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When I was an undergrad student, it was stated that because the point estimation does not exactly match the true parameter, we use confidence intervals. Then, they told that with a %95 confidence interval, we are sure that based on our sample, we are %95 sure that the true parameter is within this interval. However, as I know, this is not true and confidence interval means that if we repeat our experiments 100 times with sample size n, then, %95 of confidence intervals contain the true value. Now, I am wondering how we can use this information? For example, if we want to predict the outcome of an election (the proportion of votes in favor of a candidate), we do one experiment with one sample of size n, and it is not possible to repeat it 100 times. In this case, what does the confidence interval represent? In general, how can we use and interpret confidence intervals which are useful? Suppose we have repeated 100 experiments and found 100 confidence intervals for the mean. Now, what is the next step and how to report it.

Pitouille
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Katatonia
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  • A sample here is a poll. – dimitriy Aug 27 '21 at 03:28
  • if you could draw 100 random samples of the same size from the same population, you would expect 95 of the CIs to include the true population value. So the CIs include the point estimate with a margin of error. – Pitouille Aug 27 '21 at 03:29
  • Thanks for responses. So, how can we use a single CI? How to interpret it? – Katatonia Aug 27 '21 at 03:44
  • One could try to answer along lines similar too https://stats.stackexchange.com/questions/540797/empirical-implications-of-unbiased-estimators/540831#540831 and also the threads at https://stats.stackexchange.com/questions/2272/whats-the-difference-between-a-confidence-interval-and-a-credible-interval, https://stats.stackexchange.com/questions/2356/are-there-any-examples-where-bayesian-credible-intervals-are-obviously-inferior – kjetil b halvorsen Aug 27 '21 at 03:44
  • @katatonia, another way to read it possibly is that your single CI tells you that you can be 95% confident that the true population value fall within your range… keeping in mind that inference are made based on your random sample. – Pitouille Aug 27 '21 at 03:56
  • Now, I think the concept of confidence is subjective and I thought it is completely relevant to probability! – Katatonia Aug 27 '21 at 04:04
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    When we work with samples, nothing is really guaranteed… so it is possible to get a sample that misrepresent the population. Statistical power analysis can be helpful to reinforce detecting an effect that exists. – Pitouille Aug 27 '21 at 04:10

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