Thursday, September 11, 2008

standard error vs standard deviation

I sat in Andy's stats modeling class last Friday. Andy explained the difference between standard error and standard deviation. I am often confused about these two terms. So I think I will write down what he said as a blog entry. Just to remind myself in the future in case I forgot again.

He gave us a very simple explaination that:


Standard deviation: asymptotically, this estimate will be sigma.

\hat{\sigma}=sqrt{\frac{1}{n}\sum_{i=1}^n \left(x_i-\overline{x}_i\right)^2}

Standard error: asymptotically, this estimate will go to zero (as n is in the denominator of the formula, and as it goes to infinity, SE goes to 0).

SE_{\overline{x}}=\frac{\sigma}{\sqrt{n}

This seems to be an obvious answer once we look at the formulas of the two estimates. Nonetheless, Andy said that he sometimes uses them interchangeably.

3 comments:

Anonymous said...

Well, for what condition, they can use interchangeably?

Viper said...

Actually I would like to know the difference between" sample standard deviation" and "sample standard error" what you show above is basically the "population standard deviation" against" sample standard error"

Author said...

Standard Deviation

Standard Deviation Calculator