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Open Access Publications from the University of California

Calibration information reduces bias during estimation of factorials: A (partial) replication and extension of Tversky and Kahneman (1973)


Tversky and Kahneman (1973) found that, under time pressure, people massively underestimated the expansion of 8! (correct value 40,320), and this bias was mitigated for participants presented the descending (8x7x6x5x4x3x2x1; Median=2,250) vs. ascending order (1x2x3x4x5x6x7x8; Median=512). In a first-ever replication (N=140), we also found predominant underestimation, but no significant between-subjects descending vs. ascending order effect. However, when participants then estimated the opposite order, we reproduced this order effect within-subjects. Finally, participants received calibration information (the correct value of 6! or 10!) and again estimated both orders of 8!. Participants who received 10! made more accurate estimates for 8! (Median=38,000), which did not differ statistically from the correct value. Participants who received 6! still grossly underestimated (Median=2,678.5), despite 8! being closer to 6! than 10! in linear and log units. Thus, we surprisingly found the classic factorial estimation bias only within-subjects, and provide evidence for how calibration can reduce it.

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