Multivariate Methods • Principal Components • Statistical Details for the Principal Components Analysis Platform • Calculations for Outlier Analysis

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Calculations for Outlier Analysis
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
.
To calculate the median, use q = 0.5. To calculate the UCL, use q = (1 - α).
Contribution Statistic
The vector of T2 contribution statistics for the ith observation is calculated as follows:
Note: The sum of the squared contributions for an individual is equal to Ti2 for that individual.

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Help created on 3/19/2020