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."

Nice try!

[geekoid]

Like I'm going to click on a link with the word 'goat' in it.

Dude

[bogie]

What the hell are you talking about?

Re:Nice try!

[Ilan Volow]

It's never a good sign when the words "reveal" and "Monty" are in the same sentence.

Re:Nice try!

[mrbluze]

on the goats-and-car paradox...

In journals where this phenomenon is referred to frequently, the paradox is frequently abbreviated to goats-x

Don't worry.

[ZombieRoboNinja]

I got my facts from the infinitely more trustworthy Wikipedia.

http://en.wikipedia.org/wiki/Monty_hall_problem [wikipedia.org]

Pot, Kettle, Black

[ryu1232]

I started questioning this article before the end of the first sentence. An Economist, calling a Psychologist "wrong" about math?
One should remember what happens when you put 50 economists in a room - you get 100 opinions - one for each hand.
I recognize that the author of the article may be correct, I just couldn't help commenting on the first sentence.

Cognitive Dissonance

[jdbolick]

Amusingly, cognitive dissonance theory predicts that psychologists will rationalize their error and insist that it doesn't invalidate their conclusions.

Re:Dude

[u8i9o0]

What the hell are you talking about?

Yeah, no kidding.

The "Monty Hall problem" link in the summary informed me that I need Flash to understand the problem.
However, on that page they then offer "Need to know more? 50% off home delivery of The Times."

This confuses me terribly - if I now pick the home delivery choice, does the probability of learning about the Monty Hall problem go down 50%?

Damn - I should have picked the Flash answer from the start. :(

Re:Hmmm....

[Gat0r30y]

2) The issue seems easy enough to settle empirically, given a few monkeys and a bag of M&Ms, besides the fact that it seems to have been empirically settled decades ago anyway.

One would think, but as it turns out, there are too many complexities. You see, you have to consider the socio-economic background of the monkeys, their upbringing, and their inherent biases to figure out if they like green, blue or red M&M's best. You see, the monkeys have an inherent bias toward green, but only if they have been captured from the wild (where presumably green would be comforting, the color of trees and whatnot). And of course there is the political bias associated with red and blue, so it depends on whether the monkey's political biases. These are especially hard to sort out as monkeys tend to just throw feces at the other side, at every opportunity, so you can easily separate the two groups, but rarely can you tell which is which. Its difficult to determine if they like to eat blue M&M's because they themselves are blue (or feel blue, as depressed monkeys have a significant bias toward the blue M&M's) or because they are red as it were, and feel like eating the blue ones to get back at the other side.

Re:The problem is a fallacy

[Anonymous Coward]

This is analogous to observing that a lottery ticket can either be a winning ticket or a losing ticket, and then concluding that the odds of winning the lottery are 1 in 2.

Sweet!
I'm totally buying two tickets.

Re:I dislike things that "seem".

[jd]

I wondered why the contrast seemed a bit off. Thanks.

Inaccurate?

[jpfed]

As someone who majored in psychology, worked in two labs, and read countless psychology papers, I can tell you that 99% of psychologists avoid math when possible, and the other 10% try to use it but make obvious errors.

To the psychology researcher, it's more about getting the "story" right than actually quantifying anything.

Re:To be fair, mathemeticians didn't know math eit

[Anonymous Coward]

I remember a magazine called parade here in the UK when I was in my teens. To be honest I don't recall seeing any maths articles though, but to be honest I only looked at the pictures :D

Re:Inaccurate?

[djp928]

It was either a joke, or another data point.

Re:Pot, Kettle, Black

[squidfood]

you get 100 opinions - one for each hand.

But if they reveal their opinions, should you switch hands?

Re:To be fair, mathemeticians didn't know math eit

[Cajun Hell]

I read one of Marilyn Vos Savant's books, and in it she listed 9 as a prime...

But there's a more-than-50% chance that 9 is prime!

I test primeness by dividing the test-number by all integers, from 2 through the test-number's square root, looking for a zero remainder. So, first, I divided 9 by 2. I worked on this for a while, and ended up with a nonzero remainder. So far, 9 looks prime, and I've already tested half of the potential divisors! In fact, there's just one more potential divisor to try: the number 3. I'm almost done, and everything rides on this final calculation. There's a lot of uncertainty here.

What are the chances that 9 is just going to happen to be divisible by the very last potential divisor that I try? I'll grant you that the chances are non-zero; there really are some composite numbers out there. But the chances aren't one, either. For example, when I was testing 17 for primeness, the last potential divisor I tried was 4, and it didn't work. This last calculation could go either way.

So here we are, having tested half of the possible divisors, and so far 9 is looking prime and there's just one more divisor to test against. So, I ask you: do you want to bet 9's primeness/compositeness on this last calculation? I'll make it easier for you: I tell you right now, that 9 is just like 17, in that it is not divisible by 4. And then, I'll even give you an option: we can finish the calculation by dividing 9 by 3, or you can change your candidate divisor to 5, now that you know 4 doesn't work. Well.. what'll it be?

Re:Nice try!

[Tablizer]

Like I'm going to click on a link with the word 'goat' in it.

In the puzzle, I clicked on the car instead to avoid goat links. However, the car had a huge ugly rusted gaping hole in the back bumper, dripping oily sludge. It was horrible! I'll never look at cars the same way again. The humanity!
   

Re:Sadly, not as wrong as shown

[jelton]

On the other hand...

Are you sure you're not an economist?

Explanation glosses over the most important point!

[glwtta]

Do you get to keep the goat?

Re:Hmmm....

[msuarezalvarez]

No real mathematician would fail to grasp it with a few moments thought.

I wonder what does a true scotsman do?...

Re:Nice try!

[LrdDimwit]

I didn't really want to read the article anyway. It's for the best ...

Re:Nice try!

[Cosmic AC]

That's kind of a stretch.

Re:They don't know math?

[Z34107]

Wait... You don't have any psychological problems (other than replying to my post ^.^) You've never had sessions - you only run into this psychologist because she rents the space next to where you work. And you definitely haven't given her any money.

Do you mean to say, sir, that you are guilty of stealing psychology?!

Scientologists Paradox

[giafly]

You say you "rank Scientologists slightly above a cockroaches". Therefore by the logic of TFA, there are only three ways you can rank Scientologists, all your money, and cockroaches:

1. Scientologists, cockroaches, all your money
2. Scientologists, all your money, cockroaches
3. All your money, Scientologists, cockroaches

In two out of these three cases, you prefer Scientologists to all your money, so your best course is to join the church immediately.