Hypothesis Testing

Sequential Testing

Classical hypothesis tests are performed on samples of a fixed size (e.g., based on an a priori power analysis). In sequential analysis, the data are continuously monitored and sampling can be terminated whenever the data show a compelling result. Thereby, sequential tests can reduce required sample sizes considerably. Thus, by saving resources, sequential analysis allows for more efficient hypothesis testing, which bears many benefits for psychological researchers.

  • Erdfelder, E., & Schnuerch, M. (2021). On the efficiency of the independent segments procedure: A direct comparison with sequential probability ratio tests. Psychological Methods, 26, 501–506. 
  • Reiber, F., Schnuerch, M., & Ulrich, R. (2022). Improving the efficiency of surveys with randomized response models: A sequential approach based on curtailed sampling. Psychological Methods, 27, 198–211.
  • Schnuerch, M., & Erdfelder, E. (2020). Controlling decision errors with minimal costs: The sequential probability ratio t-test. Psychological Methods, 25, 206–226. 
  • Schnuerch, M., & Erdfelder, E., Heck, D. W. (2020). Sequential hypothesis tests for multinomial processing tree models. Journal of Mathematical Psychology, 95, 102326. 
  • Schnuerch, M., Heck, D. W., & Erdfelder, E. (2024). Waldian t tests: Sequential Bayesian t tests with controlled error probabilities. Psychological Methods, 29, 99–116.
  • Steinhilber, M., Schnuerch, M., & Schubert, A.-L. (in press). Sequential analysis of variance: Improving efficiency of hypothesis testing. Psychological Methods.

Bayesian Model Comparison

Statistical hypothesis testing is a form of model comparison (and selection): Statistical models representing psychological hypotheses are formulated and compared in light of data. In the Bayesian framework, models are compared by means of their relative predictive accuracy. The Bayes factor captures how well one model predicted the data relative to another, thus accounting for model fit and complexity. I am interesting in developing Bayes factors for relevant scenarios in psychological research (e.g., Likert-scale data), combining the advantages of Bayesian and frequentist methods, and using deep-learning techniques to calculate Bayes factors for complex (e.g., hierarchical) models.

  • Elsemüller, L., Schnuerch, M., Bürkner, P.-C., & Radev, S. T. (in press). A deep learning method for comparing Bayesian hierarchical models. Psychological Methods.
  • Schnuerch, M., Haaf, J. M., Sarafoglou, A.,  & Rouder, J. N. (2022). Meaningful comparisons with ordinal-scale items. Collabra: Psychology, 8, 38594. 
  • Schnuerch, M., Heck, D. W., & Erdfelder, E. (2024). Waldian t tests: Sequential Bayesian t tests with controlled error probabilities. Psychological Methods, 29, 99–116.
  • Rouder, J. N., Schnuerch, M., Haaf, J. M., & Morey, R. D. (2023). Principles of model specification in ANOVA designs.  Computational Brain & Behavior, 6, 50–63.
  • van Doorn, J., Haaf, J. M., Stefan, A. M., Wagenmakers, E.-J., Cox, G. E., Davis-Stober, C. P., Heathcote, A., Heck, D. W., Kalish, M., Kellen, D., Matzke, D., Morey, R. D., Nicenboim, B., van Ravenzwaaij, D., Rouder, J. N., Schad, D. J., Shiffrin, R. M., Singmann, H., Vasishth, S., … Schnuerch, M., … Aust, F. (2023). Bayes factors for mixed models: A discussion. Computational Brain & Behavior, 6, 140–158. 
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