- #1
TaliskerBA
- 26
- 0
Should Say Intervals.. I'm tired...
I am probably going wrong somewhere but I am running into problems with understanding this. My understanding of a 95% confidence interval is that in a sample of n the sample mean is 95% likely to be within 1.96 standard errors of the actual mean. I have a problem because I think I have an example where this isn't true.
I play a bit of online poker and have been playing around with my results to help me grasp some of these concepts and it is with my poker results I get the contradiction.
In 425 games I have won 58 for $51.50 profit, come 2nd in 53 for $24.50 profit, come 3rd in 41 for $11 profit and not cashed in 273 for -$16. With these figures I work out:
sample mean = $0.87
sample variance = 614
standard deviation = $24.77
So, here is my problem. Say I play another tournament (ie. n=1), based on this sample there is a 58/425 = 13.6% chance that I win $51.50 but a 95% confidence interval states that:
Pr(0.87 - 1.96*24.77 < X < 0.87 + 1.96*24.77) = 0.95
Pr(-47.7<X<49.4) = 0.95
So it suggests that I am 95% likely to have a result that yields me less than $49.40 even though I already know I am 13.6% likely to win $51.50...
I presume it's all to do with n being small but my notes don't give any acknowledgment that confidence intervals aren't completely sound when n is small. Where am I going wrong?
I am probably going wrong somewhere but I am running into problems with understanding this. My understanding of a 95% confidence interval is that in a sample of n the sample mean is 95% likely to be within 1.96 standard errors of the actual mean. I have a problem because I think I have an example where this isn't true.
I play a bit of online poker and have been playing around with my results to help me grasp some of these concepts and it is with my poker results I get the contradiction.
In 425 games I have won 58 for $51.50 profit, come 2nd in 53 for $24.50 profit, come 3rd in 41 for $11 profit and not cashed in 273 for -$16. With these figures I work out:
sample mean = $0.87
sample variance = 614
standard deviation = $24.77
So, here is my problem. Say I play another tournament (ie. n=1), based on this sample there is a 58/425 = 13.6% chance that I win $51.50 but a 95% confidence interval states that:
Pr(0.87 - 1.96*24.77 < X < 0.87 + 1.96*24.77) = 0.95
Pr(-47.7<X<49.4) = 0.95
So it suggests that I am 95% likely to have a result that yields me less than $49.40 even though I already know I am 13.6% likely to win $51.50...
I presume it's all to do with n being small but my notes don't give any acknowledgment that confidence intervals aren't completely sound when n is small. Where am I going wrong?
Last edited: