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I've seen confidence intervals constructed using $\pm 1.96 *SE$ and $\pm 1.96*SD$. Sometimes, the SD is either the (possibly estimated) population or sample SD. When is each one used?

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    $\begingroup$ Please say where you’ve seen a confidence interval constructed using standard deviation instead of standard error. $\endgroup$
    – Dave
    Jul 11, 2020 at 1:29

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You would use the standard error. Standard deviation has a tragically similar name but is a somewhat different idea.

(They’re related, just not in a way that makes much sense to someone who is just starting with statistics.)

You will go on to learn situations where $1.96*SE$ stops being the way you construct confidence intervals, but $1.96*SD$ won’t come up. That’s just wrong, and as my comment indicates, I am curious where you read that.

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  • $\begingroup$ onlinestatbook.com/2/estimation/mean.html here is one place where they seemed to use SE to compute the CI, but wrote "These limits were computed by adding and subtracting 1.96 standard deviations to/from the mean of 90 as follows:" It actually looks like a typo. $\endgroup$
    – David
    Jul 11, 2020 at 1:41
  • $\begingroup$ Also this one healthknowledge.org.uk/e-learning/statistical-methods/… -- search for "The mean plus or minus 1.96 times its standard deviation gives the following two figures:" $\endgroup$
    – David
    Jul 11, 2020 at 1:42
  • $\begingroup$ The first one has confusing phrasing, but the standard deviation they mean is the standard deviation of the sampling distribution, which is what standard error means. In the second one, the use of standard deviation instead of standard error is not in the discussion of confidence intervals, though putting that discussion so close to the discussion of confidence intervals seems like a poor teaching technique that is certain to confuse people. $\endgroup$
    – Dave
    Jul 11, 2020 at 2:10
  • $\begingroup$ @Dave I agree. This is one reason why when I teach Intro classes I choose not to teach 2*SD as a cheater method for introducing confidence intervals, though I know a lot of books use this and similar cheats (like "range rule of thumb" and the cheap sample size estimate) to start the conversation. $\endgroup$
    – Todd Burus
    Jul 11, 2020 at 3:41
  • $\begingroup$ @Dave Wait, I'm not familiar with "SE being SD of sampling distribution." This isn't equivalent to saying that "SE is the SD of a set of samples" right? Because I thought SE is the sampling SD divided by the square root of the sample size? $\endgroup$
    – David
    Jul 11, 2020 at 4:58

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