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## Dixon test

Dixon’s Q test can be used for testing a single low (or high) value in a relatively small data set (typically between 3 and 7 values). The test statistic is calculated using the equation shown below. This form of the Dixon test is also known as the r10 test. To carry out a Dixon test the data must first be arranged in ascending order so that x1 represents the lowest value and xn represents the highest value.

In each case, the calculated test statistic is compared with the critical value for the required level of confidence and number of data points, n. Some critical values for the Dixon test, at the 95% confidence level, are shown below. If the calculated value exceeds the critical value then the result of the test is significant and the outlying value requires further investigation (see section on Handling outliers).

 Critical values for Dixon Q test for a single outlier on either side(1) 95% confidence, two tailed n Q (r10) 3 0.970 4 0.829 5 0.710 6 0.625 7 0.568

(1)D. B. Rorabacher, Anal. Chem., 1991, 63, 139

Example

The table below shows the means of results returned by laboratories participating in an interlaboratory study. The results have been listed in ascending order. Use the Dixon test to determine whether there is a single low (or high) outlier in the data set at the 95% confidence level.

 64.12 64.24 65.11 65.45 65.82 65.92 69.02

The figure below shows a ‘dot plot’ of the data.

Since there are seven values, the appropriate test is the Q test (r10):

The critical value for n = 7 at the 95% confidence level is 0.568. The calculated Q value for the highest result in the data set exceeds the critical value and would therefore be considered an outlier at the 95% confidence level.

A Dixon test is simple to carry out as it does not require the calculation of any statistical parameters such as the mean or standard deviation. Grubbs’ test can also be used to test for single outliers and is generally considered more robust than a Dixon test because:

• Dixon’s test compares the extreme value to a neighbouring value rather than the mean of the data set;
• Dixon’s test uses the range which is a less efficient measure of variability than the standard deviation.