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.