While trying to understand how the T^2 threshold for extrapolation is calculated from the help section, my conclusion is that the T^2 threshold for a given sigma level should be constant for any dataset with the same number of columns (p) and rows (n) with no missing data. This is because the formula: T^2 threshold = {(n+1)(n-1)p/[n(n-p)}*F(p, n-p); is a function of "n" and "p" only.
The two tables attached below have both 10 columns and 100 rows with different covariance matrices. In both tables, the formula for their respective (non-regularized) T^2 is saved as a 11th column via Multivariate>Outlier Analysis>T^2 (saved script). In both tables, I used the profiler of this formula to call the extrapolation control (saved script). In the Simulation 1 table, the threshold is 18.20937. In the Simulation 2 table, it is 17.95714.
Given that both tables have the same "n" and "p", how can their T^2 threshold be different? Or would "n" and "p" refer to something else other than rows and columns?
Other: in the same help section, it is said that the K-sigma limit of a Normal distribution is used to define the threshold. If K=3, the default value, does it mean that the F-quantile at 0.9973 is used in F(p, n-p) since 3-sigma ~ 99.73%?
Just realized that the formula: T^2 threshold = {(n+1)(n-1)p/[n(n-p)}*F(p, n-p); is to be used for less than 10 non-missing values, otherwise it is T^2 threshold = T^2-hat + K*sigma(T^2), which explains the different thresholds in the two tables.
