Predicting Random Events Accurately 60% of the Time?

Chris Connelly

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Today, my psychology professor asserted that people can accurately predict random events roughly 60% of the time (he qualified this statement by saying that the actual figure lay around 57% and he was rounding). I asked him for an explanation of this claim, and in the following class discussion, he proceeded to assert that a random person predicting coin tosses would be right, on average, 60% of the time. I countered that that was impossible and the figure should be 50%, but he insisted on 60%. He said I was confusing the actual event with the prediction and that, while ratio of heads to tails should average 50/50, any person or machine making predictions should expect to average around 60% accuracy.

I discussed this claim further with a friend in the class, who said he had seen the study the professor referenced and insisted that a person predicting coin tosses would, in fact, average 60% accuracy. I insisted this was not possible, but he said that it was statistically proven, even though it seemed counterintuitive.

Later, I got a chance to engage the professor further, and he reaffirmed his assertion. He also added that a person predicting what card would be chosen at random from a deck of Zenner Cards would observe the same 60% success rate. He again countered my arguments by saying I was confusing the probability of the event itself with the probability of the prediction. I realize these figures are different (the ratio of heads to tails in a sequence of coin tosses may be 50/50 while the percentage of current predictions may differ substantially), but as far as I can see, the rate of accuracy for predictions should be 50% for a coin toss or 20% for the Zenner Cards no matter how you slice it.

I'm getting the feeling my friend and professor are misquoting whatever study they're trying to reference, but both were adamant about a 60% rate of prediction accuracy on coin tosses and Zenner Cards. Can anyone shed some light on what they might have been getting at?
 
The most efficient counter argument would be that if large swaths of the population could do that 60% of the time, the casinos with roulette wheels and craps tables would be out of business. They are not, therefore the claim fails.

The second most efficient argument would be to have him predict the outcome of three groups of 30 flips.
 
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If this were true, casinos would go broke tomorrow. I don't believe it and would love to see a reference to the so-called study.

ETA, bugger, Ladewig beat me by a millisecond.
 
I have no idea what they are talking about, but why not test it with them? It only costs a penny and 15 minutes.

Ward
 
What study did the professor refer to?

It sounds like he is arguing for anomalous cognition (i.e. psi), but there are some normal biases in coin tosses (the coin is more likely to land with the same side facing up, and in a toss it is more likely to land heads and in a spin it is more likely to land tails (or is it the other way around?)), which changes your knowledge about the results.

Linda
 
There's a couple of times you can utterly bug out statistics, but it all works mathematically.

If you flip two coins, and one comes up heads, there's a 67% chance the other one was tails.

It really sounds like he was getting something like that screwed up with predicting which coin flip does what.
 
Edited to add

It means someone hit the edit button because they saw something and didn't feel like double posting. Or triple posting. Or one time, 8 posts in a row.

It's much more polite ;)

ETA: See? There's now an 'edited by GreyICE at the bottom of my post'

... well, if I wait the two minutes.
 
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Sounds possible, but one study isn't enough for me, need to have a few more to be certain.
 
He's wrong... ask him for a demonstration.

The coin-toss suggestion is a good one, but 50% is not too far away from 57% -- you'd have to add-up the results, and even then he could claim the lower result was a chance anomaly, or that he wasn't at his best that day.

A Zenner-card test would be better because wrong answers would be much more frequent, and by placing cards from the correct guesses in one pile, and cards from the incorrect guesses in another you'd have a nice visual demonstration of how badly he's failing that he can't ignore.
 
Ladewig,

It's funny that you bring up casinos - I made the same point during my conversation with the professor, specifically regarding roulette. He said a roulette wheel was "different" and he'd have to think about why. He also said that a roulette wheel would need an enormous amount of trials to produce the 60% results, and most people don't gamble long enough to see it work out (inconsistent, I know - never mind the thousands of "trials" happening nonstop in Vegas).

At one point, I thought the professor might have been thinking that the person could see the coin in the air and project its outcome, but he said the results could be obtained blindfolded. He also insisted no paranormal ability was involved, and it was sheer probability.

During the same conversation, I tried to explain that a 60% rate of accuracy would be unimpressive over, say, 10 trials, while the same 60% rate would be far more impressive over a greater number of trials. The point was lost, unfortunately - the professor said it only sounded more impressive and that there was no statistical difference, while my friend said that the probability of hitting 6 out of 10 is the same as that of hitting 60,000 out of 100,000.

Unfortunately, neither my friend nor the professor has much interest in experimenting (though I do have an outstanding bet with my friend). I'll post the study here if the professor tracks it down - he said he'd look for it. My friend thought it had been conducted by the American Psychological Association.

Incidentally, would this qualify for the MDC? I brought up the Challenge, and my professor said he had heard of it, but it required a rate of accuracy of 95%. I may be mistaken, but I'd imagine if someone could predict the identity of a Zenner Card 60% of the time under properly controlled conditions, that should earn them the million.

