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

Wayne Lukens wwlukens at lbl.gov
Mon Jan 11 16:29:10 CST 2010

```Hi Andrew,

It is easier to use Fdist to calculate the probability that a given
value of F corresponds is within the noise.  The way to do this is
to use FDIST(F, (v1-v2), v1), where F, v1, and v2 are explained below.

If you have two models, model 1 and model 2, where model 1 has an
additional component versus model 2, and the chi-squared, number
of parameters, and degrees of freedom for model 1 are X1, p1, and
v1, where v1=n-p1 and n is the number of independent parameters, and
model 2 has similarly defined X2, p2, and v2, then

F= [(X2-X1)*v2]/[(v1-v2)*X1]

the probability of F is FDIST(F, (v1-v2), v1). I assume the same
is true for the PCA analysis; however, I don't know what the values
for v and p are in this case. The formula for F looks right.

At any rate, once you have done the PCA analysis, you need to figure
out which standard spectra span the components (there should be the
same number of standards as components). Then you need to fit your
experimental spectra using the standards. At that point you can
apply the F-test to determine whether the contribution from that
standard is greater than 2 sigma over the noise. I hope that makes
sense?

Sincerely,

Wayne

Andrew wrote:
>
>
> 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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>
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--
Wayne Lukens
Staff Scientist
Lawrence Berkeley National Laboratory
email: wwlukens at lbl.gov
phone: (510) 486-4305
FAX: (510) 486-5596

```