Interpreting the standard error

The 70-95-100 rule-of-thumb provides a useful interpretation of the standard error of an estimator.

There is approx 95% probability that the error is within 2SE of zero and it is almost certainly within 3SE of zero.

Note that the term standard error is often abbreviated to SE.

Example

A random sample of n values is taken from a population with distribution,

X  ~  normal (μ , σ = 0.0068)

giving a sample mean that is 0.0724. This is our estimate of µ. The standard error of this estimate is

standard error  =  SE  = 

The error in our estimate has about 95% chance of being within 2SE = 0.0034 of µ and is almost certain to be within 3SE = 0.0051 of it.