Holistic and Componential Processing for Two-Digit Numbers

Abstract

A great deal of research has been conducted to investigate how people process two-digit numbers. Researchers have found that the time to compare two two-digit numbers decreases logarithmically with the absolute difference of two numbers, which suggests a holistic processing for two-digit numbers. However, some evidence seems to support additional componential processing. A number pair can be defined as compatible if the decade-magnitude comparison and the unit-magnitude comparison of the two numbers lead to the same result (e.g., 23 vs. 78, 27 and 38), and as incompatible if this is not the case (e.g., 29 vs. 84, 28 but 94). Subjects took longer to respond the unit-decade-incompatible number pairs than to the unit-decade-compatible number pairs. The unit-decade compatibility effect suggests that the magnitude of the unit digits of numbers in addition to the whole magnitude of the numbers is activated. However, previous studies on two-digit number processing have typically used tasks involving intentional processing of numerical magnitude. To intentionally process two-digit numbers, subjects need to pay attention to decade and unit digits serially or simultaneously, which may lead to componential processing. This study addressed whether componential processing is also involved in unintentional processing of the magnitude of numbers. Stroop-like paradigm was applied. Sixteen undergraduate students participated in Experiment 1. They were asked to compare the physical size of two two-digit numbers, as well as the numerical magnitude of the two numbers (e.g., 23 vs. 78). Four hundred two-digit pairs consisting of the numbers between 21 and 98 were presented in Arabic notation, excluding numbers that contained 0 as unit (e.g., 30, 40) or the same digits for decade and unit (e.g., 22, 33). We manipulated the ratio of the physical size of two numbers (i.e., 1∶1.1 vs. 1∶1.2), the congruency of magnitude size and physical size, and the unit-decade-compatibility. To avoid confounding of the distance and problem size effect, we controlled overall distance and problem size between compatible and incompatible pairs. In addition, we also conducted Experiment 2 to avoid interference of intentional and unintentional processing. Twenty undergraduate students were asked to compare only the physical size of two two-digit numbers. Experimental design and procedure were same as Experiment 1, except the ratio of physical size of two numbers had three levels containing 1∶1.1, 1∶1.25 and 1∶1.5. The results from the magnitude comparison task in Experiment 1 replicated those found in previous studies involving the same tasks. Tasks involving physical size comparison in both Experiment 1 and Experiment 2 showed the effect of magnitude and physical size congruency. The effect supported holistic processing. The unit-decade-compatibility effect was evident for congruent number pairs, but there was no or a reverse effect for incongruent number pairs. In sum, two-digit number processing can be componential as well as holistic in both unintentional and intentional processing of numerical magnitude.