Difference between revisions of "Outlier-skewness index"

Revision as of 08:09, 8 June 2021

high-resolution terminology - matching measurements at high-resolution

Outlier-skewness index

Description

An outlier and 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. The OSI is derived from Pearson’s coefficient of skewness 2:

Pearson 2 coefficient = 3 · (average-median)/SD

The outlier and skewness index OSI introduces the absolute value of the arithmetic mean, x = ABS(average + median)/2, for normalization:

OSI = (average-median)/(x + SD)

OSI = (average-median)/[ABS(average+median)/2 + SD]

At the limit of a zero value of x, the OSI equals the Pearson 2 coefficient (without the multiplication factor of 3). At high x with small standard deviation (SD), the OSI is effectively the difference between the average and the median normalized for x, (average-median)/x.

Abbreviation: OSI, OI

Communicated by Gnaiger E (2016-10-03) updated 2021-06-08

» 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 Marks - DatLab opened by clicking on the bar of a mark in the DatLab window, the outlier index OI (equivalent to OSI) is shown for the data set selected by the mark on a specific plot. It is more specific than Pearson’s coefficient of skewness for targeting outliers or separate clusters in data series recorded with the O2k. The threshold of the absolute value of the OSI (OI) is set at 0.05. If ABS(OSI)>0.05 calculated for the data points within a defined Mark, the Mark window indicates the likely occurrence of outliers in the data sequence. In the Mark window the 'Outlier index threshold' can be set to a lab-specific or session-specific value (Lab-default or Session value) different from the System default.

MitoPedia O2k and high-resolution respirometry: DatLab, Oroboros QM

@@ Line 1: / Line 1: @@
 {{MitoPedia
-|abbr=''SIAM'', ''OI''
+|abbr=''OSI'', ''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] 2:
+|description=An '''outlier and 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. The ''OSI'' 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 outlier and skewness index ''OSI'' introduces the absolute value of the arithmetic mean, ''x'' = ABS(average + median)/2, for normalization:
-: ''SIAM'' = (average-median)/(''x'' + SD)
+: ''OSI'' = (average-median)/(''x'' + SD)
-: ''SIAM'' = (average-median)/[ABS(average+median)/2 + SD]
+: ''OSI'' = (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''.
+At the limit of a zero value of ''x'', the ''OSI'' equals the Pearson 2 coefficient (without the multiplication factor of 3). At high ''x'' with small standard deviation (SD), the ''OSI'' 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 2021-06-08
 ::::» Doane DP, Seward LE (2011) Measuring skewness: a forgotten statistic?. J Statistics Education 19,2:1-18. — [[Doane 2011 J Statistics Education |»Bioblast link«]]
@@ Line 21: / Line 21: @@
 == The outlier index in DatLab ==
-:::: In DatLab analysis, the skewness index ''SIAM'' is used as an [[Outlier index - DatLab |outlier index]] ''OI'' = ''SIAM''.
+:::: In [[Marks - DatLab]] opened by clicking on the bar of a mark in the DatLab window, the outlier index ''OI'' (equivalent to ''OSI'') is shown for the data set selected by the mark on a specific plot. It is more specific than Pearson’s coefficient of skewness for targeting [[Outlier |outliers]] or separate clusters in data series recorded with the O2k. The threshold of the absolute value of the ''OSI'' (''OI'') is set at 0.05. If ABS(''OSI'')>0.05 calculated for the data points within a defined [[Marks - DatLab |Mark]], the Mark window indicates the likely occurrence of outliers in the data sequence. In the Mark window the 'Outlier index threshold' can be set to a lab-specific or session-specific value (Lab-default or Session value) different from the System default.
 {{MitoPedia O2k and high-resolution respirometry
 |mitopedia O2k and high-resolution respirometry=DatLab, Oroboros QM
 }}