Get Standard Error Vs Standard Deviation

If the message you want to carry is about the spread and variability of the data, then standard deviation is the metric to use. If you are interested in the precision of the means or in comparing and testing differences between means then standard error is your metric.

A standard deviation is a measure of variability for a distribution of scores in a single sample or in a population of scores. A standard error is the standard deviation in a distribution of means of all possible samples of a given size from a particular population of individual scores.

The standard error of the sample mean depends on both the standard deviation and the sample size, by the simple relation SE = SD/√(sample size).

The standard error for the difference between two means is larger than the standard error of either mean. It quantifies uncertainty. The uncertainty of the difference between two means is greater than the uncertainty in either mean. So the SE of the difference is greater than either SEM, but is less than their sum.

Standard Deviation is the measure which assesses the amount of variation in the set of observations. Standard Error gauges the accuracy of an estimate, i.e. it is the measure of variability of the theoretical distribution of a statistic.

Thus, the mean tells us what the average value is and the SD tells us what the average scatter of values is, around the mean.

How Are Standard Deviation and Standard Error of the Mean Different? Standard deviation measures the variability from specific data points to the mean. Standard error of the mean measures the precision of the sample mean to the population mean that it is meant to estimate.