Compatibility effects in the perception of dispersion

In this paper, we show how one property of an average affects perceptions of the variance of the distribution that the average is derived from. Specifically, we find that when people view average ratings compatible with a possible input they perceive these ratings to come from less variable distributions-even when this is statistically less likely. Six experiments and four supplemental studies (total N = 16,988) document evidence for this effect: People perceive less dispersion in the distributions of "compatible average ratings" (i.e., averages matching a possible input; e.g., 4; 4.0; 4.00 on a discrete scale from 1 to 5 stars) compared to those of "non-compatible average ratings" (i.e., averages that do not match a possible input; e.g., 4.01 and 4.10). We argue that this error can be explained by a compatibility principle which states that the weighting of an input increases with its degree of compatibility with the output. People rely on the perceived compatibility between an output and input when forming judgments about the frequency of the input, affecting their assessment of the dispersion associated with the average. For instance, people recognize that a 4.0 average matches a 4 and thus perceive this average to be comprised of more 4s and indicative of less dispersion. We close with a discussion of consequences of this perception for choice and search.