Standard deviation of dummy variable

[Deepti Goel]

I have a dummy variable called male which has 12 values equal to 1 and 12 values equal to 0 (total of 24 observations). The sum command on this variable gives a mean of 0.5 and a std. dev. of 0.5107539. Why is the std. dev. not equal to 0.5?

[Nick Cox]

Stata uses sample size minus 1 in calculating SD, that is the estimator of SD is the root of the unbiased estimator for variance.

[Nick Cox]

Here is a demonstration:

. mata
------------------------------------------------- mata (type end to exit) -
: x = J(12,1,0) \ J(12,1,1)

: sqrt(sum((x :- 0.5):^2) :/ 24)
  .5

: sqrt(sum((x :- 0.5):^2) :/ 23)
  .5107539185