# Dixon's Q-test Calculator - Detection of a single outlier

**Dixon’s test** (or the **Q-test**) has been described in a previous post entitled “**Detection of a Single Outlier|Statistical Analysis|Quantitative Data** ”. The test is popular because the calculations involved are simple. A solved example is given in the above post.

**Are there any limitations to Dixon’s Q-test?**

- The data excluding the possible outlier must be
**normally distributed**(use the**Kolmogorov-Smirnov**test to check if data is**normally distributed**) - The
**Q-test**is valid for the detection of a single outlier (it cannot be used for a second time on the same set of data). Other forms of**Dixon’s Q-test**can be applied to the detection of multiple outliers. - The Q-test should be applied with caution – the same applies to all statistical tests used for rejecting data - since there is a probability, equal to the significance level a (a =0.05 at the 95% confidence level) that an outlier identified by the Q-test actually is not an outlier.

Moreover, if two suspect values occur, both of them might be at high end of the measurement range, both at the low end, or one at the high end and one at the low end. In situations like these the test may give erroneous results. As an example consider the following data tested for outliers:

4.0, 4.1, 4.2, 4.3, 4.3, **4.9**, **5.1**

Two of the above values (4.9 and 5.1) are suspiciously high compared with the mean of the data, yet if Q were calculated (at the 95% confidence level) would give **that the tested value 5.1 is not an outlier at the 95% confidence level**. Clearly, the possible outlier 5.1 has been masked by the other possible outlier 4.9 giving a low value for Q compared to Qcrit.

An **online calculator** is given below that can identify outliers in a data set at six different **confidence levels** (80%, 90%, 95%, 96%, 98%, 99%). To test a data set for possible outliers follow the steps below:

- Check that data is
**normally distributed**(**Kolmogorov-Smirnov test**,**Q-Q plot**) - Type data in the yellow-labeled cells
- Select the confidence level from the drop-down list
- See the tested value and the results

__Relevant Posts__

Detection of a Single Outlier|Statistical Analysis|Quantitative Data

Detection of Outliers in Analytical Data – The Grubb’s Test

Calibration and Outliers - Statistical Analysis

__References__

- D. B. Rorabacher, Anal. Chem., 63, 139–146, (1991)
- D. Harvey, “Modern Analytical Chemistry”, McGraw-Hill Companies Inc., 2000
- R.D. Brown, “Introduction to Chemical Analysis”, McGraw-Hill Companies Inc., 1982
- J. N. Miller, J. C. Miller, "Statistics and Chemometrics for Analytical Chemistry", 6th Edition, Pearson, 2010

__Key Terms__

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__normal distribution__

__detection of a single outlier__
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