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st: PCA components independent?


From   "Martell, Rodolfo" <rmartell@exchange.purdue.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: PCA components independent?
Date   Tue, 22 Mar 2005 06:40:06 -0500

Dear Statlisters,

After running the PCA command in 9 time series, I use the SCORE option
to extract the first two common components. This is what I do:

. pca s*, fa(2)
. score f1 f2

What puzzles me is the following:

. spearman f1 f2
  Number of obs =      61
Spearman's rho =       0.3477
 Test of Ho: f1sov and f2sov are independent
    Prob > |t| =       0.0060
 
Where I reject independence. I thought that by construction, they should
be orthogonal. A regular PWCORR command produces the following output:

. pwcorr f1 f2, sig

          |    f1       f2   
-------------+---------------------
       f1 |   1.0000 
          |
          |
       f2 |  -0.0000   1.0000 
          |   1.0000
             

Where correlation is zero but p-value is 1. Any ideas as to why
spearman's test fails to reject independence and I get such p-value in
the regular correlation command?
Thanks!

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