Difference between standard error and standard deviation

The standard deviation of a sample mean is closely related to the population's standard deviation:

 = 

For example,

There is a similar relationship between the standard deviation of a sample and the standard error of the mean. Do not confuse them:

Standard deviation (SD)
This describes the spread of values in the sample. It is roughly the same whatever the sample size.
Standard error of the mean (SE)
This is the standard deviation of the sample mean, , and decreases as the sample size increases.

Common mistakes in interpretation

Standard error does not describe the variability of individual values
A new value has about 95% probability of being within 2 standard deviations of sample mean.
Standard deviation does not describe the accuracy of the sample mean
The sample mean has about 95% probability of being within 2 standard errors of the population mean.

Warning

Be particularly careful when reading journal articles. Some papers use standard deviations (SD) to describe the distribution of variables, but others give the standard errors (SE) of the means of the variables.