Statistics & Probability
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Richard Feynman once said that, unfortunately, you'll never really be able to understand how the world works unless you master the mathematics (quantum mechanics, general relativity). Similarly, to be a critical thinker, you have to master a certain amount of mathematics, especially in the areas of statistics and probability. Fortunately, this mathematics is generally more accessible than quantum mechanics!
Chance by J. Laurie Snell and the Chance Team.
"Welcome to Chance! This site contains materials to help teach a Chance course...The goal of Chance is to make students more informed, critical readers of current news stories that use probability and statistics." This is a very rich resource. See especially their email newsletter Chance News, and their video and audio section.
Statistics every writer should know by Robert Niles
"Here, described in plain English, are some basic concepts in statistics that every writer should know..."
Statistical Assessment Service
"The Statistical Assessment Service (STATS) is a non-partisan, non-profit research organization in Washington, D.C. STATS is devoted to the accurate use of scientific and social research in public policy debate. STATS serves as a resource for journalists by providing timely and well-researched analysis of current statistical and scientific disputes. Since STATS seeks to weed out bad data and research before it enters the media stream, we field queries from journalists on a regular basis. Our routine interaction with the broader media is through our monthly newsletter, VitalSTATS: The Numbers Behind the News. We also publish opinion articles, which can be found in our Newsclips." [22 Feb 02]
Numberwatch by John Brignell
"All about the scares, scams, junk, panics, and flummery cooked up by the media, politicians, bureaucrats, so-called scientists and others who try to confuse you with wrong numbers." Includes [wrong] Number of the Month.
Probability Puzzles by Alex Bogomolny
Interactive widgets teaching about many fascinating puzzles and paradoxes of probability
How Polls are Conducted
Another very nice overview of the art of polling. This one from The Gallup Organization, who should know a thing or two about it.
The Vitality of Mythical Numbers by Max Singer
Classic essay about how exaggerated numbers get "made up" and then circulated, and how people fail to ask what they evidence is for them, or whether they are reasonable. [20 Aug 06]
Introduction to Probability by Charles M. Grinstead & J. Laurie Snell
An entire, 500+ page textbook on probability. Designed for use in a one-semester college course. Not the best "self-help" guide for novices, but could be a very useful resource for those who already have some familiarity with probability and are comfortable with a moderately technical treatment. [20 Oct 03]
Who's Counting by John Allen Paulos and ABCNEWS.com
An excellent collection of short newspaper columns on how thinking can go wrong, with particular focus on statistics & probability.
Do the Math by Jordan Ellenberg, Slate Magazine
Similar to Who's Counting, but slightly more substantial. Using very interesting topical examples, the column illustrates how mathematically sophisticated thinkers think about issues requiring critical thinking.
The Odds of That by Lisa Belkin
What are the odds of that? Well, actually, considerably higher than you think... A fascinating essay describing our cognitive biases in thinking about coincidences, and relating those topics to terrorism and conspiracy theories. "Most often, though, coincidence is a sort of Rorschach test. We look into it and find what we already believe." [10 Aug 02]
Telling the Truth About Damned Lies and Statistics by Joel Best
"The solution to the problem of bad statistics is not to ignore all statistics, or to assume that every number is false. Some statistics are bad, but others are pretty good, and we need statistics -- good statistics -- to talk sensibly about social problems. The solution, then, is not to give up on statistics, but to become better judges of the numbers we encounter. We need to think critically about statistics -- at least critically enough to suspect that the number of children gunned down hasn't been doubling each year since 1950..."
The Median Isn't The Message by Stephen Jay Gould
Classic. "In 1982, I learned I was suffering from a rare and serious cancer. After surgery, I asked my doctor what the best technical literature on the cancer was. She told me, with a touch of diplomacy, that there was nothing really worth reading. I soon realized why she had offered that humane advice: my cancer is incurable, with a median mortality of eight months after discovery. The problem may be briefly stated: What does "median mortality of eight months" signify in our vernacular? I suspect that most people, without training in statistics, would read such a statement as "I will probably be dead in eight months" the very conclusion that must be avoided, since it isn't so."
Shooting Crap by Shari Waxman
"Alleged psychic John Edward...has not fessed up to all of his talents. As it happens, he is more than a psychic medium; he is also a master statistician. The smoke and mirrors behind his self-professed ability to communicate with the dead is a simple application of the laws of probability...The art of intelligence insulting has rarely known such mastery." [18 Jun 02]
We've Got More Risk Than Our Brains Can Handle by Henry Petroski
Nice essay, describing how our reactions to risk are, unavoidably, governed by emotions, qualitative interpretations, and politics. Finishes by urging that "our elected leaders and decision makers are well prepared to deal with those components of risk assessment." Unfortunately, he provides no practical advice for making that happen. [29 Jun 02]
Simple tools for understanding risks: from innumeracy to insight by Gerd Gigerenzer
Useful guide by Mr. "Statistics Made Simple" himself. "Bad presentation of medical statistics such as the risks associated with a particular intervention can lead to patients making poor decisions on treatment. Particularly confusing are single event probabilities, conditional probabilities (such as sensitivity and specificity), and relative risks. How can doctors improve the presentation of statistical information so that patients can make well informed decisions?" [30 Sep 03]
Crunched by numbers by Theodore Dalrymple - review of Reckoning with Risk by Gerd Gigerenzer
Gigerenzer has very important things to say, and Dalrymple is a brilliant essayist. This review contains much pithy insight into the importance of good statistical thinking. "equivocal situations are frequent in modern medicine, as indeed they are in other spheres of life. In order to understand them and make fully informed decisions, a comprehension of statistical reasoning is essential: a comprehension that the author of this truly indispensable book says is lacking among doctors, patients, lawyers and politicians, indeed among almost everyone who needs it. He is probably right (he can prove it with statistics as well as by anecdote) and they all ought to read his book forthwith." [22 July 02]
Last updated: 22 Jun 2007