Problem with 95% CI from mean command

[Philip Clare]

Hi all,

Apologies if this has been discussed before, but I couldn't find anything on it.

I'm using Stata 14.1, and having an issue with the command 'mean'. Specifically, the 95% confidence intervals it generates don't appear to be 95%. As an example, when I run mean on a variable in my dataset, it generates the following output:

. mean day

Mean estimation Number of obs = 212

--------------------------------------------------------------
| Mean Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
day | 1659.731 326.08 1016.939 2302.523
--------------------------------------------------------------

However, when I manually calculate the 95% confidence interval based on the formula:

x̅ ± z(0.05/2) x S.E.

I get a confidence interval of 1020.626 - 2298.836. Similar, but not exactly the same.

Working backwards from the CI generated by stata, it looks like it's using a z that is smaller than 0.05 - and the exact value varies depending on the calculation/variable used.

Not a major issue, I would just like to understand why it is doing it (assuming its deliberate).

[Stephen Jenkins]

I recommend that you check the formulae that are used. You assume "z", i.e. normal approximation, when in fact "t" is used:

. sysuse auto
(1978 Automobile Data)

. mean price

Mean estimation                   Number of obs   =         74

--------------------------------------------------------------
             |       Mean   Std. Err.     [95% Conf. Interval]
-------------+------------------------------------------------
       price |   6165.257   342.8719      5481.914      6848.6
--------------------------------------------------------------

. di 6165.257 + invnorm(.975)*342.8719
6837.2736

. di 6165.257 + invttail(73,.025)*342.8719
6848.5997