Key concepts: SEM

What is the SEM?

The standard error of the mean (SEM) quantifies the precision of the mean. It is a measure of how far your sample mean is likely to be from the true population mean. It is expressed in the same units as the data.

Is the SEM larger or smaller than the SD?

The SEM is always smaller than the SD. With large samples, the SEM is much smaller than the SD.

How do you interpret the SEM?

Although scientists often present data as mean and SEM, interpreting what the SEM means is not straightforward. It is much easier to interpret the 95% confidence interval, which is calculated from the SEM.

With large samples (say greater than ten), you can use these rules-of-thumb:

The 67% confidence interval extends approximately one SEM in each direction from the mean.

The 95% confidence interval extends approximately two SEMs from the mean in each direction.

The multipliers are not actually 1.0 and 2.0, but rather are values that come from the t distribution and depend on sample size. With small samples, and certainly when N is less than ten, those rules of thumb are not very accurate.

Is the SEM the same as the SD?

No!