Editing Standard deviation (section)

==Relationship with standard error and statistical significance==

The standard deviation of a population or sample and the [[standard error]] of a statistic (e.g., of the sample mean) are quite different, but related. The sample mean's standard error is the standard deviation of the set of means that would be found by drawing an [[Infinity|infinite]] number of repeated samples from the population and computing a mean for each sample.  The mean's standard error turns out to equal the population standard deviation divided by the square root of the sample size, and is estimated by using the sample standard deviation divided by the square root of the sample size. For example, a poll's standard error (what is reported as the [[margin of error]] of the poll) is the expected standard deviation of the estimated mean if the same poll were to be conducted multiple times. Thus, the standard error estimates the standard deviation of an estimate, which itself measures how much the estimate depends on the particular sample that was taken from the population. 

In [[science]], it is common to report both the standard deviation of the data (as a summary statistic) and the standard error of the estimate (as a measure of potential error in the findings). By convention, only effects more than two standard errors away from a null expectation are considered "[[Statistical significance|statistically significant]]", a safeguard against spurious conclusion that is really due to random sampling error.