Estimation of factorial expressions and its improvement through calibration: A replication and extension of Tversky and Kahneman (1973)

Fifty years ago, Tversky and Kahneman (Cognitive Psychology, 5[2], 207-232, 1973) reported that people's speeded estimations of 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 were notably higher than their estimations for the equivalent expression in the opposite order, 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 (Median = 2,250 vs. 512, respectively). On top of this order effect, both groups grossly underestimated the correct value (40,320). The differential effect of the two orders on estimation has become famous as an early demonstration of the anchoring effect, where people's judgments under uncertainty are unduly influenced by an initial reference point (or "anchor"). Despite this fame, to the best of our knowledge, this effect has never been replicated. In a sample of 253 U.S. adults, the current study provides the first replication of this foundational example of anchoring. It extends this effect for the first time to a within-participants design, revealing its relative robustness even among participants who see the descending order first. Drawing on procedures from the mathematical cognition literature, it shows how the anchoring effect can be mitigated: calibrating to the correct value of 6! reduces this effect, and calibrating to 10! eliminates it altogether. An individual differences analysis measures the arithmetic fluency of participants and their accuracy on a new estimation assessment, and finds that higher estimation ability may be a "protective factor" against some anchoring effects. These findings affirm the anchoring effect of Tversky and Kahneman (1973, Study 6) while suggesting that calibration may be an effective strategy for helping to improve people's estimation of superlinear functions that are important in real-life contexts.