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