Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
Home Statistical Tests Outlier Tests Outlier Tests  Basic Rules  
See also: survey on statistical tests, outliers, distribution calculator, Chebyshev's Theorem  
Outlier Tests  Basic Rules
Based on the standard deviationIf we assume a normal distribution, a single value may be considered as an outlier if it falls outside a certain range of the standard deviation. In many cases a factor of 2.5 is used, which means that approx. 99 % of the data belonging to a normal distribution fall inside this range:+/ 2.5σ If the data values do not belong to a normal distribution, we have to
be more careful in selecting the thresholds for outliers. According to
Chebyshev's
theorem we have to use an interval of +/ 4 standard deviations to
ensure that at least 94 % of the data (of an arbitrary distribution)
fall inside this interval. Please note that these basic tests require at
least 10 observations (better 25, or more).
Based on the interquartile range The abovementioned strategies for identifying outliers are probably most appropriate for symmetric unimodal distributions. If a distribution is skewed, it is recommended to calculate the threshold for outliers from the interquartile distance: x_{0.25}  1.5 [x_{0.75 } x_{0.25}] < x_{i} < x_{0.75} + 1.5 [x_{0.75 } x_{0.25}]


Home Statistical Tests Outlier Tests Outlier Tests  Basic Rules 