Appendix 07: Critical Values for Grubb’s Test

The following table provides critical values for G(α, n), where α is the probability of incorrectly rejecting the suspected outlier and n is the number of samples in the data set. There are several versions of Grubb’s Test, each of which calculates a value for G_ij where i is the number of suspected outliers on one end of the data set and j is the number of suspected outliers on the opposite end of the data set. The values given here are for G₁₀, where

\[G_\ce{exp} = G_{10} = \dfrac{|X_\ce{out} - \overline{X}|}{s}\]

The suspected outlier is rejected if G_exp is greater than G(α, n).

G(α, n) for Grubb’s Test of a Single Outlier

α⇒	0.05	0.01
n⇓
3	1.155	1.155
4	1.481	1.496
5	1.715	1.764
6	1.887	1.973
7	2.202	2.139
8	2.126	2.274
9	2.215	2.387
10	2.290	2.482
11	2.355	2.564
12	2.412	2.636
13	2.462	2.699
14	2.507	2.755
15	2.549	2.755

Contributors

David Harvey (DePauw University)