Judgments of proportions.

Abstract

This study investigated the processes that underlie estimates of relative frequency. Ss performed 4 tasks using the same stimuli (squares containing black and white dots); they judged "percentages" of white dots, "percentages" of black dots, "ratios" of black dots to white dots, and "differences" between the number of black and white dots. Results were consistent with the theory that Ss used the instructed operations with the same scale values in all tasks. Despite the use of the correct operation, Ss consistently overestimated small proportions and underestimated large proportions. Variations in the distributions of actual proportions affected the extent to which Ss overestimated small proportions and underestimated large proportions in the direction predicted by range-frequency theory. Results suggest that proportion judgments, and by analogy probability judgments, should not be taken at face value.

New paradoxes of risky decision making.

“…This means that the functions should be subscripted for context. Varey, Mellers, and Birnbaum (1990) asked people to examine squares containing numbers of white and black dots and to judge the proportions of each color. Varey et al manipulated the actual numbers of white and black dots as well as the frequency distribution of actual proportions.…”

“…Figure 8 in Varey et al (1990) shows how the relationship between judged and actual proportion depended on their contextual manipulations. It seems likely that similar contextual effects would be observed if people were asked to bet on a white or black ball drawn from urns represented by their stimuli or to choose between gambles defined by those stimuli and presented in those same contexts.…”

What very small numbers mean.

“…Nevertheless, researchers often make an implicit assumption that people interpret these numerical formats equivalently (termed the assumption of numerical equivalence). The implicit assumption of numerical equivalence is prevalent in studies of psychophysics (e.g., Gescheider, 1988;Marks, 1974;Marks & Algom, 1998;Stevens, 1956Stevens, , 1986 Schwarz, & Bless, 1995), and probability estimation (e.g., Begg, 1974;Brooke & MacRae, 1977;Hollands & Dyre, 2000;Shuford, 1961;Spence, 1990;Teigen, 1973;Tversky & Fox, 1995;Varey, Mellers, & Birnbaum, 1990), to name just a few. The assumption of numerical equivalence, however, should not be made lightly because people's interpretation of numbers likely affects the data they produce, and thus the conclusions that researchers draw.…”

“…Although overestimation of proportions under 0.5 in the judgment task is a very robust finding (e.g., Brooke & MacRae, 1977;Hollands & Dyre, 2000;Spence, 1990;Varey et al, 1990), only participants in Brooke and MacRae's experiments completed both the judgment and production tasks. Brooke and MacRae found no evidence for a response bias.…”

Effects of Group Size upon Proportion Judgments of Likable and Unlikable Members and Group Impressions: Small is Bad, not that Large is Good

“…2). The centralizing tendency in proportion judgment is found in many studies, although the naming might be new (see Varey, Mellers, & Birnbaum, 1990). The disappearance of the centralizing tendency in large and small groups in Exp.…”