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

## 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 qcritα=0.05 qcritα=0.01 qcritα=0.001 f qcritα=0.05 qcritα=0.01 qcritα=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).