Analogue equivalents in number processing of simple arithmetic sums

This study had two aims. The first was to test the postulate of analogical equivalents in number processing using a stimulus set based on the differences between pairs of numbers, and second, to look for IQ-dependent differences in this processing. Participants were asked to make judgments concerning the differences between pairs of numbers—each number pair being defined according to overall numerical size and level of difference—and to draw the magnitude of the differences using a free-hand line. In agreement with previous findings, results indicated that the magnitude of participants' responses was dependent on the sizes and levels of the differences within the number pairs. In particular, participants' responses to a difference of nine units at the highest level were based on unit lengths smaller in magnitude compared with other number pairs. In contrast, participants' responses to a second test requiring them to estimate the length of a line using an independent number scale showed remarkable accuracy across all lengths. The results of the two tests did not, however, indicate any difference in responses based on IQ. The results gave support to the idea that transformation of numerical quantities to their analogical equivalents occurs during simple arithmetic sums, and that this transformation was flawed as suggested by the number size effect.