# [Ifeffit] How to calculate F-value for XANES PCA results

Andrew acampo2 at tigers.lsu.edu
Mon Jan 11 14:59:31 CST 2010

```Hi everyone,

Thank you Dr. Lukens for your help! Let me see if I understand the method
that was described for the F-value for the variances using the
Fernandez-Garcia definition (that was previously mentioned), and please
correct me if I am mistaken.

The Principal Component Analysis returns the eigenvectors. Then, to
calculate the F-value using the Fernandez-Garcia definition:

F-value for component 1 = (variance of eigenvector 1)/ summation[(variance
eigenvector 2) + (variance eigenvector 3) + . (variance eigenvector c)]

F-value for component 2 = (variance of eigenvector 2)/ summation[(variance
eigenvector 3) + (variance eigenvector 4) + . (variance eigenvector c)]

F-value for component k  = (variance of eigenvector k)/ summation[(variance
of eigenvector k+1) + . + (variance of eigenvector c)]

Where c is the number of components in the set.

Then to calculate the probability of F corresponds to noise, then the that
Excel can calculate this using the function Fdist(alpha, degree of freedom
1, degree of freedom 2).

Alpha = the confidence interval desired (where 0.05 is generally used)
degrees of freedom 1 = # of independent data points - 1 ((this is dependent
on the resolution of the beam and Dr. Lukens provided an example calc.))
degree of freedom 2 = number of components on the denominator for the
F-value being tested - 1 (i.e. for component k it would equal c-k-1-1 or
c-k-2)

Then, "if the probability of F less than 5%, these would be the components
that you would retain."

Are these equations correct? Am I using the correct equation based on the
Garcia-Fernandez definition? My main misunderstanding of this was what
equation to use for the F-value. Sorry for killing a dead horse, but is this
definition of degree of freedom 2 correct?

Thanks again for all the help and sorry if this is poorly worded, and if
this is on the outer-bounds for an IFEFFIT-relevant question.

Andrew

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