Editing Standard error (section)

==Student approximation when ''σ'' value is unknown==
{{further|Student's t-distribution#Confidence intervals|Normal distribution#Confidence intervals}}
In many practical applications, the true value of ''σ'' is unknown. As a result, we need to use a distribution that takes into account that spread of possible ''σ'''s.
When the true underlying distribution is known to be Gaussian, although with unknown σ, then the resulting estimated distribution follows the Student t-distribution. The standard error is the standard deviation of the Student t-distribution. T-distributions are slightly different from Gaussian, and vary depending on the size of the sample. Small samples are somewhat more likely to underestimate the population standard deviation and have a mean that differs from the true population mean, and the Student t-distribution accounts for the probability of these events with somewhat heavier tails compared to a Gaussian. To estimate the standard error of a Student t-distribution it is sufficient to use the sample standard deviation "s" instead of ''σ'', and we could use this value to calculate confidence intervals.

''Note:'' The [[Student's t-distribution|Student's probability distribution]] is approximated well by the Gaussian distribution when the sample size is over 100. For such samples one can use the latter distribution, which is much simpler. Also, even though the 'true' distribution of the population is unknown, assuming normality of the sampling distribution makes sense for a reasonable sample size, and under certain sampling conditions, see [[Central limit theorem|CLT]]. If these conditions are not met, then using a [[Bootstrapping (statistics)|Bootstrap distribution]] to estimate the Standard Error is often a good workaround, but it can be computationally intensive.