The universal notation for “the probability of A given B” is p(A | B). We were surprised to learn that the vertical stroke was first introduced by none other than… Sir Harold Jeffreys! At least Jeffreys himself seems to think so, and the sentiment is echoed on the website “Earliest Uses of Symbols in Probability and Statistics” Specifically, on page…
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What is commonly referred to as “Lindley’s paradox” exposed a deep philosophical divide between frequentist and Bayesian testing, namely that, regardless of the prior distribution used, high-N data that show a significant p-value may at the same time indicate strong evidence in favor of the null hypothesis (Lindley, 1957). This “paradox” is due to Dennis Lindley, one of the most…
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A number of years ago I compiled a writing checklist for students. Its primary purpose was to make my life easier, but the list was meant to be helpful for the students as well. The checklist is here. My pet peeves: (1) abrupt changes of topic; (2) poorly designed figures; (3) tables and figures that are not described properly in…
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The Misconception Posterior Bayes factors are a good idea: they provide a measure of evidence but are relatively unaffected by the shape of the prior distribution. The Correction Posterior Bayes factors use the data twice, effectively biasing the outcome in favor of the more complex model. The Explanation The standard Bayes factor is the ratio of predictive performance between two…
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One of the famous fallacies in deductive logic is known as “affirming the consequent”. Here is an example of a syllogism gone wrong: General statement When Socrates rises early in the morning, he always has a foul mood. Specific statement Socrates has a foul mood. Deduction (invalid) Socrates has risen early in…
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Back in 2011, Daryl Bem shocked the academic world by publishing an article in which he claimed to present empirical evidence for the existence of precognition, that is, the ability of people to “look into the future” (Bem, 2011). Particularly shocking was the fact that Bem had managed to publish this claim in the flagship journal of social psychology, the…
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Karoline Huth is a first-year student in our Psychology Research Master at the University of Amsterdam. This blog post describes her presentation for the recent course on Bayesian Inference for Psychology. The assignment was to conduct a Bayesian reanalysis of existing data. Kudos to Karoline for being brave enough to share her work here! [EJ] Presentation Intro and Background Bayesian…
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The Galton board or quincunx is a fascinating device that provides a compelling demonstration of one the main laws of statistics. In the device, balls are dropped from above onto a series of pegs that are organized in rows of increasing width. Whenever a ball hits a particular peg, it can drop either to the right or to the left,…
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