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2nd February 2010, 01:00 PM | #1 |
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Predicting Random Events Accurately 60% of the Time?
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? |
2nd February 2010, 01:39 PM | #2 |
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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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2nd February 2010, 01:40 PM | #3 |
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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. |
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2nd February 2010, 01:41 PM | #4 |
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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 |
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2nd February 2010, 01:55 PM | #5 |
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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 |
2nd February 2010, 01:59 PM | #6 |
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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. |
2nd February 2010, 02:02 PM | #7 |
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Not to be off topic, what does ETA mean? Lionking or anyone. SS
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2nd February 2010, 02:05 PM | #8 |
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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. |
2nd February 2010, 02:06 PM | #9 |
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Sounds possible, but one study isn't enough for me, need to have a few more to be certain.
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2nd February 2010, 02:19 PM | #10 |
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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. |
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2nd February 2010, 02:21 PM | #11 |
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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 |
2nd February 2010, 02:23 PM | #12 |
Penultimate Amazing
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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 |
2nd February 2010, 02:30 PM | #13 |
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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 |
2nd February 2010, 02:32 PM | #14 |
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Read this book, its covered in there. I am not even going to try and explain it and don't have the book with me. The thing that stood out was his comment "probability of the event itself with the probability of the prediction" i remember that's what was covered. He does a good job of explaining it.
http://www.amazon.com/Drunkards-Walk.../dp/0375424040 |
2nd February 2010, 02:33 PM | #15 |
Penultimate Amazing
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Where on earth are you going to university? This professor doesn't understand the simplest aspects of statistics.
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2nd February 2010, 02:35 PM | #16 |
Penultimate Amazing
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I wonder if they are referring to something like this:
http://www.telegraph.co.uk/science/s...cientists.html (for people unwilling to click - it points out you can learn a coin flipping technique that is biased somewhere between 54-68%, which is entirely different from predicting a fair coin toss) |
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May your trails be crooked, winding, lonesome, dangerous, leading to the most amazing view. May your mountains rise into and above the clouds. - Edward Abbey Climb the mountains and get their good tidings. Nature's peace will flow into you as sunshine flows into trees. The winds will blow their own freshness into you, and the storms their energy, while cares will drop off like autumn leaves. - John Muir |
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2nd February 2010, 02:35 PM | #17 |
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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 Ł14,000 http://www.aske-skeptics.org.uk/challenge_rules.htm Tony Youens in the UK offers Ł5,000 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 |
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2nd February 2010, 02:41 PM | #18 |
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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." |
2nd February 2010, 02:43 PM | #19 |
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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 |
2nd February 2010, 02:46 PM | #20 |
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2nd February 2010, 02:50 PM | #21 |
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That's ignoring the effect of human fallibility. Chances are, the professor isn't going to be much good at keeping track of which cards have been used (unless he's a professional card-counter -- or the Rain Man). If he's still be making his guesses on the assumption that each card is equally likely to show up, the results will still be close to 20% correct. An extreme example would when there's only two cards left. If there's only two possible outcomes, in theory he has a 50% chance of getting it right, but in practice he'll have no idea which two cards are left, and only have get it right 20% of the time. And as for the last card, there's only one possible outcome, so in theory he has a 100% chance of getting it right... but if he still has no idea which card it is, that doesn't help him at all. |
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2nd February 2010, 02:53 PM | #22 |
Penultimate Amazing
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That brings up the issue of adequate mixing (http://en.wikipedia.org/wiki/Markov_chain_mixing_time) if it was an actual experiment.
It does sound interesting. I hope the professor is able to give you more information about what he is talking about.
Quote:
Quote:
ETA: I see you've answered the question as to the source. I'll look through Drunkard's Walk to see if I can figure out which part he's referring to. Linda |
2nd February 2010, 02:55 PM | #23 |
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I'm really inclined to set up an experiment now - using coin tosses, I'd need at least 59 / 100 accurate predictions to confirm my professor's hypothesis at the .05 level of statistical significance. That still leaves wiggle room (since the actual figure may be around 57%), but Zenner Cards would do the trick pretty quickly and easily. 5/10 accurate predictions would be statistically significant while remaining below the 57-60% figure my professor is claiming.
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2nd February 2010, 03:09 PM | #24 |
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He is talking about a case where there are only two symbols in the deck, or is he talking about a standard Zenner deck where there are five different symbols in the deck. If the latter, that is an amazingly simple thing to disprove with only a few minutes time. If I were you , I would bet him money on the outcome.
