest of those presented “1—very light,” the heaviest “7—very heavy” on a typical seven-category scale, applying intermediate categories for weights intermediate between these two extremes. By systematically manipulating different features of the frequency distribution of weights presented, such as its endpoints or skewing, the experimenter can determine how these features affect the resulting ratings. The same principles of judgment have been found to apply whenever the context can be controlled experimentally: for lifted weights, numerousness of dots, sizes of squares, sweetness of lemonades, and even for the pleasantness of facial expressions (Parducci, 1995). In all of these cases, individual ratings are determined by the place of each stimulus in the contextual range and its percentile rank in the frequency distribution of contextual stimuli, with each rating a compromise between these two determinants: Ji = wRi + (1 – w)Fi, [1] where Ri , the range value of Stimulus i, represents what its judgment would have been if determined solely by the position of i in the stimulus range, specifically by the proportion of the range below it. The frequency value of this same stimulus, Fi, represents what the judgment would have been if it had been determined solely by its rank in the frequency distribution of contextual stimuli, specifically by its percentile rank (divided by 100). The relative weighting of the range and frequency values is given by w, a value between 0 and 1. The overt category rating is then a linear transformation of this judgment, depending upon the numerical values assigned to represent the categories (usually their ranks). This paper concentrates on the effect of skewing the distribution of contextual stimuli on the grand, overall mean of the judgments. It is well known that the same stimulus receives a lower judgment when presented in a negatively-skewed distribution than in a positively-skewed distribution with the same endpoints, as predicted by Equation 1. Nevertheless, the overall mean of the judgments is actually higher for stimuli presented in a negatively-skewed distribution because the higher among its stimulus values are more frequent. This effect of skewing is expressed more precisely by Equation 2 (which derives algebraically from Equation 1): _ _ J = .5 + w(S – MP)/Range, [2] _ _ where J is the overall mean of the judgments, S is the mean of all stimulus values, and MP is their midpoint (halfway between the two endpoints of the contextual range). Equation 2 is a measure of skewing that correlates almost perfectly with more conventional measures, though with algebraic sign reversed. In conventional terms, the more negatively skewed the distribution of contextual stimuli, the higher the overall mean of the judgments. As a concrete example, consider an experiment (Parducci, 1968) that is easy to describe because its stimuli came with numerals already attached to them. Each of the participants “won” a series of monetary outcomes by turning over one of the three cards presented on any given trial and rating how satisfying it was. These outcomes ranged from 1 to 21 cents in the negativelyskewed condition, with the larger values coming more frequently--as in the representative sample diagrammed in Figure 1: