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In statistics, an outlier is a data point that differs significantly from other observations.
An outlier may be due to:
Variability in the measurement, or
It may indicate experimental error.
Outlier cases are sometimes excluded from the data set as an outlier can cause serious problems in statistical analyses.
How to assess the outliers?
How to assess the outliers?
Univariate Outlier
Univariate Outlier
(Box Plot)
(Box Plot)
Examines distribution of observations for each variable and selects as outliers those cases falling at the outer ranges (high or low) of the distribution.
Bivariate Outlier
Bivariate Outlier
(Scatter Plot)
(Scatter Plot)
Relates individual independent variable with individual dependent variable.
Multivariate Outlier
Multivariate Outlier
(Mahalanobis Distance)
(Mahalanobis Distance)
Evaluates the position of each observation compared with the center of all observations on a set of variable.
Multivariate Outlier
Multivariate Outlier
To test for multivariate outliers, Hair et al. (2010) and Byrne (2010) suggested to identify the extreme score on two or more constructs by using Mahalanobis distance (Mahalanobis D2). It evaluates the position of a particular case from the centroid of the remaining cases. Centroid is defined as the point created by the means of all the variables (Tabachnick & Fidell, 2007).
Based on a rule of thumb, the maximum Mahalanobis distance should not exceed the critical chi-square value, given the number of predictors as degree of freedom. Otherwise, the data may contain multivariate outliers (Hair, Tatham, Anderson, & Black, 1998).
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