Question

Data set: 15 26 64 54 35 48 31 23 29 51 39 28 46 35...

Data set: 15 26 64 54 35 48 31 23 29 51 39 28 46 35 4 22  37 28 52.

Is the number 4 an outlier? Test with the Dixon and Standard Deviation Test.

Math   Statistics-And-Probability   
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Answer #1

The test is very simple and it is applied as follows:

(1) The observations are arranged in ascending order.

(2) The statistic experimental Q-value is calculated.

(3) The obtained Qexp value is compared to a critical Q-value (Qcrit) found in tables. This critical value should correspond to the confidence level (CL) we have decided to run the test (usually: CL=95%).

(4) If Qexp > Qcrit, then the suspect value is characterized as an outlier.

Here, the given data set in ascending order is -  4, 15, 22, 23, 26, 28, 28, 29, 31, 35, 35, 37, 39, 46, 48, 51, 52, 54, 64

The corresponding Qexp value is: Qexp = (15 - 4) / (64 - 4) = 0.1833.

Qexp is lesser than Qcrit value (=0.349, at CL:95% for N=19).Therefore we can not reject 4.

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