@article{ReikeSchwarz2019,
  author    = {Reike, Dennis and Schwarz, Wolfgang},
  title     = {Categorizing digits and the mental number line},
  series = {Attention, perception, \& psychophysics : AP\&P ; a journal of the Psychonomic Society, Inc.},
  volume    = {81},
  journal   = {Attention, perception, \& psychophysics : AP\&P ; a journal of the Psychonomic Society, Inc.},
  number    = {3},
  publisher = {Springer},
  address   = {New York},
  issn      = {1943-3921},
  doi       = {10.3758/s13414-019-01676-w},
  pages     = {614 -- 620},
  year      = {2019},
  abstract  = {Following the classical work of Moyer and Landauer (1967), experimental studies investigating the way in which humans process and compare symbolic numerical information regularly used one of two experimental designs. In selection tasks, two numbers are presented, and the task of the participant is to select (for example) the larger one. In classification tasks, a single number is presented, and the participant decides if it is smaller or larger than a predefined standard. Many findings obtained with these paradigms fit in well with the notion of a mental analog representation, or an Approximate Number System (ANS; e.g., Piazza 2010). The ANS is often conceptualized metaphorically as a mental number line, and data from both paradigms are well accounted for by diffusion models based on the stochastic accumulation of noisy partial numerical information over time. The present study investigated a categorization paradigm in which participants decided if a number presented falls into a numerically defined central category. We show that number categorization yields a highly regular, yet considerably more complex pattern of decision times and error rates as compared to the simple monotone relations obtained in traditional selection and classification tasks. We also show that (and how) standard diffusion models of number comparison can be adapted so as to account for mean and standard deviations of all RTs and for error rates in considerable quantitative detail. We conclude that just as traditional number comparison, the more complex process of categorizing numbers conforms well with basic notions of the ANS.},
  language  = {en}
}
@article{SchwarzEiselt2012,
  author    = {Schwarz, Wolfgang and Eiselt, Anne-Kathrin},
  title     = {Numerical distance effects in visual search},
  series = {Attention, perception, \& psychophysics : AP\&P ; a journal of the Psychonomic Society, Inc.},
  volume    = {74},
  journal   = {Attention, perception, \& psychophysics : AP\&P ; a journal of the Psychonomic Society, Inc.},
  number    = {6},
  publisher = {Springer},
  address   = {New York},
  issn      = {1943-3921},
  doi       = {10.3758/s13414-012-0342-8},
  pages     = {1098 -- 1103},
  year      = {2012},
  abstract  = {We present three experiments in which observers searched for a target digit among distractor digits in displays in which the mean numerical target-distractor distance was varied. Search speed and accuracy increased with numerical distance in both target-present and target-absent trials (Exp. 1A). In Experiment 1B, the target 5 was replaced with the letter S. The results suggest that the findings of Experiment 1A do not simply reflect the fact that digits that were numerically closer to the target coincidentally also shared more physical features with it. In Experiment 2, the numerical distance effect increased with set size in both target-present and target-absent trials. These findings are consistent with the view that increasing numerical target-distractor distance affords faster nontarget rejection and target identification times. Recent neurobiological findings (e.g., Nieder, 2011) on the neuronal coding of numerosity have reported a width of tuning curves of numerosity-selective neurons that suggests graded, distance-dependent coactivation of the representations of adjacent numbers, which in visual search would make it harder to reject numerically closer distractors as nontargets.},
  language  = {en}
}