Standard error

The standard error is an estimate of how much the value of a test statistic varies from sample to sample. It is a measure of the uncertainty of the test statistic. Standard error might be abbreviated as std. error.

The standard error is calculated by taking the standard deviation of the sampling distribution for the test statistic. The sampling distribution is the distribution of all possible samples.

Imagine you were conducting a survey and randomly chose 1,000 people for the survey. This group is one sample. You can choose another random sample of 1,000 people, and another sample, and another sample, and so on. You can then calculate the mean for each sample. The distribution of these sample means is the sampling distribution. By calculating the standard deviation of this distribution, you obtain the standard error of the mean. When standard error is written without qualification, it is assumed to be the standard error of the mean.

You can also calculate the standard error of the kurtosis and the standard error of the skewness. To calculate the standard error of the kurtosis, you calculate the kurtosis for each sample and take the standard deviation of the resulting distribution. The standard error of the skewness is similar except that you calculate the skewness of each sample.