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Suppose that I make a point estimate, 0.7, with a 90% CI: [0.6, 0.8].

Can I say that in the worst case, the true parameter is 0.6 and in the best case it's 0.8?

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    $\begingroup$ Possible duplicate of What, precisely, is a confidence interval? $\endgroup$
    – Firebug
    Jul 30, 2016 at 14:27
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    $\begingroup$ I think you'll get a more useful answer if: A) You don't use "best" and "worst" but rather "low" and "high". B) You give some context as to what you are measuring and what you want to find out. C) Since confidence intervals only really make sense in a situation where you measured a random(ish) sample of data and want to make conclusions about the population the data were sampled from, tell us about sample and population in the context of your work. $\endgroup$ Jul 30, 2016 at 15:32
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    $\begingroup$ There is a misunderstanding behind this, but it is a reasonable question. It doesn't merit a downvote, IMO. $\endgroup$ Jul 30, 2016 at 15:46
  • $\begingroup$ Although knowing exactly what a CI is would obviate this question, I don't think it's really a duplicate of the linked thread. $\endgroup$ Jul 30, 2016 at 16:59

3 Answers 3

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The true parameter value simply is whatever it is. It isn't clear what "best case" or "worst case" could mean. You might be happy or sad about the actual value of the parameter, if you could magically find out its true value, but it is constant.

Both @PeterFlom and @R.Carlos have accurately explained what a confidence interval is. Here is another way to think about it. In your case, if you had chosen $.6$ (or $.8$) as your null hypothesis and conducted your test at the $\alpha=.10$ level, you would not have rejected the null, but if you had chosen $.59$ (or $.81$) instead (or tested at the $\alpha=.05$ level), you would have rejected the null.

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No. That is not a correct statement; it might not even be a meaningful one.

The Wikipedia page for confidence intervals is pretty good, I think. In particular, this line:

When we say, "we are 99% confident that the true value of the parameter is in our confidence interval", we express that 99% of the hypothetically observed confidence intervals will hold the true value of the parameter.

is a good explanation of what CIs really are.

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  • $\begingroup$ Is it okay to say: "95% of the time, this will be the worst/best value that this parameter will take on"? $\endgroup$
    – user46925
    Jul 30, 2016 at 12:44
  • $\begingroup$ We are 95% confident that this is the worst case we'll get $\endgroup$
    – user46925
    Jul 30, 2016 at 12:45
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    $\begingroup$ We can say that if we did the same experiment 1000 times we would expect that approximately 950 times the 95% CI will contain the true parameter. That's all. We can't get at what you want. $\endgroup$
    – Peter Flom
    Jul 30, 2016 at 12:49
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    $\begingroup$ What does the upper/lower bound represent then? 95% of re-trials: "this will be the lower/upper bound". I'm not sure what these numbers intuitively represent. How are clients benefitted by these upper/lower numbers if they don't give intuition on worst/best case? $\endgroup$
    – user46925
    Jul 30, 2016 at 12:58
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    $\begingroup$ I don't know how to state it any more clearly than I already have. I agree that CIs (like p values) are overused and misinterpreted. You might look into credible intervals from Bayesian stats. In some cases, confidence intervals and credible intervals are similar. $\endgroup$
    – Peter Flom
    Jul 30, 2016 at 13:12
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As Peter said. Reapeating your experiment x times and calculating CIs everytime then 95% of these CIs will contain the real population parameter which you tried to estimate. The parameter is either in or not. There is no probability assigned of how close your estimate is to the population parameter.

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  • $\begingroup$ I've repeated the experiments 10000 times and I get those bounds. In the 95% worst case, the parameter will be 0.6. $\endgroup$
    – user46925
    Jul 30, 2016 at 13:21
  • $\begingroup$ Does that make sense? $\endgroup$
    – user46925
    Jul 30, 2016 at 13:21
  • $\begingroup$ It might not be right. But it makes sense. $\endgroup$
    – user46925
    Jul 30, 2016 at 13:59

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