Inferential Statistics

Standard Error

The standard error is an important element of inferential statistics. As described on the "Basics of Inferential Statistics" page, sampling error is the error that we can expect due to the fact that we're making inferences based on a sample rather than examining the entire population. The field of statistics gives us ways of estimating the sampling error, and one measure of that error is "standard error." The greater the standard error, the greater our uncertainty due to sampling error.

One common place to see a standard error is alongside a mean that's been calculated from a sample. For example: observed mean = 33.1 units, standard error = 1.4 units. The simple way to use that information is to create a 95% confidence interval with the following:

confidence interval = observed mean ± 2 * standard error

Applying that to the example, we get:

confidence interval (upper bound)  =  33.1 + 2*1.4  =  35.9

confidence interval (lower bound)  =  33.1 - 2*1.4  =  30.3

So, we are 95% confident the true value in the population is between 35.9 and 30.3. Our best estimate for the population value is 33.1 (i.e., the observed mean), and the confidence interval tells us how uncertain we should be due to the fact that we have observations only from a sample instead of the entire population. Let me say that another way: The true mean of the population could easily be as high as 35.9 units and as low as 30.3 units, and that uncertainty is simply due to the fact that we only talked to a sample of people rather than the entire population.