#1
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Just What IS Statistically Significant?
I've read ad nauseum here that 1000 hands is a statistically insignificant sample size to draw valid conclusions regarding one's play. So, just how big does the sample size need to be to conclude some kind of result at let's say 90% confidence? Or 95% How is this derived?
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#2
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Re: Just What IS Statistically Significant?
P(X-1.96(sigma/square root of n)<u<X+1.96(sigma/square root of n)= 0.95 or 95%
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#3
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Re: Just What IS Statistically Significant?
What conclusions are you trying to draw? If you have been dealt AKs 1000 times, you can make some reasonable predictions, except for the caveat that the game was slightly different each time.
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#4
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Re: Just What IS Statistically Significant?
My win rate or if I have improved. Could you apply an F or t test between two blocks of hands to see if you've improved your win rate or maybe lowered your variance in a statistically significant way? I think that really is the basis of my original question in that how big should the sample size be to get a valid conclusion whether one has improved or not.
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#5
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Re: Just What IS Statistically Significant?
I think for a game like LHE, for the statistics to be
meaningful, a player may have to keep track of a lot of data (much more than most people are willing to record!). A good suggestion (though not many players would want to do this!) would be to record your results for each orbit, just before you are going to post your BB that round. Online is much easier even if you are playing multiple games: keep a program like wordpad open and just type in your chip total for each of the tables (often you'll be utg and mucking). Suppose a hypothetical player has a win rate of 0.3 BB per orbit (or per ten hands for simplicity; say this player only plays ring games) and has a SD of about 7 BB per orbit. The above amounts to the usual B&M statistics for a typical solid winning player in medium limits. Most statisticians use the normal approximation for very good theoretical reasons (e.g., central limit theorems) but for a 95% confidence interval, the results for this player for one orbit should fall within +/- 1.96 x SD or about 14 BB with a probability of 95%. By the way, that 1.96 is just the z-value so that the tails of the normal distribution only add up to 5% in area so that the central 95% of the results are only considered (for more details, consult a statistics text!). In reality, of course, the results after each orbit would be slightly skewed to the right (it's much more likely this player will win a bunch of chips than lose an equivalent amount!) but this is just an approximation anyway. As the number of orbits increase, this 95% confidence interval of the raw results will clearly increase in size. By how much? By the square root of the number of orbits. For example, suppose this player played 100 orbits. The 95% confidence interval would now be 100 x (0.3) +/- 1.96 x 7 x sqrt(100) or 30 +/- 137.2 (in BBs) Similarly, for 10000 orbits, it would be 3000 +/- 1372. Thus, this player could argue that his win rate would be determined within 0.14 BB per orbit with 95% confidence after playing 10000 orbits. This would be true of any other player with the same SD as this is the determining factor for how wide the confidence interval is. But notice that fraction 1372/3000 is not that small which means that the hourly rate cannot really be determined with much accuracy. Besides, game conditions change, the player may improve (or get worse!), and he may play short-handed, etc. For someone who is not sure how much he should expect to make playing, then I would encourage him to keep detailed records of all results. 10000 orbits is easily obtained by playing one table online in a year. For those playing two or more games, the data would obviously be more significant. Of course, we didn't have to keep track of data for orbits; it could have been for hours, 15 minute time intervals or every 100 hands. Usually people keep their personal data with hours in mind but this seems quite artificial as the game moves not according to the clock! |
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