DIXON outlier tests, critical values

Selected Critical Values for DIXON Outlier Tests... 

For a quick investigation of a small number of data (less than 20 values), one can use the Dixon Q test, which is ready-made for testing small sets of experimental data. The test is performed by comparing the difference between a suspected outlier and its nearest data point with the range of the data, producing a ratio of the two (i.e., a 0ca c value, see Equation 2.22), which is then compared with critical values of Q from tables (see Table 2.3). 

TABLE 6.6. Critical Values for Dixon s Test. The Suspected Value is an Outlier if the Calculated 2-Statistic is Above the Critical Value... 

The first method is Dixon s Q-test. The data points are ranked and the difference between a suspected outlier and the observation closest to it is compared to the total range of measurements. This ratio is the Q-value. As with the f-test, if the computed Q-value is greater than tabulated critical values for some pre-selected level of significance, then the suspect data value can be identified as an outlier and may be rejected. 

To perform Dixon s test, we start by calculating the smallest and largest differences between the suspect element and the rest of the values of the data set. Then we take the ratio of the smallest difference to the largest, and compare the result with a tabulated critical Q-value that depends on the desired confidence level and the total niunber of elements in the sample. If the calculated ratio is larger than the tabulated value, we can consider the suspect value as an outlier. In oiu example, there exists only one suspect value (the 56.3 min. time obtained in the ninth experiment), so we will use the Q-values for a one-sided tail test. Since the extreme... 

Table 4 Critical values of Q (P=0.05) for a two-sided Dixon s test for outliers...

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