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2nd February 2010, 03:16 PM | #25 |
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Ladewig,
He's talking about a packet of 5 cards, one of each symbol. The cards would be mixed, then a prediction would be made and a card would be chosen. The card would be replaced (after being recorded of course), the packet would be shuffled, and the procedure would be repeated. I couldn't believe he was making that claim, but he was adamant that that was the probability, and insisted I was confusing the probability of the event with the probability of the prediction being accurate. It would be very easy to disprove - the chances of his predictions being accurate even 50% of the time over 10 trials is just over 3% - but I'll have to see if I can interest him in trying it. Chris ETA: I do have money riding on this, but not with the professor - I bet my friend $50 that he and the professor were wrong. |
2nd February 2010, 03:23 PM | #26 |
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2nd February 2010, 03:34 PM | #27 |
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Did the professor say that the number of trials would be fixed in advance? This is crucial. If not, then don't bet against him. Flip coins for long enough, and he could well indeed end up with a 60% hit rate, eventually. At that point he stops the experiment and collects his winnings. It's called "cheating".
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2nd February 2010, 03:37 PM | #28 |
Penultimate Amazing
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I'd ask if he understands the result to be a consequence of the probabilities involved, or if he believes the study demonstrated an unknown factor at play, for example "humans have some unknown ability to predict at better than chance". If it's the former, he ought to be able to find a proof. If it's the latter, the circumstances of the trial need to be examined carefully. Will it work if it is a perfectly balanced coin, and if the human is isolated from clues about how the flip is being performed? Will it work if it is a random number generator rather than a physical coin?
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2nd February 2010, 03:43 PM | #29 |
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One other thing that comes to mind - the professor said that 60% of people choose 60% of their lottery numbers correctly. In other words, if you could gather up all the lotto tickets that have ever been played, 60% of them will have 3 out of 5 numbers correct.
ETA: Ctamblyn, we didn't get into an experimental design - it was discussed as a function of the laws of probability. I agree that setting the number of trials would be crucial. Gnome, he seems to think it's a matter of probability - he did say a machine could perform just as well as a human. |
2nd February 2010, 03:44 PM | #30 |
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2nd February 2010, 03:50 PM | #31 |
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just cut to the chase, bet your professor $100 that he can't predict the outcome of a coin toss 60% of the time in front of the rest of the class
thats that solved eh |
2nd February 2010, 03:52 PM | #32 |
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Can you get a math professor to talk to this professor?
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2nd February 2010, 03:53 PM | #33 |
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2nd February 2010, 03:54 PM | #34 |
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Well, it was the reference to drunken walks that made me wonder about the number of trials. The ratio hits/trials would fluctuate up and down as the experiment progressed. If you're extremely patient, it seems to me that you would be very likely to see that ratio fluctuate as high as 0.6, at which point you halt the process. I've been trying to find some good references, but I expect some bright statistician will beat me to it
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2nd February 2010, 04:00 PM | #35 |
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Somebody help me out with how that's not slippery language on the slope toward the Gambler's fallacy.
There are four possible outcomes to a set of two coin flips: HH, HT, TH, TT If you flip two coins, and you know at least one has come up heads (TT didn't happen) there's a 2/3 chance that at least one has come up tails (one of HH, HT, or TH). Fixing which one has come up heads (say, the first), however, eliminates *two* of the possible outcomes for the set (TH and TT now out of play), leaving only a 50% chance that the specified other will be tails (either HH or HT) |
2nd February 2010, 04:07 PM | #36 |
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Furthermore, sites like this one Texas lotto show that in the last drawing, only 35,207 people got three out of six. No one could seriously believe that 35,207 represents 60% of all the people who bought lotto tickets in Texas.
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2nd February 2010, 04:08 PM | #37 |
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I hear what you're saying, but this is an informal discussion forum.
The prof's statements are a sort of 'this one goes to eleven' type of thing that is so not right it's not even wrong. It's hard to know where to start with a refutation. "Dogs are not animals", "the sky is made of fish", "three is a colour, not a number" - how do you refute these claims that are just so obviously wrong? After 20+ years of dealing with cranks as a skeptic, I want to start a proper debate carefully, lest it go all Neal Adams. |
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2nd February 2010, 04:08 PM | #38 |
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I can't help but think that if he truly understood what he was talking about, he would have been able to explain or indicate what he was talking about much better. It sounds like he misunderstood something or it's a trick.
Linda |
2nd February 2010, 04:12 PM | #39 |
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You gave me different information than I asked for.
All I asked is if one came up Tails. If it did, the chance the other one was Heads is 67%. Period. You can do this in all sorts of ways. If a family has two kids, and one of them is a boy, the chances that the other one is a girl is 67%. You worked this out yourself, and then tried to deny what you found out P.S. Fixing which one was tails totally doesn't help you at all. If I ask 'did one come up tails' and you respond 'the first one came up tails' the second one still has a 67% possibility to be heads. You only decouple the system if I ask 'what did the first coin do' at which point it goes back to 50/50 that you want to see. P.P.S. This doesn't let you predict the outcomes of any one coin flip 67% of the time, just the outcome of a pair of coin flips given information about the pair. |
2nd February 2010, 04:22 PM | #40 |
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It sounds to me like your psych prof needs help with rudimentary statistics, if such an obviously-bright student thinks he is saying what it sounds like he's saying. Coinflip = 50/50. Next question.
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