WHEN NUMERICAL DIFFERENCES DON'T MATTER: JUDGMENTS OF APPROXIMATELY EQUAL (≈) FOR BREAST-CANCER STATISTICS

Purpose: To understand the conditions under which laypeople ignore irrelevant differences and appropriately judge two breast-cancer statistics as approximately equal (e.g. nominally different rates of breast cancer), an essential judgment in medical decision-making.

Method: Three studies investigated how people make “roughly the same” or “approximately equal” judgments. Participants judged the smaller of two numbers as either less than or approximately equal to the larger number. Number pairs were presented in sentences regarding breast-cancer statistics and as numbers only, displayed either as percentages (to reduce denominator neglect) or as frequencies (X in 100,000). We used reputable health sources to designate half of the breast-cancer items as justifiably approximately equal and half unambiguously different. This allowed us to conduct Signal Detection Theory (SDT) analyses of the factors affecting judgment sensitivity and bias. We investigated numerical properties and a gist-evoking manipulation based on Fuzzy-Trace Theory (FTT). In Study 1, number pairs, devoid of medical context, were presented to 355 participants. In Study 2, 150 participants made approximately equal judgments for numbers out-of-context or the same numbers as breast-cancer statistics, and completed individual-difference measures.  In Study 3, following FTT, half of 229 participants received a brief gist-evoking text (“Thinking about the gist of what you know, is this a substantial difference?"), judged numbers out-of-context or breast-cancer statistics, and completed individual-difference measures.

Result: In Study 1, the greater the ratio of the smaller to larger number, the greater the proportion judged approximately equal. In Study 2, as predicted by FTT, participants were more likely to appropriately judge quantities as approximately equal in the context of breast cancer than numbers alone and when data were presented as percentages compared to frequencies. Mean d’ (sensitivity) was significantly larger for breast-cancer items presented as percentages than those presented as frequencies. Knowledge of breast cancer correlated with d’. In Study 3, Study 2 results replicated and receiving gist-evoking text yielded significantly more appropriate judgments. SDT analyses indicated greater sensitivity (d’) in the gist text condition and, again, d’ and knowledge were correlated.

Conclusion: Laypeople’s ability to ignore irrelevant differences is important for medical decision-making. Instructions to think about gist, presenting numbers as percentages rather than frequencies, and breast-cancer knowledge improved judgments of approximate (fuzzy) equality. FTT explains our results, with implications for shared decision-making.