A diffusion model decomposition of the unit-decade compatibility effect in two-digit number comparison

Mechanisms of number processing have been of interest to cognitive psychologists for many years. There are multiple competing theories to explain how people form mental represenations of two-digit numbers. Nuerk et al. (2001) proposed a decomposed representation, where the decade and unit digits are processed separately. Primary evidence came from the unit-decade compatibility effect, where comparisons when both unit and decade digits obey the same order relation (e.g., 23 versus 55, where both 2 < 5 and 3 < 5) are faster than trials where the order of digit relations is opposite (e.g., 27 versus 55, where 2 < 5 but 7 > 5). In this study, we used mathematical modeling to perform a decomposition of the unit-decade compatibility effect. We analyzed data from 53 adult observers, each of whom completed a two-digit number comparison task. Each observer’s distribution of RTs (split by compatibility condition) was fit to a diffusion model. We used the EZ-diffusion method (Wagenmakers et al., 2007) to obtain estimates of drift rate and nondecision time for each design cell. The estimates were then compared with a Bayesian paired samples t-test. As expected, compatible trials were faster than incompatible trials. This mean effect manifested almost entirely in the drift rate, which was smaller for incompatible trials than for compatible trials. Critically, the nondecision time did not differ between conditions. This implies that the unit-decade compatibility effect is due entirely to decision-related processes (e.g., stimulus information uptake) but not auxiliary nondecision processes (e.g., encoding, motor preparation, etc.). This work helps to shed light on the locus of the unit decade compatibility effect, and more broadly, on the nature of decomposed processing in numerical cognition.