Outlier-skewness index

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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. 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.

Abbreviation: OSI, OI

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


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.


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