Difference between revisions of "Outlier-skewness index"
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{{MitoPedia | {{MitoPedia | ||
|abbr=''SIAM'', ''OI'' | |abbr=''SIAM'', ''OI'' | ||
|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 [http://www.statisticshowto.com/pearsons-coefficient-of-skewness/ Pearson’s coefficient of skewness] | |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 [http://www.statisticshowto.com/pearsons-coefficient-of-skewness/ 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: | The skewness index ''SIAM'' introduces the absolute value of the arithmetic mean, ''x'' = ABS(average + median)/2, for normalization: | ||
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: ''SIAM'' = (average-median)/[ABS(average+median)/2 + SD] | : ''SIAM'' = (average-median)/[ABS(average+median)/2 + SD] | ||
At the limit of a zero value of ''x'', the ''SIAM'' equals | 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''. | ||
}} | }} | ||
Communicated by [[Gnaiger E]] (2016-10-03) updated 2021-06-07 | Communicated by [[Gnaiger E]] (2016-10-03) updated 2021-06-07 | ||
::::» [https://ww2.amstat.org/publications/jse/v19n2/doane.pdf Doane_2011_J Statistics Education: Measuring skewness: a forgotten statistic?] | |||
::::» [http://www.statisticshowto.com/pearsons-coefficient-of-skewness/ Pearson’s coefficient of skewness] | |||
== The outlier index in DatLab == | == The outlier index in DatLab == | ||
:::: In DatLab analysis, the skewness index ''SIAM'' is used as an | :::: In DatLab analysis, the skewness index ''SIAM'' is used as an [[Outlier index - DatLab |outlier index]] ''OI'' = ''SIAM''. | ||
{{MitoPedia O2k and high-resolution respirometry | {{MitoPedia O2k and high-resolution respirometry | ||
|mitopedia O2k and high-resolution respirometry=DatLab, Oroboros QM | |mitopedia O2k and high-resolution respirometry=DatLab, Oroboros QM | ||
}} | }} |
Revision as of 09:11, 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
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