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There are many Q&A's on SE related to coin tossing - the simplest stochastic process. My Q is about relating mathematics and statistics to what in biomedicine and healthcare is termed "evidence" based on real world data.

In 46 SuperBowls, NFC teams have won the last 15 coin tosses and overall lead AFC teams ~2:1. A graphic of the realized process (up to SuperBowl XLV) superimposed on pseudorandom tosses generated with Mathematica is shown on my infotainment site understars (shameless promo).

There's no reason to presume the coins and tosses are biased (unless NFC teams have developed telekinesis lately) - the streak and bias is obviously a coincidence, however the probability of 15 wins in a row is 1/32,000 I think.

I would be glad to offer a bounty for statisticians to explain and compute all the standard study-design related parameters associated with this process, like power and p-values associated with the null hypothesis of unbiased, independent tosses.

If you believe this is a trivial issue, I'll remind you that healthcare is about 15% of US GDP and much of the evidence is quantified based on statistical analysis with sample sizes often in the hundreds - not much larger than the number of SuperBowls.

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Are you asking for someone to explain hypothesis testing for relative frequencies? – Joel Cornett May 6 '12 at 21:58
@Joel Cornett - yes, to explain and compute them for this particular example – alancalvitti May 7 '12 at 0:43
Do you have a link to the data? Small sample sizes are best dealt with using Student's T distribution and not the standard normal distribution. – Joel Cornett May 7 '12 at 1:00
Yes, I scraped the toss results up to SB43. They are presented in the caption to the picture here on statigrafix... However, the power analysis is prior to data, at least that's how it works with NIH and VA studies. – alancalvitti May 7 '12 at 16:18
Yeah that makes sense. If you do it after seeing the data, you risk researcher's bias in formulating and testing your hypothesis. – Joel Cornett May 7 '12 at 16:26

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