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Posted By: Glenn

Ted,

I agree that 576 cards is a decent sample size, but I have no clue if the sample is random. With a mean of 12 and a standard deviation of 3.43, 3 examples of a card represents a z score of -2.62 (applying the standard normal curve, which again, is not exactly accurate but very close). 0.88% of the frequencies should be outliers of this magnitude or greater in either direction.

[That is, cards that occur 0, 1, 2, 3, 21, 22, 23,..., or 576 times in the sample. Since the distribution can't run into negative numbers, our sampling distribution isn't entirely symmetrical. Though vanishingly unlikely, it is certainly possible to have a random sample with n=576 that yielded 576 of the same card, but since the tails of the distribution as we approach and exceed three standard deviations from the mean contain so little area, I figure it's safe to ignore that minor asymmetry.]

In a majority of samples of this size we wouldn't get any cards that showed up fewer than 4 or more than 20 times, but it will happen a noteworthy minority of the time. (So it usually wouldn't be even 1 card, let alone 2.)

I don't disagree that the Paige was a short-print. Given all the evidence out there, I'm pretty sure it is. I just don't think this particular find of 576, on its own, makes a convincing case or is especially remarkable IF the Paige IS NOT a short print.

edited to add: Though it doesn't affect the math much, I was thinking there were only 48 different cards. Now I realize there are actually 49. (Confusion related to the debate about whether the cards were produced in the year '48 or '49?)