Basics of Environmental Sampling and Analysis - Fundamentals of Environmental Sampling and Analysis - page 27

Grubbs' test

This test is recommended by the U.S. EPA (1992). First arrange the data in an
increasing order (x 1 ; x n ), the lowest (x 1 ) and the highest (x n ) data points can be

tested for outlier by the following t-statistic:

x 2 ; ...

T ¼

x x 1
s

x n x

or T ¼ ð2 : 25Þ

s

The T value is then compared with a critical T value (Table 2.3) at the specified
sample size and selected a (normally 5%). The data point is deemed to be an outlier
if T < T critical . The test can be continued to test for further possible outlier(s)

(i.e., x 2 ; ). EPA also recommends the use of Grubbs' test for log-normal data

after the log transformation.

x n1 ; ...

Table 2.3 Critical values used for the Grubbs' test

Critical T Critical T

Degree of Degree of

freedom (n1) T 0.05 T 0.01 freedom (n1) T 0.05 T 0.01

3 1.153 1.155 13 2.331 2.607

4 1.463 1.492 14 2.371 2.659

5 1.672 1.749 15 2.409 2.705

6 1.822 1.944 16 2.443 2.747

7 1.938 2.097 17 2.475 2.785

8 2.032 2.221 18 2.504 2.821

9 2.110 2.323 19 2.532 2.854

10 2.176 2.410 20 2.557 2.884

11 2.234 2.485 30 3.103 2.745

12 2.285 2.550 50 2.956 3.336

Dixon's test

This test is used for a small number of outliers with a sample size between 3 and 25
(Gibbons, 1994). First arrange data in an increasing order, x 1 <

x n ,
then calculate the D value based on the number of observations (Table 2.4). An

x 2 < x 3 < ...<

Table 2.4 Formula to calculate D values for the Dixon's test

n If x n is suspected If x 1 is suspected

x n x n1
x n x 1

x 2 x 1
x n x 1

37 D 10 ¼ D 10 ¼

x n x n1
x n x 2

x 2 x 1
x n1 x 1

810 D 11 ¼ D 11 ¼

x 3 x 1
x n1 x 1

x n x n 2
x n x 2

1113 D 21 ¼ D 21 ¼