Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more.

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. This test is eminently suitable for small sample sizes; for samples having more than 30 observations the test for significance of Pearson and Hartley can be used as well. In order to perform the Dean-Dixon 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 (N is the number of observations, α is the level of significance): If the calculated value of Q is greater than the critical threshold the corresponding data value x1 is regarded to be an outlier.

Nα=0.001α=0.002α=0.005α=0.01α=0.02α=0.05α=0.1α=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

 

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
Nα=0.001α=0.002α=0.005α=0.01α=0.02α=0.05α=0.1α=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
Nα=0.001α=0.002α=0.005α=0.01α=0.02α=0.05α=0.1α=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
Nα=0.001α=0.002α=0.005α=0.01α=0.02α=0.05α=0.1α=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: 2012-10-08