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Outlier-skewness index |
Description
An outlier-skewness index OSI is defined for evaluation of the distribution of data sets with outliers including separate clusters or skewness in relation to a normal distribution with equivalence of the average and median.
Abbreviation: OSI, OI
The OSI is derived from Pearson’s coefficient of skewness 2:
- Pearson 2 coefficient = 3 · (average-median)/SD
The outlier-skewness index OSI introduces the absolute value of the arithmetic mean, m = ABS(average + median)/2, for normalization:
- OSI = (average-median)/(m + SD)
- OSI = (average-median)/[ABS(average+median)/2 + SD]
At the limit of a zero value of m, the OSI equals the Pearson 2 coefficient (without the multiplication factor of 3). At high m with small standard deviation (SD), the OSI is effectively the difference between the average and the median normalized for m, (average-median)/m.
The outlier index in DatLab: Outlier index threshold
Communicated by Gnaiger E (2016-10-03) updated 2021-06-26
- » Doane DP, Seward LE (2011) Measuring skewness: a forgotten statistic?. J Statistics Education 19,2:1-18. — »Bioblast link«
- » Pearson’s coefficient of skewness
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