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Instead of perusing through many more textbooks, I thought it's easier to ask here. Say I would like to express the mean for a variable with a certainty of 95 percent, how exactly do ("should") I do this?

Maybe like:

  • $x_{P = 95\%} = 373.334$ mm $\pm 8.82$ or

  • $x (P = 95\%) = 373.334$ mm $\pm 8.82$

I know I could always write

$x = 373.334$ mm $\pm 8.82$ with a probability of \SI{95}{\percent} but I'd prefer a more compact way.

henry
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    Are these "certainties" confidence or credibility intervals? If so, just call them that (and drop the notion of "certainty" in the former case and append "given the posterior is correct" in the second). – Momo Jun 15 '14 at 20:00
  • @Momo Yes they are. – henry Jun 15 '14 at 20:10
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    OK but which of the two? – Momo Jun 15 '14 at 20:36
  • @Momo Woops sorry I thought you used that synonymously. They are confidence intervals. – henry Jun 16 '14 at 07:06
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    No, they are anything but synonyms. See here http://stats.stackexchange.com/questions/2272/whats-the-difference-between-a-confidence-interval-and-a-credible-interval Should you choose to follow @Alexis's sugestion make sure you understand what a confidence intreval is and how it's interpreted, it certainly isn't certainty.Here's a good start http://stats.stackexchange.com/questions/26450/why-does-a-95-ci-not-imply-a-95-chance-of-containing-the-mean – Momo Jun 16 '14 at 13:46
  • I wasn't aware of the term *credibility interval* before. I meant to address CIs. Using "certainty" in the op, I must say this was probably (75%) all because of the "lost in translation" effect. I had **p**robablity in mind. Besides .... well to make it short, the style of writing of the user in your second linked post is way too complicated for my lack of enthusiasm. – henry Jun 16 '14 at 18:38
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    Thanks for the explanation. I think when you use or list a CI is definitely worthwhile to read and comprehend the meaning of it, particularly because it can neither be interpreted to mean "95% certainty" nor even "95% probability". @Dikran's explanation is so complicated because it has to be, as a CI is a surprisingly subtle thing to grasp. – Momo Jun 16 '14 at 20:08

1 Answers1

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It is not clear what you mean by certainty? Do you mean confidence? Credibility? Something else? Where does the "8.82" in your example come from?

For confidence intervals a fairly standard notation is along the lines of (I am using three significant figures, but your precision may be more or less):

The mean was 373 (95%CI: 365, 382).

There are variations on this. You might read a recent article in a popular journal in your field to see how folks are reporting their confidence (or other) intervals.

Alexis
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