non-parametric confidence intervals for mean

[Li Chen]

If the data I have is not normally distributed, is it possible to compute sample mean in stata using some non-parametric confidence intervals? Thanks!

[Carlo Lazzaro]

Li Chen:
you may want to take a look at -help bootstrap- and related entry in Stata .pdf manual.

[daniel klein]

Computing a sample mean does not require a normal distribution of the data (variable, I suppose) at hand. If the variable is highly skewed and you are worried that the mean does not accurately represent what you are trying to say about your data, you may want to report additional statistics like a median or range. Or maybe some graphical approach?

Best
Daniel

[Li Chen]

Thanks! But I to compute confidence intervals we need to assume normality? The idea is very simple: I want to check in a data, given people from the same characteristics, how many of them their academic performance lie outside the average with a confidence interval.

But I think you are right, I should consider median probably if the data is skewed.

Computing a sample mean does not require a normal distribution of the data (variable, I suppose) at hand. If the variable is highly skewed and you are worried that the mean does not accurately represent what you are trying to say about your data, you may want to report additional statistics like a median or range. Or maybe some graphical approach?

Best
Daniel

[Nick Cox]

Some basic confusions seem present here that are covered in any detailed introductory course.

The most commonly used confidence interval procedure rests on the assumption that the sampling distribution of the mean is normal, not that the data are normal. Convergence to that sampling distribution will be faster if the data are normal; that's all. although it could be an important detail if the sample size is very small or the distribution very far from normal.

How many people fall outside the confidence interval for the mean is not a particularly good question to ask. As the sample size gets larger, the answer will be "almost all of them". So, this is a poor way to identify under- or over-performers. Looking at the extremes in the data is more direct and more appropriate.