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

## Significance of Outliers

For random samples larger than 30 objects(1) possible outliers may be identified by using the significance thresholds of Pearson and Hartley. For this purpose the test statistic q has to be calculated as follows:

 x1 .... object to be tested .... mean of all objects (including the value of x1) s .... standard deviation of all objects

x1 is regarded to be an outlier if the test statistic q exceeds the critical threshold qcrit for a given level of significance α and a sample size n.

 n qcritα=0.05 qcritα=0.01 n qcritα=0.05 qcritα=0.01 1 1.645 2.326 55 3.111 3.564 2 1.955 2.575 60 3.137 3.587 3 2.121 2.712 65 3.160 3.607 4 2.234 2.806 70 3.182 3.627 5 2.319 2.877 80 3.220 3.661 6 2.386 2.934 90 3.254 3.691 8 2.490 3.022 100 3.283 3.718 10 2.568 3.089 200 3.474 3.889 15 2.705 3.207 300 3.581 3.987 20 2.799 3.289 400 3.656 4.054 25 2.870 3.351 500 3.713 4.106 30 2.928 3.402 600 3.758 4.148 35 2.975 3.444 700 3.797 4.183 40 3.016 3.479 800 3.830 4.214 45 3.051 3.511 900 3.859 4.240 50 3.083 3.539 1000 3.884 4.264

 (1) For small random samples the Dean-Dixon test should be used.