Chris
 
It's also important to realize that the probability of each event is not necessarily one divided by the number of possible events. And when you are dealing with an ordered set, like a deck of Zener cards, then the probability is described by permutations instead of combinations, which increases the probability of getting it right compared to one in five.

Linda
 
fls,

Regarding the Zenner Cards, I did bring up that issue, but the professor had in mind an experiment with 5 shuffled cards where a prediction was made and one was selected. The card would then be replaced and the deck shuffled before another prediction was made, making each trial independent.

If I do decide to experiment, are there any online calculators or tools that would help me calculate the odds of, say, getting 60 coin tosses right out of 100? I'm also thinking about doing something with a coin toss simulator or random generator - if there was a way to generate two lists of coin toss results (prediction and trial) and cross reference them, that would be a fairly quick way of showing the professor's claim wrong.

Chris
 
Where on earth are you going to university? This professor doesn't understand the simplest aspects of statistics.
 
I would think that a 60% Zener card test would easily qualify for the MDC. As a professor, it should be easy for him to get whatever academic affidavits he'd need and if he does that, the media should not be far behind. And depending on where you are, there are other challenges (for less than a million) available:

There's the Australian Skeptics' AU$100,000 Prize
http://www.skeptics.com.au/features/prize/

There's the IIG's US$50,000 Challenge
http://www.iigwest.org/challenge.html

There's the North Texas Skeptic's US$12,000 Challenge
http://www.ntskeptics.org/challenge/challenge.htm

There's Prabir Ghosh's 2,000,000 Rupee Challenge in India
http://rationalistprabir.bravehost.com/

There's the Swedish 100,000SeK prize offered by Humanisterna
http://www.humanisterna.se/index.php...d=27&Itemid=49

The Tampa Bay Skeptics offers a US$1000 prize in Florida, USA
http://www.tampabayskeptics.org/challenges.html

In Canada there's the CAN$10,000 from the Quebec Skeptics
http://www.sceptiques.qc.ca/activites/defi

In the UK, the ASKE organization offers £14,000
http://www.aske-skeptics.org.uk/challenge_rules.htm

Tony Youens in the UK offers £5,000
http://www.tonyyouens.com/challenge.htm

In Finland, Skepsis offers 10,000 Euros
http://www.skepsis.fi/haaste/

The Fayetteville Freethinkers offer a US$1000 prize
http://fayfreethinkers.com/

There's a 1,000,000 Yuan prize in China offered by Sima Nan
I've found a lot written about it, but no official web address for it. If anyone's got one, let me know.

The Belgian SKEPP organization offers a 10,500 Euro prize
http://www.skepp.be/prijzen/de-sisyphus-prijs/

Good Luck,
Ward
 
Chris Connelly said:
If I do decide to experiment, are there any online calculators or tools that would help me calculate the odds of, say, getting 60 coin tosses right out of 100? I'm also thinking about doing something with a coin toss simulator or random generator - if there was a way to generate two lists of coin toss results (prediction and trial) and cross reference them, that would be a fairly quick way of showing the professor's claim wrong.

Chris
Click to expand...

Here you go http://www.graphpad.com/quickcalcs/binomial1.cfm
Here is the probability for 60 out of 100.

"Number of "successes": 60
Number of trials (or subjects) per experiment: 100

Sign test. If the probability of "success" in each trial or subject is 0.500, then:

* The one-tail P value is 0.0284
This is the chance of observing 60 or more successes in 100 trials."
 
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back2basics,

That's exactly the book my professor was using (The Drunkard's Walk by Leonard Mlodinow) - he had it in hand as he lectured and read an excerpt to the class! Unfortunately, he couldn't track down the part specifically addressing the issue I posted about.

I understand the distinction between the probability of the event and the probability of the prediction - if you predict heads-tails-heads-tails... and the coin toss comes out exactly that way, the results are 50% heads and 50% tails with a 100% rate of accuracy for the prediction (that part is from my professor). The probability of predicting accurately, however, is still 50% on a coin toss!

Roger,

I'm actually taking a college-level (AP) course as part of my senior year in high school. I hear you though - I mentioned this to a statistics professor in the same school and he just shook his head.

ETA: On your second post, the same thought occurred to me (manipulation of the coin toss), but the professor said I'd still get the same results if I threw the coin from a cup while a blindfolded participant made predictions.

Maybe someone who has read The Drunkard's Walk can shed some light - I'm stumped at the moment as to what they were getting at.

Chris
 
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Chris Connelly said:
back2basics,

That's exactly the book my professor was using (The Drunkard's Walk by Leonard Mlodinow) - he had it in hand as he lectured and read an excerpt to the class! Unfortunately, he couldn't track down the part specifically addressing the issue I posted about.

I understand the distinction between the probability of the event and the probability of the prediction - if you predict heads-tails-heads-tails... and the coin toss comes out exactly that way, the results are 50% heads and 50% tails with a 100% rate of accuracy for the prediction (that part is from my professor). The probability of predicting accurately, however, is still 50% on a coin toss!


Chris
Click to expand...


Listen to fls, she explained it simpler than they did in the book. The book covers it in more detail.
 
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