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Psychologists Don't Know Math
stupefaction writes "The New York Times reports that an economist has exposed a mathematical fallacy at the heart of the experimental backing for the psychological theory of cognitive dissonance. The mistake is the same one that mathematicians both amateur and professional have made over the Monty Hall problem. From the article: "Like Monty Hall's choice of which door to open to reveal a goat, the monkey's choice of red over blue discloses information that changes the odds." The reporter John Tierney invites readers to comment on the goats-and-car paradox as well as on three other probabilistic brain-teasers."
The psychologists were claiming that if you choose X over Y then you are more likely to choose Z over Y because your *choice* causes bias against Y. (This fits the observed data).
The new suggestion is that if you choose X over Y then you are more likely to choose Z over Y because the choice indicates prior bias against Y. The important part being that this holds even if the bias against Y is so small that it is hard to detect. The only thing required is that there is a fixed "preferred order" of the three.
At least, that's what I understand from the article. Given the field, I also understand that I am most probably wrong :)
Marilyn vos Savant explained the problem in Parade magazine, and a whole bunch of math professors wrote in to tell her that she was wrong... turns out it's kind of a bad idea to play "gotcha" with someone who has an IQ of 228.
This reminds me the story my high school teacher told me:
Some researchers involved in pchycology (social behaviour etc.) came to high schools and drew up the friendship graph of the class. (Maybe school works differently where you live, we had a class of size 30-40 students attending exactly the same lectures.)
They assumed friendship to be mutual (if not, than it was not considered friendship). One clever cookie made the observation that almost always there is a group of 6 students who all friends to each other (a clique), or alternatively a group of 4 students, who do not like each other.
There were excited discussions among the researchers what social forces are the reason that one of the above situations always seemed to occur.
They were somewhat disillusioned when our math teacher explained them Ramsey's theorem. Since R(6, 4) is between 35 and 41, indeed one can expect either a frienship or hateship clique to appear with quite high probability... (This does not mean that properties of the frienship graph worth not examining, but one needs to know the math to do it properly.)
Indeed. There's considerable evidence in favor of reductions in cognitive dissonance as a motivating psychological force from other types of studies and other disciplines. For instance, in my field of political science, the evidence is pretty overwhelming that citizens systematically misperceive candidates' positions to make them more similar to the citizens' own preferences. Voters often engage in "projection," believing that candidates' they prefer hold positions like the voters' own, even when those aren't the positions the candidates actually hold. The opposite process also occurs, where voters believe that candidates they dislike hold positions those voters dislike regardless of the candidates' true preferences. My own dissertation research on voters for the British Liberal Party in the 1960's and 1970's also confirmed these hypotheses.
TFA has been adequately refuted, so I'll forego more on that. And despite the inflammatory nature of the title and claims here, it is unfortunately too correct too often.
.05 significance level to have an individual p value in the 10^-6 to 10^-9 range. That's a hell of a requirement for a single test, and very unlikely to actually exist. "Figure the odds" applies, and they don't seem to grasp that they don't grasp it.
I've been told by "superiors" to perform certain analyses because "everyone does", and they gave me references which supposedly showed these were proper. When I looked these up, the authors not only made no claims supporting their necessity, but both stated that the researcher should know enough about what they're doing to know what analyses to perform. I took my instructions to the statistics consultant for our department, and without showing him the references he made the same claims as both authors, contradicting the rationale given by those who gave me the instructions. I've seen many cases of psychologists performing statistical analyses based on their knowledge of how to use SPSS et al., rather than any fundamental grasp of the maths required by the design. Perhaps the most egregious error is their faith in fMRI analyses via statistical probability mapping, when the correction factor required by the 10^4 to 10^5 simultaneous T-tests makes any one result within the traditional collective p >
On the other hand, some of us can apply such analyses as tensor calculus and Gabor transforms to dendritic electrical fields, showing where each of those are correct and where each fail, and can correctly apply nonlinear, N-dimensional statistical testing of time/frequency maps produced by continuous wavelet transform. But of those of us who can do these things, I know of none who learned of them, much less how, within the confines of a psychology department. (Well, except for the Gabor stuff, as used and taught by Karl Pribram, that being the only case I know of).
"Everything I Needed To Know I Learned At The Santa Fe Institute". No, not everything, but that'd make a hell of a book.
"I may be synthetic, but I'm not stupid." -- Bishop 341-B
(That last pair of points are important. Monkeys do not see all colours with equal clarity. Neither do humans, which is why monitors actually have more real-estate set aside for blue than for anything else. Complicating things, colours are usually the product of mixing. They are not "pure". We don't know what the monkeys saw, therefore cannot tell if their decision was influenced by their ability to even see the treats.)
Personally, I have developed a skepticism of such observational science. Too many possible explanations, yes, but more importatly too little experimentation to eliminate alternatives. If an explanation is put forward and then acted upon, especially in an area like psychology where those being acted upon are likely vulnerable groups, it's important to make sure the explanation is likely to be correct. Likely to be possible isn't good enough.
What would I suggest? Well, in the 1950s through to the last few years, options have been limited. These days, though, you can take fMRIs, MRIs and CAT scanners into the field. During the Chernobyl accident, it was fairly standard procedure for MRIs on trucks to be used to scan farm animals for contamination. See the brain in action as it makes the choices. See when the choice is made and which neural pathways were involved. Much better than speculating about what's going on. If you want more data, scientists decoded the optic fibre transmissions of cats ten years ago, or thereabouts. We can literally see if that plays a part in the decision.
You still end up doing statistics, sure, but with far more numbers that have far more meaning behind them and far less room for interpretation.
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
The percentages were a joke. But I do mean in all seriousness to suggest that psychology researchers are often averse to math and tolerate math errors in papers. Psychology is often only quantitative insofar as there are certain numerical rituals associated with null hypothesis significance testing that researchers must use to be accepted by other researchers.
It's kind of depressing, so I try to make light of it when I can.
I find it even funnier that it is an economist that is saying it. Admittedly some economists are really mathematicians that have wandered in to try to bring some professionalism to a bunch of fortune tellers but in general economists have a bad reputation every time there is an attempt to assert itself as a science. Years ago when I had the misfortune to do an engineering economics subject I was astounded to find that the university level economics text we were using had one version of the compound interest formula for every variable - it was assumed that economics students could not do introductory algebra.
Here's an even better problem:
Suppose Monty Hall gives you a choice of two envelopes. Each envelope contains a check, and one of them is written for TWICE the amount of the other. So you pick an envelope.
Now, Monty gives you the chance to switch envelopes. (Assume Monty always gives you the chance to switch.) Logically, since your envelope contains X, the other envelope can contain either 0.5X or 2X, with 50% probability... So the expected value of switching envelopes is 50% (0.5X + 2X), or 1.25X. So, you should switch.
But here's the tricky part: Monty now gives you the chance to switch back! Since your new envelope contains Y, then by the same logic as above, the expected value of switching back is 1.25Y... So you should switch back. Right?
Clearly, something is wrong with this chain of thinking. Can you figure out what it is?
Weeks of coding saves hours of planning.