Grubbs Test

Null Hypothesis and other hypothesis:

$$\begin{array}{r}{H}_0:\text{No outliers}\\ H_1:\text{Exactly one outlier}\end{array}$$

Test Statistic

$G=\frac{\max |x_i-\bar{x}|}{s}$ with Arithmetic Mean $\overline{x}$ and sample standard deviation $s$.

Reject Null Hypothesis when $G>\frac{N-1}{\sqrt{N}}\sqrt{\frac{t_{\frac{\alpha }{2N},N-2}^2}{N-2+t_{\frac{\alpha }{2N},N-2}^2}}$ where $t$ is the t-Distribution.