On the temporal dynamics of digit comparison processes.

Abstract

The authors studied the temporal dynamics of digit comparison processes by presenting the digits with a stimulus onset asynchrony (SOA) of 0,70,140, or 210 ms. Experiment 1 used the standard complete paired comparison design that confounds numerical and probabilistic information in the digit presented first. The results showed large effects of SOA that differed characteristically for different digit pairs. These results changed considerably in Experiment 2, using a design that removed any probabilistic contingencies. Experiment 3 examined a form of congruity effect related to the temporal order of the digits. The authors formulated and compared to the data 2 models that differed in their assumptions about the loci of digit-specific and SOA-specific effects: Either the participants use partial numerical advance information to prepare for the suggested response, or they start to process numerical information only after both digits are presented. When probabilistic contingencies were removed, the data favored the latter model.

Number Compasison and Number Line Estimation Rely on Different Mechanisms

“…If number is represented linearly, no SE in comparison should be present; small numbers and large numbers are equally discriminable. Contrary to this expectation, a SE is still observed in comparison tasks (Laski & Siegler, 2007;Schwarz & Stein, 1998). This inconsistency between both tasks is difficult to explain on the basis of a common mechanism.…”

“…Performance on the comparison task results in a size effect (e.g., Holloway & Ansari, 2009;Schwarz & Stein, 1998): when numerical distance is kept fixed, discrimination performance is more difficult when the numerical size increases. The performance of young children on a number line estimation task is characterised by a logarithmic mapping (e.g., Siegler & Opfer, 2003): small numbers are put further away from one another on this empty line than larger numbers.…”

Effects of Parametrical and Trial-to-Trial Variation in Prior Probability Processing Revealed by Simultaneous Electroencephalogram/Functional Magnetic Resonance Imaging

“…We adapted the number comparison task from Schwarz and Stein (1998) to meet our requirements. The same task was used in the previous EEG study (Scheibe et al, 2009).…”

The ex-Wald distribution as a descriptive model of response times

“…This is consistent with the interpretation, suggested by previous related work (cf. Schwarz & Stein, 1998;Smith & Mewhort, 1998), that partial numerical information about the digit presented is gradually accumulated at a rate that increases with the numerical distance of that digit to the standard. Also, the amount of evidence required before a go response is initiated increases with decreases of the a priori probability that a go response will be required on any given trial.…”

“…The price at which those advantages are bought is that most process-oriented models are formally and computationallydemanding, and their implementation in specific experimental contexts often requires flexible adjustments and nonstandard elaborations. For example, in the context of diffusion models of RT, the incorporation of psychologically important model features such as state-or time-dependent drift rates (Heath, 1992; P. L. Smith, 1995), probabilistic randomizations of response barriers (Ratcliff & Rouder, 1998), or transitions from reflecting to absorbing response barriers (Schwarz & Stein, 1998) requires a firm background in formal diffusion theory and does not easily lead to readily applied standard tools for data analysis. These factors are very likely a main reason why, despite their undisputed advantages, detailed process-oriented models are perhaps more often discussed than actually applied to data.…”