An experiment with Babylon and LMNO

[Roaring Biscuit!]

I calculated the mean from your percentages where the guaranteeds were rejected.  Then I worked out standard deviation of the data.  None of the values fell outside 1 standard deviation.  Considering a result would normally be considered an outlier if it was more than 2 standard deviations from the mean, we can probably conclude that all the results are statistically probable.

For those wondering, the mean I calculated was 51% which is much closer to our expected value when disregarding 3's and 4's

EDIT:  This is why I was asking requia about his method, its quite possible I made a mistake/used a different possibly inferior method

[Cain]

Gotta love the standard deviation.

[LMNO]

I just realized that I hardly understood any of that, and now be forced to read "statistics for dummies" until I figure it out.

[Cain]

http://en.wikipedia.org/wiki/Standard_deviation

Admittedly, you might need to use Wikipedia to look up the terms explaining the article as well...

[Requia ☣]

Um, statistically speaking the accuracy of both Horuv and all 4 guessers as a whole was above what should have been guessed, if not quite up to what Horuv claimed.

Horuv should have gotten 56.6-76.6 correct, he got 77, just outside the statistical expectation.  The 4 guessers together got 300/400 right, they should have had 253.1-279.7, which is *way* outside.

If those results are repeated at similar levels then I'm dragging you assholes down to vegas.

What about the fact that 3 and 4 came up 45 times out of 100?

The "average" for either 3 or 4 to come up is 33.3%.  The fact that it came up 45% of the time should significant, as it means that any guesser, no matter what, will get 45 right.  Everyone's score was raised because of it.  Is there a way to account for that statistical deviation?

That actually solves the reason for high accuracy across the board nicely.  No reason to expect anything unusual in repeat experiments then.

As for my method, standard deviation = +/- (sqrt(n)/n)%  (so with a sample of 100 the SD is +/-10%, with 400 its +/- 5% the group as a whole was off by a whopping 12%*, significant until you take into account what was pointed out above).  Though given the variance caused by a high or low number of 3s and 4s in this rolling method, this looks like it fails, at least when multiple guessers for the same rolls are considered, I'm not as sure what will happen with one guesser yet, this whole experiment may actually fall completely outside what standard deviation is capable of handling in a simple matter.

*Except of course I did make a mistake here, the SD is percent of total not percent of the percentage, so its really only 8.5 % off.

[LMNO]

Which is why I want to try another experiment, this time ensuring that there are only two possible choices every instance, and a 66% chance to pick one of them right.

[Requia ☣]

Thats not really possible.  if there are two possible choices and each has a 2/3 chance of happening, there *has* to be overlap 1/3rd of the time.  Even if you have working magic you can't violate that.

Repeating the original experiment and seeing if 3s and 4s show up with high frequency repeatedly has merit though, at least to the extent the experiment as a whole has merit.

[LMNO]

Ok, tell me what you think of this experiment:

I have six tarot cards: the 10 of cups, 10 of swords, 10 of coins, 10 of wands, the Fool and the Devil.

I shuffle each time I draw a card.

I draw 100 times.

You choose whether I drew a 10 or a Major Arcana.

As far as I can see, I have a 4/6 chance of picking a 10, with no overlap of possibilities. That's a 66% chance, right?

[Triple Zero]

Horuv should have gotten 56.6-76.6 correct, he got 77, just outside the statistical expectation.  The 4 guessers together got 300/400 right, they should have had 253.1-279.7, which is *way* outside.

outside what expectation?

Checking my numbers, the 4 guessers as a whole had about a .5% chance to be that accurate.  Doing that twice in a row would be a statistically impossible event.

huh??  

