Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [paradox]

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

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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, they will put you back to sleep with a drug that…
whuber
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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.
Nick
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At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?

The question (slightly modified) goes as follows and if you have never encountered it before you can check it in example 6a, chapter 2, of Sheldon Ross' A First Course in Probability: Suppose that we possess an infinitely large urn and an infinite …
Carlos Cinelli
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Please explain the waiting paradox

A few years ago I designed a radiation detector that works by measuring the interval between events rather than counting them. My assumption was, that when measuring non-contiguous samples, on average I would measure half of the actual interval.…
Stephen Sackett
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Famous easy to understand examples of a confounding variable invalidating a study

Are there any well-known statistical studies that were originally published and thought to be valid, but later had to be thrown out due to a confounding variable that wasn't taken into account? I'm looking for something easy to understand that…
NathanLite
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What is the Wine/Water Paradox in Bayesian statistics, and what is its resolution?

I have just heard about the Wine/Water Paradox in Bayesian statistics, but didn't understand it very well (see Mikkelson 2004 for an introduction). Can you explain in simple terms what the paradox is (and why is it a paradox), why it matters for…
user314217
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Paradox in model selection (AIC, BIC, to explain or to predict?)

Having read Galit Shmueli's "To Explain or to Predict" (2010) and some literature on model selection using AIC and BIC, I am puzzled by an apparent contradiction. There are three premises, AIC- versus BIC-based model choice (end of p. 300 - start…
Richard Hardy
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Average value paradox - What is this called?

I have a dataset. Say $10$ observations and $3$ variables: obs A B C 1 0 0 1 2 0 1 0 3 1 0 1 4 1 1 0 5 1 0 1 6 1 0 0 7 1 1 0 8 0 0 1 9 0 1 1 10 0 1 1 Say that is $10$…
James Adams
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Does Stein's Paradox still hold when using the $l_1$ norm instead of the $l_2$ norm?

Stein's Paradox shows that when three or more parameters are estimated simultaneously, there exist combined estimators more accurate on average (that is, having lower expected mean squared error) than any method that handles the parameters…
Craig Feinstein
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Two envelope problem revisited

I was thinking of this problem. http://en.wikipedia.org/wiki/Two_envelopes_problem I believe the solution and I think I understand it, but if I take the following approach I'm completely confused. Problem 1: I will offer you the following game. You…
evan54
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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 since the problem does not specify an orientation…
Neil G
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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 Democratic than poor states. Is there a name for…
Peter Flom
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How to program a Monte Carlo simulation of Bertrand's box paradox?

The following problem has been posted on Mensa International Facebook Page: $\quad\quad\quad\quad\quad\quad\quad\quad$ The post itself received 1000+ comments but I won't go into details about the debate there since I know this is Bertrand's box…
Anastasiya-Romanova 秀
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Blackwell's bet

I have read about Blackwell's bet paradox on Futility closet. Here is the summary: you are presented with two envelopes, $E_x$ and $E_y$. The envelopes contain a random amount of money, but you don't know anything about the distribution about the…
January
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Abraham Wald survivorship bias intuition

During World War II, the statistician Abraham Wald took survivorship bias into his calculations when considering how to minimize bomber losses to enemy fire. Wald noted that the study only considered the aircraft that had survived their missions;…
Luis P.
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