Dixon Q-test

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). 

The hypothesis we propose to test is that 71 ng/g is not an outlier in this data. Using the Dixon Q test, we obtain the following result ... 

On occasion, a data set appears to be skewed by the presence of one or more data points that are not consistent with the remaining data points. Such values are called outliers. The most commonly used significance test for identifying outliers is Dixon s Q-test. The null hypothesis is that the apparent outlier is taken from the same population as the remaining data. The alternative hypothesis is that the outlier comes from a different population, and, therefore, should be excluded from consideration. 

Dixon s Q-test statistical test for deciding if an outlier can be removed from a set of data. (p. 93) dropping mercury electrode an electrode in which successive drops of Hg form at the end of a capillary tube as a result of gravity, with each drop providing a fresh electrode surface, (p. 509)... 

Q Test statistic (estimate) of Dixon s outlier test (4.35)... 

The Q test, suggested by Dean and Dixon (1951) is statistically correct and valid, and it may be applied easily as stated below ... 

If the data as a whole appear normally distributed but there is concern that an extreme point is an outlier, it is not necessary to apply the Rankit procedure. The Grubbs s outlier test (1950) is now recommended for testing single outliers, replacing Dixon s Q-test. After identifying a single outlier, which, of course, must be either the maximum or minimum data value, the G statistic is calculated ... 

Table 21.4—Abridged table of critical values of Q (Dixon s test).

Critical Values of Dixon s Q Test for a Two-Tailed Test at the 95% Confidence Level [2]... 

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. 

Decision limit 32, 33 Degrees of freedom, 8 Dendrogram, 97, 105 Detection limit, 32, 33 Determination limit, 32, 33 Differentiation, 55 Savitsky-Golay, 57 Discriminant function, 124, 130 Discriminant score, 130 Discrimination, 123 Dispersion matrix, 82 Distance measures, 99 Dixon s Q-test, 13... 

Quantity Attribute or phenomenon, body or substance that may be distinguished qualitatively and determined quantitatively. (Section 1.4) Q-test (Dixon s Q-test) An outlier test. Grubbs s test is the preferred test to use. (Section 3.5)... 

We now return to the apparently anomalous value. Many tests to detect outlying data have been proposed. One of the most frequently used in chemistry is Dixon s Q test, which assumes that the values being tested are normally distributed. Actually there are several tests identified as Dixon s, all based on comparing differences between the suspect value and the other values of the sample. You can obtain more information about these tests in Skoog et al. (1996), and in Rorabacher (1991). Here we will limit our discussion to the following question can we consider the 56.3 min. time of experiment 9 as an element of the same distribution that produced the other times recorded for path C ... 

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...

Dixon s test (sometimes called the Q-test) is another test for outliers which is popular because the calculation is simple. For small samples (size 3 to 7) the test assesses a suspect measurement by comparing the difference between it and the... 

In order to use Dixon s test for an outlier, that is to test Hq all measurements come from the same population, the statistic Q is calculated ... 

To prove that the outlier is outside the expected range of observations a statistical test may be of help. A common statistical approach may be to apply the Q-test of Dixon. Q is defined as the ratio of the deviation of the discordant value from its nearest neighbours with respect to the range of the values. 

If it does, then an outlier test is performed, for example Dixon s Q-test ... 

Table 20.4 Dixon s Q-test limit values (Gardner-version)...

Efstathiou, C. E., Dixon s Q-test Detection of a single outlier, http // www.chem.uoa.gr/applets/AppletQtest/Text Qtest2.htm, Laboratory of Analytical Chemistry, Department of Chemistry, National and Kapodistrian University of Athens, 2008. 

Also known as Dixon s Q-test, this is one of several that have been devised to test suspected outliers in a set of replicates. It involves the calculation of a ratio, Qexptu defined as the absolute difference between a suspect value and the value closest to it divided by the spread of all the values in the set ... 

Dixon s Q, used to test for outliers product-moment correlation coefficient number of rows in two-way ANOVA... 

With the hypothesis and confidence level selected, the next step is to apply the chosen test. For outliers, one test used (perhaps even abused) in analytical chemistry is the Q or Dixon test ... 

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