Combine Statistical Thinking With Scientific Practice: A Protocol of a Bayesian Thesis Project For Undergraduate Students.

Current developments in the statistics community suggest that modern statistics education should be structured holistically, i.e., by allowing students to work with real data and answer concrete statistical questions, but also by educating them about alternative statistical frameworks, such as Bayesian statistics. In this article, we describe how we incorporated such a holistic structure in a Bayesian thesis project on ordered binomial probabilities. The project was targeted at undergraduate students in psychology with basic knowledge in Bayesian statistics and programming, but no formal mathematical training. The thesis project aimed to (1) convey the basic mathematical concepts of Bayesian inference, (2) let students experience the entire empirical cycle including the collection, analysis, and interpretation of data, and (3) teach students open science practices.

[1]  Jeffrey N. Rouder,et al.  Teaching Bayes’ Theorem: Strength of Evidence as Predictive Accuracy , 2018, The American Statistician.

[2]  D. Heck,et al.  Multinomial Models with Linear Inequality Constraints: Overview and Improvements of Computational Methods for Bayesian Inference. , 2018, Journal of mathematical psychology.

[3]  Brian A. Nosek,et al.  Evaluating the replicability of social science experiments in Nature and Science between 2010 and 2015 , 2018, Nature Human Behaviour.

[4]  Alexander Etz,et al.  Introduction to Bayesian Inference for Psychology , 2018, Psychonomic bulletin & review.

[5]  Jeff Witmer,et al.  Bayes and MCMC for Undergraduates , 2017 .

[6]  M. Baker 1,500 scientists lift the lid on reproducibility , 2016, Nature.

[7]  T. Demuynck,et al.  Transitivity of Preferences: When Does it Matter? , 2015 .

[8]  Johanna S. Hardin,et al.  Teaching the Next Generation of Statistics Students to “Think With Data”: Special Issue on Statistics and the Undergraduate Curriculum , 2015 .

[9]  H. Hoijtink,et al.  Evaluating Manifest Monotonicity Using Bayes Factors , 2015, Psychometrika.

[10]  Michael C. Frank,et al.  Estimating the reproducibility of psychological science , 2015, Science.

[11]  G. Cobb Mere Renovation is Too Little Too Late: We Need to Rethink our Undergraduate Curriculum from the Ground Up , 2015, 1507.05346.

[12]  E. Wagenmakers,et al.  Bayesian tests to quantify the result of a replication attempt. , 2014, Journal of experimental psychology. General.

[13]  H. Pashler,et al.  Editors’ Introduction to the Special Section on Replicability in Psychological Science , 2012, Perspectives on psychological science : a journal of the Association for Psychological Science.

[14]  Eric-Jan Wagenmakers,et al.  An encompassing prior generalization of the Savage-Dickey density ratio , 2010, Comput. Stat. Data Anal..

[15]  E. Wagenmakers,et al.  Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method , 2010, Cognitive Psychology.

[16]  C. Davis-Stober Analysis of multinomial models under inequality constraints: Applications to measurement theory , 2009 .

[17]  S. Vyse,et al.  Science Versus the Stars: A Double-Blind Test of the Validity of the NEO Five-Factor Inventory and Computer-Generated Astrological Natal Charts , 2008, The Journal of general psychology.

[18]  Irene Klugkist,et al.  The Bayes factor for inequality and about equality constrained models , 2007, Comput. Stat. Data Anal..

[19]  Jay I. Myung,et al.  A Bayesian approach to testing decision making axioms , 2005 .

[20]  Herbert Hoijtink,et al.  Bayesian model selection using encompassing priors , 2005 .

[21]  S. Carlson A double-blind test of astrology , 1985, Nature.

[22]  J. Dickey,et al.  The Weighted Likelihood Ratio, Sharp Hypotheses about Chances, the Order of a Markov Chain , 1970 .

[23]  Michel Regenwetter,et al.  Heterogeneity and Parsimony in Intertemporal Choice , 2017 .

[24]  Daniel R. Cavagnaro,et al.  Transitive in Our Preferences, But Transitive in Different Ways: An Analysis of Choice Variability , 2014 .

[25]  Michel Regenwetter,et al.  Quantitative tests of the Perceived Relative Argument Model: comment on Loomes (2010). , 2014, Psychological review.