Nonsymbolic numerical magnitude comparison: reliability and validity of different task variants and outcome measures, and their relationship to arithmetic achievement in adults

The numerical ratio effect (NRE) and the Weber fraction (w) are common metrics of the precision of the approximate numbers sense (ANS), a cognitive mechanism suggested to play a role in the development of numerical and arithmetic skills. The task most commonly used to measure the precision of the ANS is the numerical comparison task. Multiple variants of this task have been employed yet it is currently unclear how these affect metrics of ANS acuity, and how these relate to arithmetic achievement. The present study investigates the reliability, validity and relationship to standardized measures of arithmetic fluency of the NRE and w elicited by three variants of the nonsymbolic number comparison task. Results reveal that the strengths of the NRE and w differ between task variants. Moreover, the reliability and validity of the reaction time NRE and the w were generally significant across task variants, although reliability was stronger for w. None of the task variants revealed a correlation between ANS metrics and arithmetic fluency in adults. These results reveal important consistencies across nonsymbolic number comparison tasks, indicating a shared cognitive foundation. However, the relationship between ANS acuity and arithmetic performance remains unclear.