Standard Error

Calculating the Standard Error.

Depending on your situation, you don't have to actually construct a distribution. The value of the standard error can be calculated.

For our example, with a single mean, the standard error of the sampling distribution of the mean = S_x/N.

S_x equals the standard deviation calculated from your sample.

The standard error formula can vary for different sample statistics. One can determine the standard error for a proportion, different between means, a correlation coefficient, slope of a regression line, intercept and other items. Your texts can supply these.

The important idea is that you have a sample statistic and want to build a frequency distribution of all the possible samples. Then, you want to describe the variability of these samples. This is the use of the standard error.

Here are some important points about samples:

Bottom Line:

The standard error describes the variability of a frequency distribution of sample statistics.
It is the standard deviation of this distribution.
The larger the sample, the smaller the standard error.
The smaller the sample, the greater the chance of extreme sample statistics.
The Sampling Distribution is Not Normal.
For many statistics, it has a shape called the t-distribution.
This shape is based on the df.
You will use the sampling distribution and standard error to make decisions about statistical significance.