Estimation error
The difference between the sample means, ,
is a point estimate of the difference between the means of the underlying populations, µ2 - µ1.
In order to properly interpret it, we must understand the distribution of
the estimation error.
Replacing σ12 and σ22 by s12 and s22 gives an approximate error distribution,
The standard deviation of these errors is the standard error of the estimator.
Examples
Our best estimate is that anticipation of hypnosis results in a mean ventilation rate that is 0.491 higher than the control group. From the error distribution, the error in this estimate is unlikely to be more than about 0.6.