Blog Archives

Blue Bonnet Bayes

October 28, 2014
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Blue Bonnet Bayes

Blue Bonnet™ used to run commercials with the jingle “Everything’s better with Blue Bonnet on it.” Maybe they still do. Perhaps in reaction to knee-jerk antipathy toward Bayesian methods, some statisticians have adopted knee-jerk enthusiasm for Bayesian methods. Everything’s better with Bayesian analysis on it. Bayes makes it better, like a little dab of margarine […]

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How well does sample range estimate range?

October 25, 2014
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How well does sample range estimate range?

I’ve been doing some work with Focused Objective lately, and today the following question came up in our discussion. If you’re sampling from a uniform distribution, how many samples do you need before your sample range has an even chance of covering 90% of the population range? This is a variation on a problem I’ve […]

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Common sense and statistics

September 18, 2014
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College courses often begin by trying to weaken your confidence in common sense. For example, a psychology course might start by presenting optical illusions to show that there are limits to your ability to perceive the world accurately. I’ve seen at least one physics textbook that also starts with optical illusions to emphasize the need […]

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Intuition and Data at KeenCON

August 14, 2014
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Intuition and Data at KeenCON

I will be giving a talk “Bayesian statistics as a way to integrate intuition and data” at KeenCon, September 11, 2014 in San Francisco. Update: Use promo code KeenCon-JohnCook to get 75% off registration.

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Chances of being picked twice for drug testing

June 18, 2014
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Chances of being picked twice for drug testing

Suppose in a company of N employees, m are chosen randomly for drug screening [1]. In two independent screenings, what is the probability that someone will be picked both times? It may be unlikely that any given individual will be picked twice, while being very likely that someone will be picked twice. Imagine m employees […]

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Normal approximation details

May 29, 2014
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The normal distribution can approximate many other distributions, though the details such as quantitative error estimates and what factors improve or degrade the approximation are harder to find. Here are some notes on normal approximations to several ...

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Robust in one sense, sensitive in another

May 14, 2014
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When you sort data and look at which sample falls in a particular position, that’s called order statistics. For example, you might want to know the smallest, largest, or middle value. Order statistics are robust in a sense. The median of a sample, for example, is a very robust measure of central tendency. If Bill […]

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Distribution of a range

April 23, 2014
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Suppose you’re drawing random samples uniformly from some interval. How likely are you to see a new value outside the range of values you’ve already seen? The problem is more interesting when the interval is unknown. You may be trying to estimate the end points of the interval by taking the max and min of […]

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Timid medical research

April 15, 2014
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Cancer research is sometimes criticized for being timid. Drug companies run enormous trials looking for small improvements. Critics say they should run smaller trials and more of them. Which side is correct depends on what’s out there waiting to be discovered, which of course we don’t know. We can only guess. Timid research is rational […]

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The mean of the mean is the mean

April 9, 2014
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The mean of the mean is the mean

There’s a theorem in statistics that says You could read this aloud as “the mean of the mean is the mean.” More explicitly, it says that the expected value of the average of some number of samples from some distribution is equal to the expected value of the distribution itself. The shorter reading is confusing […]

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