The p-value ritual

The p-value and its implicit symbolism

The Aristotelian conditional syllogistic logic behind the Fisherian p-value is widely misunderstood which leads to fallacious logical inferences. The p-value resembles a Kantian paralogism, i.e., it appears objective and logically valid even though it is not. The p-value is an irrational social ritual (cf. Gigerenzer, 2004). Social conformity, obedience to authority, groupthink, and other aspects of Social Identity Theory (SIT) play an important role in this context.

Given the well-documented paralogisms associated with classical Fisherian null hypothesis significance testing (cf. Cohen, 1994) I advocate alternative inferential research methods. For the statistical analyses of the experimental data I collected during my PhD I utilised Bayesian bootstrapping, Bayes Factor analysis, and Bayesian parameter estimation via Markov chain Monte Carlo simulations (in addition to classical NHST).

“Few researchers are aware that their own heroes rejected what they practice routinely. Awareness of the origins of the ritual and of its rejection could cause a virulent cognitive dissonance, in addition to dissonance with editors, reviewers, and dear colleagues. Suppression of conflicts and contradicting information is in the very nature of this social ritual.”
(Gerd Gigerenzer, 2004, p. 592; Director Emeritus of the Center for Adaptive Behavior and Cognition at the Max Planck Institute for Human Development, inter alia)

Statistical Research Methods workshop at the University of Plymouth in 2014:
The pitfalls of hypothesis testing

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The primary objective of prep is to provide an estimate of replicability (based on the empirical data) which does not involve Bayesian assumptions with regards to a priori distributions of θ. The submission guidelines of the APA flagship journal 'Psychological Science' for some time explicitly encouraged authors to “use prep rather than p-values” in the results section of their articles. This factoid is documented in the internet archive, a digital library which provides a mnemonic online system containing the history of the web, a “digital time machine” (Rackley, 2009; Rogers, 2017). However, this official statistical recommendation by Psychological Science has now been retracted (but the internet never forgets…).

The URL of the relevant internet archive entry is as follows:

By default, (...)

"...lying full length on the back like a corpse is called Savasana. With this asana, tiredness caused by other asanas is eliminated; it also promotes calmness of the mind."
~ Hatha Yoga Pradipika 1.32
Shavasāna (Sanskrit: शवासन; transl. "corpse pose") is an asana in hatha yoga which is often used at the end of a series of asanas for deep relaxation and meditation.

Thönes, S., & Wittmann, M.. (2016). Time perception in yogic mindfulness meditation—Effects on retrospective duration judgments and time passage.. Psychology of Consciousness: Theory, Research, and Practice, 3(4), 316–325.
Plain numerical DOI: 10.1037/cns0000088

“Over the last few years, several studies investigated possible effects of mindfulness meditation on the perception of time. however, these effects (...)


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Definition of Type I error:
Probability of rejecting null hypothesis when it is TRUE.

Definition of Type II error:
Probability of not rejecting null hypothesis when it is False.

Imagine tests on 1000 hypotheses 100 of which are true.

The tests have a false positive rate of 5%. That means they produce 45 false positives (5% of 900). They have a power of .8, so they can confirm only 80 of the true hypotheses, producing 20 negatives.

Not knowing what is false and what is not the researcher sees 125 hypotheses as true, 45 of which are not. The negative results are much more reliable but less likely to be published.

A parable concerning editorial policies

There's this desert prison, see, with an old prisoner, resigned to his life, and a young one (...)

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