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The Monty Hall Problem has struck again, and this time it’s not merely embarrassing mathematicians. If the calculations of a Yale economist are correct, there’s a sneaky logical fallacy in some of the most famous experiments in psychology.
The economist, M. Keith Chen, has challenged research into cognitive dissonance, including the 1956 experiment that first identified a remarkable ability of people to rationalize their choices.
[snip]
For half a century, experimenters have been using what’s called the free-choice paradigm to test our tendency to rationalize decisions. This tendency has been reported hundreds of times and detected even in animals.
And Behind Door Number 1, A Fatal Flaw
John Tierney
NY Times April 8, 2008
death by data
bonus points: After you play the Monty Hall game online you can fire up the National Geographic jigsaw generator.
And don't forget Glumbert.
low birth weight & Monty Hall
more on false positives
Monty Hall part 2
Monty Hall in Curious Incident
Doug Sundseth on Monty Hall problem
probability question from Saxon Math
5 comments:
Here's something cool. Back when we were all first writing about the Monty Hall problem I could barely grasp it. It was a huge struggle.
Today I still didn't predict what Tierney was going to say while reading the article (I'd forgotten the details of the Monty Hall problem), but the instant I looked at the graphic, I got it. I'm radically ahead of where I was.
That was a great feeling.
Well, that's terrific that you instantly got it--now if only the psych academics and economists would!
This is a really important finding. It points out the problem with most social sciences: econometrics and other statistics courses simply aren't enough to teach math and science to the level that's really needed to create valid experiments.
how many more invalid experiments are out there? Thousands? more?
The statistical explanation in the picture above for the M&Ms is really simple and clear--all it took was properly enumerating the "State space" as it's called. But knowing the right state space is DIFFICULT. combinatorics and probability theory are DIFFICULT. They are often mistaught even at the college level. But the idea that we can ignore math and just compute some T statistic is deep in the social sciences. Fixing this will take generations--most of the psychologists of today won't even understand why there's a problem in the first place.
well --- "I got it" meaning I followed the explanation.
I agree with you about stats -- one of my major goals is to learn enough math to take a good statistic course (or more - I don't even know what I need to take in order to be able to read social science studies intelligently).
combinatorics and probability theory are DIFFICULT. They are often mistaught even at the college level. But the idea that we can ignore math and just compute some T statistic is deep in the social sciences.
AND -- (this is where I can't not have sympathy for the new tenure law) we have now entered the era of data mining and data warehousing in schools and the people being hired to do this don't even know high school algebra.
You should look at some of the books on sale at Amazon. They have titles like, "Using data to improve instruction made easy" (not that exactly, but that idea).
Schools are buying software packages, plugging in numbers, and assuming they've just described reality.
Of course, hailing from SPED, I know how to fight back: get my kid tested and bring my own data.
That's what we did in the science meeting where the chair of the entire science department tried to tell us C. doesn't think conceptually or inferentially. He'd been tested; his scores were very high.
Of course, that had no effect on their behavior but it did undermine the "narrative," which is the best one can hope for.
The abuse of statistics and software is breathtaking.
Our report card software comes with a "Comment Bank" that allows teachers to punch in comments about our kids' ability to think.
I'm going to push them on this.
One can make an argument that they're skating on thin ice; they're close to triggering the Child Find provision in SPED law.
("Child Find" means a school has a duty to identify children who need services.)
I don't think you could make this argument stick in court (although I wouldn't bet against it, either), but I do think no district wants the headache of a parent saying, "If my child can't think well enough to succeed in this course you need to spend $10,000 testing him & writing up a formal report."
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