Mods, if this isn’t really a GQ feel free to lock this puppy up or move it, whichever’s easiest.
The theory of using Rhine cards to test ESP is–
Stop laughing, dammit! I’m being (sort of) serious here.
Anyway, the theory of using Rhine cards to test ESP is that you have a deck of five cards with distinctive designs to pick from. One person - or in this case, a computer program - picks a card at random, the person being tested tries to pick the same card. Repeat 100 or more times with a full deck of five cards each time.
Yes, I have too much free time.
The question is, I would assume the “pure chance” success rate of something like this to be around 20 hits per hundred trials, right? I’m no good at statistics, but they say the chance of my score of 34 hits per hundred trials is 1 in 1357, or 70% above chance. Someone who’s better with numbers than me, please tell me; are those numbers bullhockey or not?
Please note, I’m not advocating any kind of psychic phenoma for my hit rate, or even saying it’s better than chance. I just want to know if what they are saying is accurate.
[sub]Did that make sense?[/sub]
All right, let’s see if I understand this. There are 5 cards in the deck, and both people have to choose the same one. I assume they’re using different decks, as it wouldn’t make sense otherwise.
We’re not concerned with what card the other guy picked, just whether you pick the same one. So you have a 20% chance of success. There are 100 trials, so this is a binomial (100, .2) distribution. Your expected number of successes is 20, as you thought.
I get that your chance of having 34 successes is .0004, which is about 1 in 2495. On the other hand, your chance of having 34 or more successes is roughly 1 in 1357. I don’t know exactly what’s meant by “70% above chance”, so I can’t comment.
That may seem like a low probability, but if you do the experiment enough times, you’d start to be really surprised if it never happened. IOW, I don’t think there’s anything going on here that can’t be ascribed to chance.
I think that there might be cultural influences that would lead to a better than pure number crunching result would predict.
Colours and shapes can subconsciously be significant, one example might be if there was a crescent shape, this might be picked out more by Islamic types, I’m sure others can see possoble weaknesses in this kind of test.
All it would prove to me is perhaps a little psychology, I have seen it mentioned before that when folk are asked to choose a number between 1 and ten then 7 is selected most often, but there is no logical reason for that and I bet that’s the same with shapes.
I’ll defer to ultrafilter’s math and just point out that “better than chance” is meaningless in a single trail. Pure chance could result in a single trail with 100% accuracy, it would just be a rare occurrence. Purely random choices (i.e. chance) result in an average of 20% over many trials, but it doesn’t dictate that every trial be exactly 20%.
“Better than chance” is only meaningful if you repeat the experiment many times and your average over all trials is greater than 20%.
When you hear someone talking in terms of an experiment coming out “70% higher than chance” (or 100% or 50% or anything similar), you know that they have no idea how probability really works. Suppose you do 10 Rhine cards. Since you expect to pick 20% of them right, you expect to pick 2 cards right. 100% higher than chance is 4 cards. But picking 4 cards right out of 10 when you have a 20% chance of picking each one of them right isn’t a rare thing at all.
On the other hand, suppose you do 10,000 Rhine cards. You know that chance would say that you should pick 2,000 of them right. If instead you picked 4,000 of them right, you would again be 100% higher than chance. But this is incredibly rare. The fact that both cases were 100% higher than chance means absolutely nothing. The only thing that someone should tell you about the outcome of an experiment is the answer to the question: “How rare is that outcome if it were just chance?”
It’s true that 20 right is the most likely result, but it’s not really all that likely. If it’s truly random, only about 1 trial in 10 will yield exactly 20 right.
You’ll also sometimes see the term “statistically significant” thrown around. That means that you’d only expect see those (or more extreme) 5% of the time (sometimes 10% or 1% is used instead). On the other hand, suppose that you test a thousand people, and call each subject a separate trial. This means that you’re going to find about fifty people whose individual results are “statistically significant”. This doesn’t mean that one person in twenty is actually psychic, though. This, by the way, is one reason that “psychic” studies tend not to be reproduceable. Suppose that you test 8,000 people, and 400 get “statistically significant” results. Aha! Those 400 must be psychics! Let’s test them some more! Well, you run the tests again on those 400 people, and about 20 get “significant” results. Well, they must be the real psychics, and the others were just lucky… Et cetera.
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