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Oct 16, 2022 at 10:17 history edited Sextus Empiricus CC BY-SA 4.0
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May 21, 2022 at 14:53 comment added Sextus Empiricus So if you would have some selection process where people make a test and need to be with 95% confidence among the top 2%, then among the people that succeed with this test you probably have less than 95% that are truly top 2%. Given that you got selected your do not have 95% probability to be truly in the top 2%. But, given that you are on the 2% boundary you have 95% probability to succeed in the selection.
May 21, 2022 at 14:46 comment added Sextus Empiricus @RichardHardy, conditional on the true value you will have that the confidence interval contains the parameter $\alpha\%$ of the time. The example 2 is different in the parameter $\alpha$ being a variable and conditioning on the observation ("Then in extreme cases, low or high, outcome of results..."). This makes that conditional on the observation the confidence interval does not contain the parameter $\alpha\%$ of the time.
May 21, 2022 at 14:42 history edited Sextus Empiricus CC BY-SA 4.0
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May 21, 2022 at 13:05 comment added Richard Hardy Does your Example 2 not contradict the statement in Example 3: An $\alpha$%-confidence interval will contain the parameter a fraction $\alpha$% of the time, independent from the true parameter? Also, are different font sizes for Example 3 vs. Examples 1 and 2 intentional?
Jun 11, 2020 at 14:32 history edited CommunityBot
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May 22, 2020 at 10:12 history edited Sextus Empiricus CC BY-SA 4.0
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May 22, 2020 at 10:06 history edited Sextus Empiricus CC BY-SA 4.0
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May 12, 2018 at 10:40 history edited Sextus Empiricus CC BY-SA 4.0
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May 12, 2018 at 10:32 history edited Sextus Empiricus CC BY-SA 4.0
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Aug 10, 2017 at 11:58 history edited Sextus Empiricus CC BY-SA 3.0
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Aug 10, 2017 at 11:53 history answered Sextus Empiricus CC BY-SA 3.0