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BGonline.org Forums
more raw data
Posted By: Nick Kravitz In Response To: more raw data (Chuck Bower)
Date: Thursday, 27 September 2012, at 3:20 a.m.
Chuck
I am not sure what you are 99% certain of. I am reading between the lines here, but it appears you are 99% certain the tube produces random results, based on the following argument:
1) Assume the tube is perfectly random; if so repeats and flips should each happen with probability 1/6 (16.67%)
2) Experiment by rolling dice to see how many repeats and flips you get over a large sample set (around 1000 rolls)
3) If your initial hypothesis were true, we would expect to get repeats and flips within a calculated frequency interval 95% of the time
4) Since that indeed happened 4 out of 4 times, you are therefore 99% confident the tube produces random results.
This is flawed reasoning, and a good example of how statistics can be misleading. To see why this is flawed, you can replace your initial assumption with a close (but different) assumption - for example you assume that repeats and flips happen with probability 16.00% instead of 16.67%. In this case, the confidence interval you calculate would include smaller frequencies of repeats and flips, yet all 4 experiments would still fall within the interval. Would you therefore conclude that the true probability of repeats and flips was less than perfectly random?
The correct way to go about statistical testing is not to bias yourself by making any such assumptions before you run your experiments. In fact most organizations required to run periodic statistical tests (for example, factories) design their tests ahead of looking at any data. Going further, here are the steps you should follow:
1) Do not make any assumptions about whether the tube is random or not. Repeats and flips could happen with probability 1 (certain), probability zero (never) or somewhere in between
2) Experiment by rolling dice to see how many repeats and flips you get over a large sample set
3) Calculate a confidence interval that should include the true probability of a flip/repeat with probability 95%
If the confidence interval is too wide, you have a choice of rolling more dice, or lowering your confidence. Since you cannot roll your dice an infinite number of times, you can never remove all uncertainty. In the case of your own experiment, your 95% confidence interval for repeats would be (14.8%, 18.1%) Flips gives (15.5%, 18.8%).
The other flaw in your argument is incompleteness; you are only testing repeats and flips. No testing was done on the whether a 1 turns into a 2 more often than a 3. But I think you realize that.
You also may not have understood my original point - this may be my fault since I tend to be verbose and should have stated my conclusions more clearly. The tests run by Brett Meyer were very convincing that the tube produces random results. So convincing in fact that it rises to the level of suspicion that the results have been doctored before publishing them. Therefore, I recommend an impartial and independent experiment by someone without an interest (financial or otherwise) in its success.
If you want to roll the tube 3000 times yourself and send me the results I will analyze them and report my findings.
Nick
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