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See also: Outlier Tests 

Nalimov Test

Assuming a normal distribution of the sample the following simple test on outliers provides a quick hint (this test is also known as Nalimov test1, especially in German publications). A particular value x1 is considered to be an outlier if the statistic q

.... mean of all values (incl. the value x1)
s .... standard deviation of all values
n .... number of values

exceeds the critical threshold qcrit for a given level of significance. The number of degrees of freedom is defined as f= n-2 (table according to Kaiser/Gottschalk ).

f qcrit
α=0.05		 qcrit
α=0.01		 qcrit
α=0.001		   f qcrit
α=0.05		 qcrit
α=0.01		 qcrit
α=0.001
1 1.409 1.414 1.414  19 1.936 2.454 2.975
2 1.645 1.715 1.730  20 1.937 2.460 2.990
3 1.757 1.918 1.982  25 1.942 2.483 3.047
4 1.814 2.051 2.178  30 1.945 2.498 3.085
5 1.848 2.142 2.329  35 1.948 2.509 3.113
6 1.870 2.208 2.447  40 1.949 2.518 3.134
7 1.885 2.256 2.540  45 1.950 2.524 3.152
8 1.895 2.294 2.616  50 1.951 2.529 3.166
9 1.903 2.324 2.678  100 1.956 2.553 3.227
10 1.910 2.348 2.730  200 1.958 2.564 3.265
11 1.916 2.368 2.774  300 1.958 2.566 3.271
12 1.920 2.385 2.812  400 1.959 2.568 3.275
13 1.923 2.399 2.845  500 1.959 2.570 3.279
14 1.926 2.412 2.874  600 1.959 2.571 3.281
15 1.928 2.423 2.899  700 1.959 2.572 3.283
16 1.931 2.432 2.921  800 1.959 2.573 3.285
17 1.933 2.440 2.941 1000 1.960 2.576 3.291
18 1.935 2.447 2.959 


1 There is some scientific discussion about this test. It is thus recommended to use other tests instead of the Nalimov test (Dean-Dixon test for small samples, the test of Pearson and Hartley for larger ones).


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