Standard error is the estimated standard deviation of a parameter estimate.

Example 1

To examine the mean change of blood pressure (BP) after taking an anti-hypertensive drug in hypertensive patients, we may randomly recruit a number of patients and measure their BP before and after the administration of the drug. We may use the sample mean BP change to estimate the "true" mean BP change. Note that this same mean may vary if we obtained other samples. Such variation can be quantified by the standard deviation of the sample mean across all possible samples. The corresponding estimated standard deviation would be the standard error for the mean.

Example 2

A researcher wants to determine the proportion of Hong Kong school children with habitual snoring. A sample of 3047 school children was contacted by phone. Of which, 45 (1.5%) children were found with habitual snoring. The corresponding standard error was 0.0022.

The proportion of Hong Kong school children with habitual snoring is the parameter of interest. The 1.5% obtained from the sample is an estimate of this parameter. The standard error is the estimated standard deviation of this parameter estimate.