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


Outliers are extreme values that stand out from the other values of a sample. Outliers normally have a considerable influence on the calculation of statistics (see e.g. the leverage effect with linear regression) and should be removed in most cases. You should also note that outliers may result simply from the fact that you assume a distribution which does not fit the real distribution of the data.

Typical examples of outliers are errors in measurement, errors in acquisition (human influences...), or (rare) outstanding values. An important question concerning outliers is whether it is legitimate to remove a particular value after it has been recognized as an outlier.  Of course, statistical tests cannot decide, if it is appropriate to remove such values. They can only give you a hint if a significant deviation exists (basically, outlier tests are based on the probabilities to belong to the assumed distribution).