Standard Error of the Mean (2 of 2)
A graph of the effect of sample size on the standard error for a standard deviation of 10 is shown below:
As you can see, the function levels off. Increasing the sample size by a few subjects makes a big difference when the sample size is small but makes much less of a difference when the sample size is large. Notice that the graph is consistent with the formulas. If σM is 10 for a sample size of 1 then σ M should be equal to
for
a sample size of 25. When s is used as an estimate of σ,
the estimated standard error of the mean is 
.
The standard error of the mean is used in the computation of confidence
intervals and significance tests for the
mean.