How to estimate how well people estimate: Evaluating measures of individual differences in the approximate number system

At a glance, one can tell that there are more individual fruits in a pile of 100 apples than in a pile of 20 watermelons, even though the watermelons take up more space. People's ability to distinguish between such nonsymbolic numerical magnitudes without counting is derived from the approximate number system (ANS). Individual differences in this ability (ANS acuity) are emerging as an important predictor in research areas ranging from children's understanding of arithmetic to adults' use of numbers in judgment and decision making. However, ANS acuity must be assessed through proxy tasks that might not show consistent relationships with this ability. Furthermore, practical limitations often confine researchers to using abbreviated measures of this ability, whose reliability is questionable. Here, we developed and tested several novel ANS acuity measures: a nonsymbolic discrimination task designed to account for participants' lapses in attention; three estimation tasks, including one task in which participants estimated the number of dots in a briefly presented set, one in which they estimated the ratio between two sets of dots, and one in which they indicated the correct position of a set of dots on a "number-line" anchored by two sets of dots, as well as a similar number-line task using symbolic numbers. The results indicated that the discrimination task designed to account for lapses in participants' attention holds promise as a reliable measure of ANS acuity, considered in terms of both internal and test-retest reliability. We urge researchers to use acuity measures whose reliability has been demonstrated.