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 qcrit
α=0.05
qcrit
α=0.01
  n qcrit
α=0.05
qcrit
α=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.

Last Update: 2012-10-08