Standard deviation measures the scatter in a group of observations. It is a calculated summary of the distance each observation in a data set is from the mean. Standard deviation gives us a good idea whether a set of observations are loosely or tightly clustered around the mean.
Sampling error is the difference between a population characteristic and the estimate of this characteristic based on a sample. Sampling error arises because it's often not possible to collect data on a whole population, and samples aren't often identical in character to their parent population. The larger a sample becomes the more likely it will look like the whole population it was sampled from, resulting in a smaller sampling error. If we did a complete enumeration of the population, such as in a census, there would be no sampling error.
The Standard Error (SE) is one way of measuring the sampling error of an estimate. The theory shows that there are about two chances in three that an estimate from a sample is within one standard error of the true value (the value for the whole population). As such, the larger the standard error, the less confident we are that the estimate from the sample is close to the true value.
There are several types of Standard Error (SE). A commonly used type of standard error in the Australian Bureau of Statistics is the Standard Error of the Mean.
Relative Standard Error:
The relative standard error (RSE) is the standard error of the estimate divided by the estimate itself. It is another way of expressing the standard error to make interpretation easier. It's useful for comparing the size of the standard error across different samples, and is often expressed as a percentage. As with the standard error, the higher the RSE, the less confident we are that the estimate from the sample is close to the true value.
This page last updated 26 June 2008