@article{ReikeSchwarz2016,
  author    = {Reike, Dennis and Schwarz, Wolfgang},
  title     = {One Model Fits All: Explaining Many Aspects of Number Comparison Within a Single Coherent Model-A Random Walk Account},
  series = {Journal of experimental psychology : Learning, memory, and cognition},
  volume    = {42},
  journal   = {Journal of experimental psychology : Learning, memory, and cognition},
  publisher = {American Psychological Association},
  address   = {Washington},
  issn      = {0278-7393},
  doi       = {10.1037/xlm0000287},
  pages     = {1957 -- 1971},
  year      = {2016},
  abstract  = {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.},
  language  = {en}
}
@article{SchwarzMiller2016,
  author    = {Schwarz, Wolfgang and Miller, Jeff},
  title     = {GSDT: An Integrative Model of Visual Search},
  series = {Journal of experimental psychology : Human perception and performance},
  volume    = {42},
  journal   = {Journal of experimental psychology : Human perception and performance},
  publisher = {American Psychological Association},
  address   = {Washington},
  issn      = {0096-1523},
  doi       = {10.1037/xhp0000247},
  pages     = {1654 -- 1671},
  year      = {2016},
  abstract  = {We present a new quantitative process model (GSDT) of visual search that seeks to integrate various processing mechanisms suggested by previous studies within a single, coherent conceptual frame. It incorporates and combines 4 distinct model components: guidance (G), a serial (S) item inspection process, diffusion (D) modeling of individual item inspections, and a strategic termination (T) rule. For this model, we derive explicit closed-form results for response probability and mean search time (reaction time [RT]) as a function of display size and target presence/absence. The fit of the model is compared in detail to data from 4 visual search experiments in which the effects of target/distractor discriminability and of target prevalence on performance (present/absent display size functions for mean RT and error rate) are studied. We describe how GSDT accounts for various detailed features of our results such as the probabilities of hits and correct rejections and their mean RTs; we also apply the model to explain further aspects of the data, such as RT variance and mean miss RT.},
  language  = {en}
}
@article{SchwarzReike2020,
  author    = {Schwarz, Wolfgang and Reike, Dennis},
  title     = {The M{\"u}ller-Lyer line-length task interpreted as a conflict paradigm},
  series = {Attention, perception, \& psychophysics : AP\&P ; a journal of the Psychonomic Society, Inc.},
  volume    = {82},
  journal   = {Attention, perception, \& psychophysics : AP\&P ; a journal of the Psychonomic Society, Inc.},
  number    = {8},
  publisher = {Springer},
  address   = {New York},
  issn      = {1943-3921},
  doi       = {10.3758/s13414-020-02096-x},
  pages     = {4025 -- 4037},
  year      = {2020},
  abstract  = {We propose to interpret tasks evoking the classical M{\"u}ller-Lyer illusion as one form of a conflict paradigm involving relevant (line length) and irrelevant (arrow orientation) stimulus attributes. Eight practiced observers compared the lengths of two line-arrow combinations; the length of the lines and the orientation of their arrows was varied unpredictably across trials so as to obtain psychometric and chronometric functions for congruent and incongruent line-arrow combinations. To account for decision speed and accuracy in this parametric data set, we present a diffusion model based on two assumptions: inward (outward)-pointing arrows added to a line (i) add (subtract) a separate, task-irrelevant drift component, and (ii) they reduce (increase) the distance to the barrier associated with the response identifying this line as being longer. The model was fitted to the data of each observer separately, and accounted in considerable quantitative detail for many aspects of the data obtained, including the fact that arrow-congruent responses were most prominent in the earliest RT quartile-bin. Our model gives a specific, process-related meaning to traditional static interpretations of the Muller-Lyer illusion, and combines within a single coherent framework structural and strategic mechanisms contributing to the illusion. Its central assumptions correspond to the general interpretation of geometrical-optical illusions as a manifestation of the resolution of a perceptual conflict (Day \& Smith, 1989; Westheimer, 2008).},
  language  = {en}
}