How to measure if a statistic is accurate?

[chingkui]

I am studying the performance statistic of some coding techniques on messages of 380 bits long. I studied it by generating bit sequences randomly and test the performance on each sample. But the sample space is so large (2^380) and practically I can only randomly test about 10^5-10^6 samples, how can I know if the statistic I get is accurate enough? Is there any mathematical theory that could be used to estimate how accurate it is?

 

[EnumaElish]

Start by assuming you have 10⁶ independent random variables. Although this is a finite number and is much smaller than 2³⁸⁰ (my guess), it is a sizeable sample size by any standard. You should be able to estimate a confidence interval around any statistic you have happened to calculate; the conf. int. is also a function of the sample size.