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Bayesian Advantages for the Pragmatic Researcher: Slides from a Talk in Frankfurt

This Monday in Frankfurt I presented a keynote lecture for the 51th Kongress der Deutschen Gesellschaft fuer Psychologie. I resisted the temptation to impress upon the audience the notion that they were all Statistical Sinners for not yet having renounced the p-value. Instead I outlined five concrete Bayesian data-analysis projects that my lab had conducted in recent years. So no p-bashing, but only Bayes-praising, and mostly by directly demonstrating the practical benefits in concrete application.

The talk itself went well, although at the beginning I believe the audience was fearful that I would just drone on and on about the theory underlying Bayes’ rule. Perhaps I’m just too much in love with the concept. Anyway, it seemed the audience was thankful when I switched to the concrete examples. I could show a new cartoon by Viktor Beekman (“The Two Faces of Bayes’ Rule”, also in our Library; concept by myself and Quentin Gronau), and I showed two pictures of my son Theo (not sure whether the audience realized that, but it was not important anyway).

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Redefine Statistical Significance XVII: William Rozeboom Destroys the “Justify Your Own Alpha” Argument…Back in 1960

Background: the recent paper “Redefine Statistical Significance” suggested that it is prudent to treat p-values just below .05 with a grain of salt, as such p-values provide only weak evidence against the null. The counterarguments to this proposal were varied, but in most cases the central claim (that p-just-below-.05 findings are evidentially weak) was not disputed; instead, one group of researchers (the Abondoners) argued that p-values should simply be undervalued or replaced entirely, whereas another group (the Justifiers) argued that instead of employing a pre-defined threshold α for significance (such as .05, .01, or .005), researchers should justify the α used.

The argument from the Justifiers sounds appealing, but it has two immediate flaws (see also the recent paper by JP de Ruiter). First, it is somewhat unclear how exactly the researcher should go about the process of “justifying” an α (but see this blog post). The second flaw, however, is more fundamental. Interestingly, this flaw was already pointed out by William Rozeboom in 1960 (the reference is below). In his paper, Rozeboom discusses the trials and tribulations of “Igor Hopewell”, a fictional psychology grad student whose dissertation work concerns the study of the predictions from two theories, T_0 and T_1. Rozeboom then proceeds to demolish the position from the Justifiers, almost 60 years early:

“In somewhat similar vein, it also occurs to Hopewell that had he opted for a somewhat riskier confidence level, say a Type I error of 10% rather than 5%, d/s would have fallen outside the region of acceptance and T_0 would have been rejected. Now surely the degree to which a datum corroborates or impugns a proposition should be independent of the datum-assessor’s personal temerity. [italics ours] Yet according to orthodox significance-test procedure, whether or not a given experimental outcome supports or disconfirms the hypothesis in question depends crucially upon the assessor’s tolerance for Type I risk.” (Rozeboom, 1960, pp. 419-420)

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