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Outlier Test
Dean and Dixon

A test for outliers of normally distributed data which is particularly simple to apply has been developed by J.W. Dixon. In order to perform this test for outliers, the data set containing N values has to be sorted either in an ascending or descending order, with x1 being the suspect value. Then the test statistic Q is calculated using the equation

The decision whether x1 is an outlier is performed by comparing the value Q to the critical values listed in the following table:

Na=0.001a=0.002a=0.005a=0.01a=0.02a=0.05a=0.1a=0.2
30.9990.9980.9940.9880.9760.9410.8860.782
40.9640.9490.9210.8890.8470.7660.6790.561
50.8950.8690.8240.7820.7290.6430.5590.452
60.8220.7920.7440.6980.6460.5630.4840.387
70.7630.7310.6810.6360.5870.5070.4330.344
80.7160.6820.6330.5910.5420.4670.3980.314
90.6750.6440.5960.5550.5080.4360.3700.291
100.6470.6140.5680.5270.4820.4120.3490.274
150.5440.5150.4730.4380.3980.3380.2840.220
200.4910.4640.4260.3930.3560.3000.2510.193
250.4550.4300.3950.3640.3290.2770.2300.176
300.4300.4070.3710.3420.3100.2600.2160.165

where N is the number of values and a is the level of significance.

 

Please note that Dean and Dixon suggested in a later paper to take a more elaborate approach by using different formulas for different sample sizes in order to avoid the problem of two outliers on the same side of the distribution. They defined the following ratios and recommended that the various ratios be applied as follows: for 3 <= N <=7 use r10; for 8 <= N <=10 use r11; for 11 <= N <= 13 use r21, and for n >= 14 use r22:

The following tables show the critical values for r11, r21, and r22, respectively. r10 is equal to Q, its critical values can be obtained from the table above.

Critical values for r11
Na=0.001a=0.002a=0.005a=0.01a=0.02a=0.05a=0.1a=0.2
80.7990.7690.7240.6820.6330.5540.4800.386
90.7500.7200.6750.6340.5860.5120.4410.352
100.7130.6830.6370.5970.5510.4770.4090.325

 

Critical values for r21
Na=0.001a=0.002a=0.005a=0.01a=0.02a=0.05a=0.1a=0.2
110.7700.7460.7080.6740.6360.5750.5180.445
120.7390.7140.6760.6430.6050.5460.4890.420
130.7130.6870.6490.6170.5800.5220.4670.399

 

Critical values for r22
Na=0.001a=0.002a=0.005a=0.01a=0.02a=0.05a=0.1a=0.2
140.7320.7080.6720.6400.6030.5460.4910.422
150.7080.6850.6480.6170.5820.5240.4700.403
160.6910.6670.6300.5980.5620.5050.4530.386
170.6710.6470.6110.5800.5450.4890.4370.373
180.6520.6280.5940.5640.5290.4750.4240.361
190.6400.6170.5810.5510.5170.4620.4120.349
200.6270.6040.5680.5380.5030.4500.4010.339
250.5740.5500.5170.4890.4570.4060.3590.302
300.5390.5170.4840.4560.4250.3760.3320.278
350.5110.4900.4590.4310.4000.3540.3110.260
400.4900.4690.4380.4120.3820.3370.2950.246
450.4750.4540.4230.3970.3680.3230.2830.234
500.4600.4390.4100.3840.3550.3120.2720.226
600.4370.4170.3880.3630.3360.2940.2560.211
700.4220.4030.3740.3490.3210.2800.2440.201
800.4080.3890.3600.3370.3100.2700.2340.192
900.3970.3770.3500.3260.3000.2610.2260.185
1000.3870.3680.3410.3170.2920.2530.2190.179

 

Hint: Please note that the critical values listed in the tables above have been calculated by performing 106 random experiments per value. These values differ slightly from values published by various authors, many of them using interpolation techniques to estimate the critical values.


Last Update: 2005-Mai-08