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

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875 views

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 ...
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0answers
16 views

Defining a paradox in proxy variables

I'm looking for a formal name or write-up of this phenomenon: When you are using a proxy variable (A) to measure a true variable (B), taking actions based on the proxy variable can decrease the ...
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1answer
47 views

What Are Some Historical Applied Stats Problems [closed]

What are some interesting, historical applied statistics problems ? i.e. sometime in the past that statistics have been used to affect the course of events? The kind of problems I am looking for ...
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0answers
85 views

A mathematical explanation of the Simpson's Paradox?

In general, Simpson's Paradox occurs because situations such as following occur for some arbitrary events $A, B,$ and $C$: $P(A|B,C) < P(A|B^c,C)$ $P(A|B,C^c) < P(A|B^c,C^c)$ But, $P(A|B) &...
2
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0answers
26 views

What basis should be used to devize a significance/hypothesis test?

I am trying to understand the basis of hypothesis testing and I came up with a paradox. Let me explain with an example. Consider the case of trying to determine whether is coin is fair. The null ...
3
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1answer
66 views

Probability to be the millionth customer (What Would You Do?)

I saw this episode of "What Would You Do?" a few months ago, and I keep wondering what would statistically be the best thing to do in this situation. Here is the problem formulation: You are waiting ...
19
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1answer
282 views

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 ...
3
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1answer
297 views

Simulating the waiting paradox

After seeing this question, I thought I would try to simulate the bus waiting time paradox to help my understanding. However, what I got was the "intuitive" result, rather than that predicted by the ...
46
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4answers
9k views

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 ...
1
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0answers
70 views

Simpson's Paradox with new sample

Suppose you constructing model whose training data is cumulative in nature; meaning each year you can add new observations with all prior observations being kept the same. (e.g. training set is non-...
1
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1answer
226 views

Unkown 6-sided dice. After 600 rolls frequency for all sides exactly equal. What is the chance, that rolling “6” with this dice has frequency > 1/6?

Although it is unknown dice, the symmetry of the evidence tells us, that we can treat the dice as fair, so the chance should be exactly 50%. But if we simulate it by hand, the result is less then 50%:...
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6answers
3k views

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. ...
5
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3answers
327 views

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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1answer
131 views

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 ...
12
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2answers
344 views

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 ...
0
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2answers
99 views

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 ...
5
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1answer
458 views

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 ...
93
votes
19answers
22k views

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, ...
13
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2answers
363 views

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 ...
6
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4answers
6k views

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 ...
5
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1answer
435 views

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 ...
85
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19answers
20k views

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.