A paradox is a statement or proposition that seems self-contradictory or absurd but in reality expresses a possible truth.

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A seeming paradox with rational agents not coming to the same conclusion given the same data

So one day after a tasty dinner full of bananas, an idea comes to your mind (you are person A) - "What if eating bananas can cure cancer?". Being a scientist at heart, you conduct a double blind study ...
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Possible Paradox: Calculating a confidence interval with within-experiment error

This is a spinoff of How to calculate the confidence interval of the mean of means? and related to When making inferences about group means, are credible Intervals sensitive to within-subject ...
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Name of the “paradox” reported by Gelman

In Andrew Gelman's book "Red State, Blue State" he analyzes the fact that rich people within particular states tend to vote more Republican than poor people, but that wealthy states tend to vote more ...
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Question about Harrington paradox

Model The firm and enforcement agency interact in more than one domain. This may arise because a single agency is responsible for enforcing more than one regulation or because it enforces the same ...
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Swapping X and Y in a regression that contains a grouping predictor?

Suppose I'm doing a linear regression and I want to investigate how the association between a predictor X and a response Y changes according to levels of a 2-level factor G. The model would look like ...
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The Sleeping Beauty Paradox

The situation Some researchers would like to put you to sleep. Depending on the secret toss of a fair coin, they will briefly awaken you either once (Heads) or twice (Tails). After each waking, ...
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Does the principle of indifference apply to the Borel-Kolmogorov paradox?

Consider Jaynes' solution to the Bertrand paradox using the principle of indifference. Why doesn't a similar argument apply to the Borel-Kolmogorov paradox? Is there something wrong with arguing that ...
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What will be the correct answer, if we modify the “Best statistics question ever”?

There is a popular question, called "Best statistics question ever". If you choose an answer to this question at random, what is the chance you will be correct? A) 25% B) 50% C) 60% D) 25% This ...
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Why can't we trust our intuition with probability?

If ever there was a case where this become clear is with the Monty Hall problem. Even the great Paul Erdos got fooled by this problem. My question which may be difficult to answer is what is it ...
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Most interesting statistical paradoxes

Because I find them fascinating, I'd like to hear what folks in this community find as the most interesting statistical paradox and why.