Statistical Details for Outlier Analysis Calculations

In the Principal Components platform, the calculations in the Outlier Analysis report use the following notation:

n = number of observations

A = number of principal components

Xci = the standardized data for the ith observation

T2 Statistic

The T2 statistic for the ith observation is calculated as follows:

where PA is a matrix containing the first A eigenvectors and L is a diagonal matrix containing the first A eigenvalues.

The median and UCL for the T2 plot are calculated as follows:

where

the qth quantile of the Beta distribution.

To calculate the median, use q = 0.5. To calculate the UCL, use q = (1 - α).

For information about the contribution statistic, see Statistical Details for Contributions in Quality and Process Methods.

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