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Outliers - Reasons for Screening Data
Outliers are due to data entry errors, subject is not a member of the population that the sample is trying to represent, or the subject is really different. Statistical tests are quite sensitive to outliers so this problem should be addressed.
Univariate outliers are easy to detect (z-scores, box plots, histograms, etc.) standard scores larger than +/-3 are outliers (consider 4 is n>100 or 2.5 if n<10)
Multivariate outliers are difficult to detect. Mahalanobis distance is one powerful technique to use in this case (discussed later). This is evaluated as a chi-square statistic with degrees of freedom equal to number of variables in the analysis. A chi-sqaure statistic value that is significant beyond p<0.001 level determines outliers.
In most cases, it is ok to drop the value from the sample. One can also take steps to reduce the relative influence of outliers if the researcher decides to include the values in the analysis.
Cauchy distribution : The probability distribution, f (x), can be given as follows where α is the position of the parameter (median) and the beta β a scale parameter. Moments
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