Dixon's extreme value test is used by VSP to test whether an extreme observation is a statistical outlier. This test can be used to detect an outlier that is either much smaller or much larger than the rest of the selected data values.
Dixon's test is appropriate only when the data, excluding the suspected outlier, are approximately normally distributed, and when the sample size is less than or equal to 25.
Data should not be excluded from analysis solely on the basis of the results of this or any other statistical test. If any values are flagged as possible outliers, further investigation is recommended to determine whether there is a plausible explanation that justifies removing or replacing them.
The \(n\) observed values are ordered from smallest to largest. The test statistic \(C\) is then calculated according to the appropriate formula from the following table:
\(3 \le n \le 7\) |
\(8 \le n \le 10\) |
\(11 \le n \le 13\) |
\(14 \le n \le 25\) |
|
Lowest value (\(X_1\)) suspected outlier |
\(C=\frac{X_2-X_1}{X_n-X_1}\) |
\(C=\frac{X_2-X_1}{X_n-X_1}\) |
\(C=\frac{X_3-X_1}{X_{n-1}-X_1}\) |
\(C=\frac{X_3-X_1}{X_{n-2}-X_1}\) |
Highest value (\(X_n\)) suspected outlier |
\(C=\frac{X_n-X_{n-1}}{X_n-X_1}\) |
\(C=\frac{X_n-X_{n-1}}{X_n-X_2}\) |
\(C=\frac{X_n-X_{n-2}}{X_n-X_2}\) |
\(C=\frac{X_n-X_{n-2}}{X_n-X_3}\) |
This test statistic \(C\) is compared with a critical value \(d_{\alpha}\) obtained from a table (Table A-4, EPA), where \(\alpha\) is the required significance level.
If the test statistic \(C\) exceeds the critical value \(d_{\alpha}\), the null hypothesis that there are no outliers in the data may be rejected, and there is sufficient evidence to conclude that the selected most extreme value is an outlier.
If the test statistic \(C\) does not exceed the critical value \(d_{\alpha}\), the null hypothesis that there are no outliers in the data cannot be rejected.
EPA. 2006. Data Quality Assessment: Statistical Methods for Practitioners EPA QA/G-9S, EPA/240/B-06/003, U.S. Environmental Protection Agency, Office of Environmental Information, Washington DC.