Is sample standard deviation same as standard error with a value sigma/root of n?

Sample standard deviation is an estimator of the population std. dev… A distribution from which you draw a sample has a standard dev. and you take the std dev of your sample to estimate it. When you calculate a statistic since its based on random data, it is random also. If its random it has a distribution called its sampling distribution. The std error is the std dev of this distribution. For X-bar the s.e. is sigma/Sqrt(n).

Joey, you sound like a statistics professor!

That was my job for 10 yrs…

Also, your sample standard deviation is calculated based on n-1…but sample std deviation is already given to you So, std error is based on n…

Whoa Your sample standard deviation is calculated using n-1 because that makes the sample variance unbiased (of course, the sample std deviation is biased anyway so it’s not all that clear why you did it). The Var(X-bar) = Sigma^2/n so any unbiased estimator of sigma^2 gives you and unbiased estimator for Var(X-bar) (and then of course s.e. is biased again so it’s still not clear why you did it).