Difference between revisions of "Outlier-skewness index"
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Communicated by [[Gnaiger E]] (2016-10-03) updated 2021-06-07 | 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. — [[Doane 2011 J Statistics Education |»Bioblast link«]] | ||
::::» [http://www.statisticshowto.com/pearsons-coefficient-of-skewness/ Pearson’s coefficient of skewness] | ::::» [http://www.statisticshowto.com/pearsons-coefficient-of-skewness/ Pearson’s coefficient of skewness] | ||
Revision as of 08:14, 7 June 2021
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