I am trying to build confidence interval for mean of a metrics. To build confidence interval whether standard error or standard deviation should be used ?
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Use the standard error $SE$ (not the standard deviation $s$) to calculate confidence intervals.
The confidence interval for a population mean is equal to:
$$CI=\bar{X} \pm t_{crit}\times SE_{\bar{X}}$$
$$SE_{\bar{X}}= \frac{s}{\sqrt{n}}$$ where $\bar{X}$ is the sample mean and $n$ is the sample size. The assumption for the formula is standard normal distribution.
answered Dec 15, 2016 at 3:21
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1$\begingroup$ It is really the population mean that you determine confidence intervals for. In your example you have a confidence interval centered at the sample mean and the interval is exact only for iid normals. $\endgroup$ Commented Dec 15, 2016 at 3:42
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$\begingroup$ Thanks for the response. Let assume the case - I have access to entire population. In this case is it meaningful to use standard deviation ? (inferential vs descriptive) $\endgroup$– NaveenanCommented Dec 15, 2016 at 3:54
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$\begingroup$ If you have access to the population parameter, there is no need for estimation using sample statistics. You can just present the population mean and standard deviation. $\endgroup$ Commented Dec 15, 2016 at 4:01
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$\begingroup$ If by access to the entire population you mean that you have say a normal distribution with the mean and variance known you don't have an inference problem. For a confidence interval to make sense you would possibly know the variance but not the mean. Then the true standard deviation replaces the sample mean and the t crit with the zcrit but the standard error is still used and the square root of n remains in the denominator. $\endgroup$ Commented Dec 15, 2016 at 4:08
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1$\begingroup$ @JeffreyGirard I see you changed t_crit in your answer to z_crit. I had no objection to assuming normality With the change you need to assume large n and enough central moments for the central limit theorem to apply is you want to make the population distribution more general. Here I am stating the conditions for the Lyapunov version of the central limit theorem. $\endgroup$ Commented Dec 15, 2016 at 9:00