ON THE TIME TO SUBTRACT: DONDERS REVISITED

  • William M. Petrusic

Abstract

Extending Muensterberg’s (1889) application of Donders’ (1868)subtraction method, participants were required to subtract and compare thedifference with a number (e.g., 9-7 vs. 3) and on other trials to simplycompare comparable numbers (e.g., 2 vs. 3). The time to subtract andcompare depended on the difference between the numbers compared.Problem size effects were also shown to depend on decisional difficulty,permitting the rejection of the intuitively compelling retrieve and comparemodel. The findings provide support for a model of the subtract andcompare task in which numbers are represented as noisy extents, and theproblem size effect is captured through the assumption that the variabilityof the representation is proportional to the square of its expectation. Thesimple discrete evidence accumulator is used to model the comparisonprocess. These assumptions taken together permit a quantitative account ofboth the response time and the accuracy data.
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