@article{SchadVasishth2022,
  author    = {Schad, Daniel and Vasishth, Shravan},
  title     = {The posterior probability of a null hypothesis given a statistically significant result},
  series = {The quantitative methods for psychology},
  volume    = {18},
  journal   = {The quantitative methods for psychology},
  number    = {2},
  publisher = {University of Montreal, Department of Psychology},
  address   = {Montreal},
  issn      = {1913-4126},
  doi       = {10.20982/tqmp.18.2.p011},
  pages     = {130 -- 141},
  year      = {2022},
  abstract  = {When researchers carry out a null hypothesis significance test, it is tempting to assume that a statistically significant result lowers Prob(H0), the probability of the null hypothesis being true. Technically, such a statement is meaningless for various reasons: e.g., the null hypothesis does not have a probability associated with it. However, it is possible to relax certain assumptions to compute the posterior probability Prob(H0) under repeated sampling. We show in a step-by-step guide that the intuitively appealing belief, that Prob(H0) is low when significant results have been obtained under repeated sampling, is in general incorrect and depends greatly on: (a) the prior probability of the null being true; (b) type-I error rate, (c) type-II error rate, and (d) replication of a result. Through step-by-step simulations using open-source code in the R System of Statistical Computing, we show that uncertainty about the null hypothesis being true often remains high despite a significant result. To help the reader develop intuitions about this common misconception, we provide a Shiny app (https://danielschad.shinyapps.io/probnull/). We expect that this tutorial will help researchers better understand and judge results from null hypothesis significance tests.},
  language  = {en}
}
@article{RabeChandraKruegeletal.2021,
  author    = {Rabe, Maximilian Michael and Chandra, Johan and Kr{\"u}gel, Andr{\´e} and Seelig, Stefan A. and Vasishth, Shravan and Engbert, Ralf},
  title     = {A bayesian approach to dynamical modeling of eye-movement control in reading of normal, mirrored, and scrambled texts},
  series = {Psychological Review},
  volume    = {128},
  journal   = {Psychological Review},
  number    = {5},
  publisher = {American Psychological Association},
  address   = {Washington},
  issn      = {0033-295X},
  doi       = {10.1037/rev0000268},
  pages     = {803 -- 823},
  year      = {2021},
  abstract  = {In eye-movement control during reading, advanced process-oriented models have been developed to reproduce behavioral data. So far, model complexity and large numbers of model parameters prevented rigorous statistical inference and modeling of interindividual differences. Here we propose a Bayesian approach to both problems for one representative computational model of sentence reading (SWIFT; Engbert et al., Psychological Review, 112, 2005, pp. 777-813). We used experimental data from 36 subjects who read the text in a normal and one of four manipulated text layouts (e.g., mirrored and scrambled letters). The SWIFT model was fitted to subjects and experimental conditions individually to investigate between- subject variability. Based on posterior distributions of model parameters, fixation probabilities and durations are reliably recovered from simulated data and reproduced for withheld empirical data, at both the experimental condition and subject levels. A subsequent statistical analysis of model parameters across reading conditions generates model-driven explanations for observable effects between conditions.},
  language  = {en}
}