# No, its not correct to say that you can be 95% sure that the true value will be in the confidence interval

Hans van Maanen writes:

Mag ik je weer een statistische vraag voorleggen?

If I ask my frequentist statistician for a 95%-confidence interval, I can be 95% sure that the true value will be in the interval she just gave me. My visualisation is that she filled a bowl with 100 intervals, 95 of which do contain the true value and 5 do not, and she picked one at random.
Now, if she gives me two independent 95%-CI’s (e.g., two primary endpoints in a clinical trial), I can only be 90% sure (0.95^2 = 0,9025) that they both contain the true value. If I have a table with four measurements and 95%-CI’s, there’s only a 81% chance they all contain the true value.

Also, if we have two results and we want to be 95% sure both intervals contain the true values, we should construct two 97.5%-CI’s (0.95^(1/2) = 0.9747), and if we want to have 95% confidence in four results, we need 0,99%-CI’s.

I’ve read quite a few texts trying to get my head around confidence intervals, but I don’t remember seeing this discussed anywhere. So am I completely off, is this a well-known issue, or have I just invented the Van Maanen Correction for Multiple Confidence Intervals? ;-))

Ik hoop dat je tijd hebt voor een antwoord. It puzzles me!