Grubbs Test

Null Hypothesis and other hypothesis:

H0:No outliersH1:Exactly one outlier\begin{aligned} H_{0}: \text{No outliers} \\ H_{1}: \text{Exactly one outlier} \end{aligned}

Test Statistic

G=max⁡∣xi−xˉ∣sG=\frac{\max \left|x_i-\bar{x}\right|}{s}

with Arithmetic Mean x‾\overline{x} and sample standard deviation ss.

Reject Null Hypothesis when

G>N−1Ntα2N,N−22N−2+tα2N,N−22G>\frac{N-1}{\sqrt{N}} \sqrt{\frac{t^2_{\frac{\alpha}{2 N}, N-2}}{N-2+t^2_{\frac{\alpha}{2 N}, N-2}}}

where tt is the t-Distribution.