I suppose it's time for me to re-check the figures myself. They're all posted ITT, right?

cause I'm hearing a littlebit too much of vague pseudo statistics here (not only Requia btw, and perhaps it's just that I'm used to different terminology).

so, a .5% chance to be what accurate? exactly that accurate? that accurate or more accurate? or this large or larger deviation from the norm? they all have different chances, I suppose you mean the second though (but I doubt the chance would be that low). The first would be (nearly) zero, and the third would be about twice the probability of the second.

either way, doing that twice in a row, would be a possibility of 0.0025%, a chance of 1 in 40,000. unlikely maybe, but to call it "statistically impossible" is going quite far.

in fact, if an event X happening is "statistically possible", then (given that both events are independent--which they are in this case), X happening twice is also "statistically possible", because numbers don't just go from "pretty small" to "arbitrarily small" just by squaring them.

anyway, I'll run some calculations myself and post the results.

by the way, people using the Normal distribution for checking the probabilities on this one should be careful, it averages out well enough on 100 tries, but in the end it still is a discrete problem with uniform probabilities (to throw a 1 to 6 on a die).

[Requia ☣]

At least according to my physics professors, statistically impossible is anything with a probability worse than 1 in 10000.

I also fucked up my standard deviation on the group as a while (was 1.6 SDs not 2.5).  Also see the stuff LMNO pointed out.

[Triple Zero]

'Statistically Impossible' means less than a .01% chance of occurring.  Which is why its 'statistically impossible', not 'impossible'.

say what now?

sir, where I'm from, we define our confidence intervals before qualifying them, preferably before even executing the experiment. also we give a rationale for choosing them. what is so special about a 1 in 10,000 chance?

At least according to my physics professors, statistically impossible is anything with a probability worse than 1 in 10000.

get yourself some new physics professors. that is retarded.

i hope you just misunderstood them.

are you sure they didnt say "for this experiment/hypothesis, we will call a probability lower than 1 in 10,000 statistically impossible"?

cause I can flip a coin 14 times and call the result "statistically impossible" that way, after all, it's only a 1 in 16,384 chance that it ended up that way.

and especially in computational physics, with some monte carlo methods you're dealing with cumulative probabilities much lower than that.

[Cramulus]

  this thread rules in so many ways

I'm glad you guys can grok the stats. I struggled through my stat class. So this all sounds very familliar to me, but it's only one step removed from clicks and whistles.


LMNO: a six-card pull might not be a great method for generating random outcomes. when shuffling six cards, it'll be hard to return them to a truly randomized state. With a 52 card deck, the randomness is related to the number of shuffles¹. With a six card deck... hard to say. If you shuffle basically the same way every time for all 100 pulls, patterns will emerge in the results.

[Triple Zero]

Ok, tell me what you think of this experiment:

I have six tarot cards: the 10 of cups, 10 of swords, 10 of coins, 10 of wands, the Fool and the Devil.

I shuffle each time I draw a card.

I draw 100 times.

(i see cram just said this, but)

unfortunately, shuffling cards by hand is quite difficult to do properly, random.

if you repeat 100 times a bias might show.

better roll a die and assign a card to each number.

better yet to get your random numbers from random.org, as those numbers are guaranteed to be "clean" (gathered from thermal noise with some whitening transformations applied to it), which avoids the possibility of any manufactoring faults in the die.

[That One Guy]

I'm not understanding the need for the 66% part of things. Is it just an artificial constriction, or is there something significant statistically or mathematically regarding the 2/3 thing? All it really seems to be doing is artificially inflating the number of probable hits, which was confirmed in the 45 "both" results.

There are a ton of already-in-existence tests and methods for determining accuracy of predictions, like the Zener Cards (here is an online card test for those interested in seeing the style). Why are we reinventing the wheel, and only using statistically meaningless sample sizes? Only 100 rolls/cards/whatever is FAR too small a sample size to determine any meaning beyond "random luck", especially with the results being weighed towards so many potential hits via the 1-4/3-6 methodology.

It's a neat parlor trick, I guess, but I'm having trouble figuring out what this might actually show, other than that random chance is, in fact, random.

[Requia ☣]

Ok, tell me what you think of this experiment:

I have six tarot cards: the 10 of cups, 10 of swords, 10 of coins, 10 of wands, the Fool and the Devil.

I shuffle each time I draw a card.

I draw 100 times.

You choose whether I drew a 10 or a Major Arcana.

As far as I can see, I have a 4/6 chance of picking a 10, with no overlap of possibilities. That's a 66% chance, right?

If he guesses Arcana he only has a 33% chance to be right though.  So he only gets to use the theoretical magic power on half the guesses.