Confidence interval question

[CallMeIshmael]

I'm looking to compute a confidence interval for the number of hands a player plays and rasies with preflop, after X number of hands.

Does anyone know a stardard deviation for this data?

Thanks

[gaming_mouse]

If there true preflop raising percentage is p, then the sample percentage after N hands has a binomial distribution with parameters with mean p and standard deviation sqrt(p*(1-p)/N).

You can now apply the normal approximation to the binomial (ie, assume a normal distribution with the same mean and SD that I calculated above) to obtain confidence intervals.

For example, if you observed a PFR=.1 after 50 trials, a 95% CI for the true PFR is about [.015,.185], which is a fairly large interval.

I think in general people give too much credence to stats after for small sample size.

[jason1990]

[ QUOTE ]
If there true preflop raising percentage is p, then the sample percentage after N hands has a binomial distribution with parameters with mean p and standard deviation sqrt(p*(1-p)/N).

You can now apply the normal approximation to the binomial (ie, assume a normal distribution with the same mean and SD that I calculated above) to obtain confidence intervals.

For example, if you observed a PFR=.1 after 50 trials, a 95% CI for the true PFR is about [.015,.185], which is a fairly large interval.

I think in general people give too much credence to stats after for small sample size.

[/ QUOTE ]

If we do this with X=0.1 and N=50, then (approximately)

P(-2 < |X-p|/sqrt{p*(1-p)/N} < 2) = 0.95.

There is a significant amount of algebra needed to convert this to a statement of the form

P(A < p < B) = 0.95.

I think what you have done is to use

P(-2 < |X-p|/sqrt{X*(1-X)/N} < 2) = 0.95.

While this may be close enough in many cases, the nitpicky part of me wanted to point this out. /images/graemlins/wink.gif

[gaming_mouse]

eh. while you are technically correct, what i've done is completely standard practice and is what most people mean when they say 95% CI. so there. /images/graemlins/tongue.gif