Comparative judgments of multidigit numbers.

Abstract

The greater of two multidigit integers could be chosen by (a) generating and comparing internal representations of the integers (holistic models), (b) sequentially comparing corresponding digits in the integers (sequential place-value models), or (c) simultaneously comparing corresponding digits (parallel place-value models).In Experiments 1 and 2, subjects chose the greater of 2 four-digit or 2 six-digit integers. As predicted by sequential place-value models, latencies did not depend on the number of unequal digits in the two numbers, and latencies increased linearly with the position of the leftmost unequal digits except when only the rightmost digits were unequal. In Experiment 3, latencies increased linearly for all positions when two letters were presented to the right of the integers. These results imply that multidigit integers are compared by sequentially comparing digits.

A neural model of how the brain represents and compares multi-digit numbers: spatial and categorical processes

“…A major controversy arising from the data concerns the response times in numerical comparison experiments (Brysbaert, 1995;Dehaene et al, 1990;Hinrichs, Yurko, & Hu, 1981;Poltrock & Schwartz, 1984). All results agree on the general trend when the numbers are compared to a fixed standard: response time becomes longer as the difference between the presented number and the standard becomes smaller.…”

“…The controversial portion of the data is related to how the reaction times behave at a decade boundary (for two-digit numbers). Experiments on two-digit (Dehaene et al, 1990) and multi-digit (Poltrock & Schwartz, 1984) number comparisons reported no fine-grain patterns in the reaction time data beyond the conventional Numerical Distance effect. In contrast, the study by Hinrichs et al (1981) mentioned a statistically significant increase in the reaction time change for the two boundaries between the decades (49 -50 and 59 -60) versus the adjacent intervals in the number comparison experiment with stimuli ranging from 11 to 99 and a fixed standard of 55.…”

“…Many studies addressed single-digit (Parkman, 1971), twodigit (Bryzbaert, 1995Dehaene, Dupoux, & Mehler, 1990;Link, 1990), and multi-digit (Poltrock & Schwartz, 1984) number comparisons that showed longer reaction times for smaller distances between numbers for most cases, thereby demonstrating the temporal side of Numerical Distance effect. The amount of priming in number priming experiments was also shown to be a decreasing function of the numerical distance from the prime to the target number (den Heyer & Briand, 1986).…”

“…The lexicographic approach predicts numerical comparison times based solely on the leftmost digit information (the decades digit in the case of two-digit numbers), completely ignoring the other information (Poltrock & Schwartz, 1984). The holistic approach-in which the symbolic numerical notation first would be converted to a magnitude representation and only then would the two numbers be compared-is supported by the experiments by Dehaene et al (1990).…”

Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison.

“…The literature contains several examples in which the lexicographic model is better supported by the data. Thus, the comparison of three-to six-digit numbers (Hinrichs, Berie, & Mosell, 1982;Poltrock & Schwartz, 1984) appears to depend on the symbolic appearance of the stimuli: The two variables governing comparison times are (a) whether the two numbers have the same number of digits or not and (b) the position of the first set of differing digits when the numbers are scanned from left to right. Even in two-digit number comparison, when the standard is 50 and the targets range from 40 to 60, the units digit of the target number does not influence comparison times (Hinrichs et al,198 l,Experiment 2).…”