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Revision as of 07:41, 8 June 2021 by Gnaiger Erich (talk | contribs) (Gnaiger Erich moved page Skewness index to Outlier and skewness index)
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Outlier-skewness index
Description
A skewness index based on average-median (SIAM) is defined for evaluation of skewness in relation to normal distribution. The SIAM is derived from Pearson’s coefficient of skewness 2:
- Pearson 2 coefficient = 3 · (average-median)/SD
The skewness index SIAM introduces the absolute value of the arithmetic mean, x = ABS(average + median)/2, for normalization:
- SIAM = (average-median)/(x + SD)
- SIAM = (average-median)/[ABS(average+median)/2 + SD]
At the limit of a zero value of x, the SIAM equals the Pearson 2 coefficient (without the multiplication factor of 3). At high x with small standard deviation (SD), the SIAM is effectively the difference between the average and the median normalized for x, (average-median)/x.
Abbreviation: SIAM, OI
Communicated by Gnaiger E (2016-10-03) updated 2021-06-07
- » Doane DP, Seward LE (2011) Measuring skewness: a forgotten statistic?. J Statistics Education 19,2:1-18. — »Bioblast link«
- » Pearson’s coefficient of skewness
The outlier index in DatLab
- In DatLab analysis, the skewness index SIAM is used as an outlier index OI = SIAM.
MitoPedia O2k and high-resolution respirometry: DatLab, Oroboros QM
