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$begingroup$ I am incorporating to some excellent responses below that I gave upvotes to. I do think there is a bit more that needs to be said to completely very clear up the summary. I like the phrases exact and proper as Efron defines them. I gave a lengthy discussion on this pretty not long ago on a different dilemma. The moderator whuber truly favored that answer. I will never Visit the same duration to repeat that right here. On the other hand, to Efron precision relates to The boldness amount and correctness from the width or tightness on the interval.
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$begingroup$ @user31466 your initial assertion was correct in some instances (almost certainly most). But it surely's not likely a concern considering that self-confidence intervals aren't about person observations.
I realize the problems involved, but located them irrelevant for the concern. I haven't noticed a realistic scenario exactly where the real difference mattered possibly, hence the "for all useful functions". $endgroup$
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$begingroup$ To illustrate the numerical stability issue talked about by @cbeleites, here is an example from Simon Wood on how to "break" lm(). Initial we'll produce some easy info and suit an easy quadratic curve.
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$begingroup$ To get a provided dataset, expanding The arrogance volume of home a confidence interval will only result in larger intervals (or at least not smaller
upaboveupabove 3,1771010 gold badges3535 silver badges3939 bronze badges $endgroup$ three 2 $begingroup$ I feel you imply "You will find a smaller sized potential for obtaining an observation exterior that interval". Sadly, a Self esteem Interval may not indicate what it appears to indicate, due to complex, statistical issues, but on the whole the narrower the interval (in a provided assurance degree) the a lot less uncertainty There's about the final results.