TY  - JOUR
A1  - Reike, Dennis
A1  - Schwarz, Wolfgang
T1  - One Model Fits All: Explaining Many Aspects of Number Comparison Within a Single Coherent Model-A Random Walk Account
JF  - Journal of experimental psychology : Learning, memory, and cognition
N2  - The time required to determine the larger of 2 digits decreases with their numerical distance, and, for a given distance, increases with their magnitude (Moyer & Landauer, 1967). One detailed quantitative framework to account for these effects is provided by random walk models. These chronometric models describe how number-related noisy partial evidence is accumulated over time; they assume that the drift rate of this stochastic process varies lawfully with the numerical magnitude of the digits presented. In a complete paired number comparison design we obtained saccadic choice responses of 43 participants, and analyzed mean saccadic latency, error rate, and the standard deviation of saccadic latency for each of the 72 digit pairs; we also obtained mean error latency for each numerical distance. Using only a small set of meaningfully interpretable parameters, we describe a variant of random walk models that accounts in considerable quantitative detail for many facets of our data, including previously untested aspects of latency standard deviation and error latencies. However, different from standard assumptions often made in random walk models, this account required that the distributions of step sizes of the induced random walks are asymmetric. We discuss how our findings can help in interpreting complex findings (e.g., conflicting speed vs. accuracy trends) in applied studies which use number comparison as a well-established diagnostic tool. Finally, we also describe a novel effect in number comparison, the decrease of saccadic response amplitude with numerical distance, and suggest an interpretation using the conceptual framework of random walk models.
KW  - numerical distance effect
KW  - random walk models
KW  - error latency
KW  - saccadic latency
KW  - saccadic amplitude
Y1  - 2016
U6  - https://doi.org/10.1037/xlm0000287
SN  - 0278-7393
SN  - 1939-1285
VL  - 42
SP  - 1957
EP  - 1971
PB  - American Psychological Association
CY  - Washington
ER  -