Outlier Test - Dean and Dixon

A test for outliers of normally distributed data which is particularly simple to apply has been developed by J.W. Dixon. This test is eminently suitable for small sample sizes; for samples having more than 30 observations the test for significance of Pearson and Hartley can be used as well. In order to perform the Dean-Dixon test for outliers, the data set containing N values has to be sorted either in an ascending or descending order, with x₁ being the suspect value. Then the test statistic Q is calculated using the equation

The decision whether x₁ is an outlier is performed by comparing the value Q to the critical values listed in the following table (N is the number of observations, α is the level of significance): If the calculated value of Q is greater than the critical threshold the corresponding data value x₁ is regarded to be an outlier.

Critical values for r₁₁

N	α=0.001	α=0.002	α=0.005	α=0.01	α=0.02	α=0.05	α=0.1	α=0.2
8	0.799	0.769	0.724	0.682	0.633	0.554	0.480	0.386
9	0.750	0.720	0.675	0.634	0.586	0.512	0.441	0.352
10	0.713	0.683	0.637	0.597	0.551	0.477	0.409	0.325

Hint:

Please note that the critical values listed in the tables above have been calculated by performing 106 random experiments per value. These values differ slightly from values published by various authors, many of them using interpolation techniques to estimate the critical values.