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.

 

[tacman]

There are several ways to measure the accuracy of a statistic, but it ultimately depends on the specific statistic you are studying and the data you have collected. In your case, studying the performance of coding techniques on messages of 380 bits long, there are a few potential approaches you could take to measure the accuracy of your statistic.

One way to measure accuracy is by calculating the margin of error. This is commonly used in opinion polls and other surveys, but can also be applied to other types of data. The margin of error is a range of values that is likely to include the true value of the statistic. It is influenced by factors such as sample size and variability in the data. In your case, you could calculate the margin of error by using a formula such as the one used for calculating the margin of error in a proportion (since your statistic is a proportion of successful coding techniques). This would give you a range of values that your statistic likely falls within, providing some indication of its accuracy.

Another approach is to use confidence intervals. Similar to the margin of error, confidence intervals provide a range of values that is likely to include the true value of the statistic. However, confidence intervals take into account the variability in the data and provide a more accurate estimate of the true value. In your case, you could calculate a 95% confidence interval for your statistic, which would give you a range of values that is likely to include the true proportion of successful coding techniques in the population.

In terms of estimating the accuracy of your statistic, there are also mathematical theories that can be used. For example, the Central Limit Theorem states that as sample size increases, the distribution of sample means will approach a normal distribution. This means that as you test more samples, your statistic is likely to become more accurate. Additionally, you could use statistical tests such as a t-test or z-test to determine the statistical significance of your results and provide evidence for the accuracy of your statistic.

Overall, there are various methods and mathematical theories that can be used to estimate the accuracy of a statistic. It is important to carefully consider the specific statistic and data you are studying and choose an appropriate method for measuring accuracy. Additionally, it may be helpful to consult with a statistician or conduct further research to determine the best approach for your specific study.