(Please note that a problem was discovered with the original version of the script that was made available before 09Oct2014. The problem occurred when the sample size was greater than 30. has been corrected and the updated of the version replaced. The available tables of critical values only go to a sample size of 30, so the critical value for sample size 30 is used for all sample sizes greater than 30.)
(Please note further that a another problem was discovered with the version of the script made available before 25Nov2017. The problem occurred by skipping the case for the computation of the Dixon q statistic for the single upper outlier by R10. Credit to user Julie Grender for identifying this problem and bringing it to our attention.)
This script implements the outlier tests by Dixon. The chosen test is appended to a Distribution platform. These tests are intended for small samples of data, where n is no more than 30. These tests are not intended to be used repeatedly or iteratively with the same data sample.
Simply open the data table with the data column suspected to include an outlier. (Note it is a good idea to examine the data with the Distribution platform before applying a test. The presence and nature of the suspected outlier will suggest an appropriate choice of the Dixon test.) Select the data column and click Y, Data. Select the appropriate test and the desired level of significance.
Q0 is the critical value of the statistic. A sample statistic Q that is greater than the critical value is significant. The test for an extreme outlier (low or high) was not significant at the 0.05 level.
A different test (single low outlier) is significant in this case.
(1) R. B. Dean and W. J. Dixon (1951) Simplified Statistics for Small Numbers of Observations. **bleep**. Chem., 1951, 23 (4), 636–638.
(2) Barnett V. and T. Lewis (1994) Outliers in Statistical Data, 3rd Edition, New York: John Wiley & Sons.