$ s_{\bar x} = \frac{s}{\sqrt{n}} $ - $s$ is the [Sample Standard Deviation](Sample%20Standard%20Deviation.md) - $n$ is the sample size For a sequence of **Bernoulli trials**, calculating $s_{\bar x}$ can be simplified to: $ s_{\bar x} = \frac{ \sqrt{p \times (1-p)} }{ \sqrt{n} } = \sqrt{\frac{ p \times (1-p) }{n} }$ - $p$ is the probability of success of a single Bernoulli trial Because the [Variance](Variance.md) for Bernoulli trials is $p \times (1-p)$ The SEM estimates the location of the population mean based on a sample of normally distributed variables. (Said differently, it measures the deviation of the sample mean from the population mean.) The SEM effective represents the standard deviation of the statistic (i.e., of the the sampling distribution). The standard error therefore is a statistic that reveals how accurately the sample represents the population. The SEM is useful to compare if two samples are most likely from the same distribution: If their SEM intervals overlap, the probability that they are from the same distribution is $p > 0.05$. The SEM is considered an **inferential** statistic.