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Why psychologists must change the way they analyze their data: the case of psi: comment on Bem (2011).

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TLDR
It is concluded that Bem's p values do not indicate evidence in favor of precognition; instead, they indicate that experimental psychologists need to change the way they conduct their experiments and analyze their data.
Abstract
Does psi exist? D. J. Bem (2011) conducted 9 studies with over 1,000 participants in an attempt to demonstrate that future events retroactively affect people’s responses. Here we discuss several limitations of Bem’s experiments on psi; in particular, we show that the data analysis was partly exploratory and that one-sided p values may overstate the statistical evidence against the null hypothesis. We reanalyze Bem’s data with a default Bayesian t test and show that the evidence for psi is weak to nonexistent. We argue that in order to convince a skeptical audience of a controversial claim, one needs to conduct strictly confirmatory studies and analyze the results with statistical tests that are conservative rather than liberal. We conclude that Bem’s p values do not indicate evidence in favor of precognition; instead, they indicate that experimental psychologists need to change the way they conduct their experiments and analyze their data.

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References
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Book

Theory of probability

TL;DR: In this paper, the authors introduce the concept of direct probabilities, approximate methods and simplifications, and significant importance tests for various complications, including one new parameter, and various complications for frequency definitions and direct methods.
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Probability theory : the logic of science

TL;DR: In this article, a survey of elementary applications of probability theory can be found, including the following: 1. Plausible reasoning 2. The quantitative rules 3. Elementary sampling theory 4. Elementary hypothesis testing 5. Queer uses for probability theory 6. Elementary parameter estimation 7. The central, Gaussian or normal distribution 8. Sufficiency, ancillarity, and all that 9. Repetitive experiments, probability and frequency 10. Advanced applications: 11. Discrete prior probabilities, the entropy principle 12. Simple applications of decision theory 15.
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