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<p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif";
color:black'>Hi everyone,<o:p></o:p></span></p>

<p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif";
color:black'><o:p> </o:p></span></p>

<p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif";
color:black'>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. <o:p></o:p></span></p>

<p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif";
color:black'><o:p> </o:p></span></p>

<p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif";
color:black'>The Principal Component Analysis returns the eigenvectors. Then,
to calculate the F-value using the Fernandez-Garcia definition:<o:p></o:p></span></p>

<p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif";
color:black'><o:p> </o:p></span></p>

<p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif";
color:black'>F-value for component 1 = (variance of eigenvector 1)/
summation[(variance eigenvector 2) + (variance eigenvector 3) + … (variance
eigenvector c)]<o:p></o:p></span></p>

<p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif";
color:black'>F-value for component 2 = (variance of eigenvector 2)/ summation[(variance
eigenvector 3) + (variance eigenvector 4) + … (variance eigenvector c)]<o:p></o:p></span></p>

<p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif";
color:black'>F-value for component k  = (variance of eigenvector k)/
summation[(variance of eigenvector k+1) + … + (variance of eigenvector
c)]<o:p></o:p></span></p>

<p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif";
color:black'><o:p> </o:p></span></p>

<p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif";
color:black'>Where c is the number of components in the set.<o:p></o:p></span></p>

<p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif";
color:black'><o:p> </o:p></span></p>

<p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif";
color:black'>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).<o:p></o:p></span></p>

<p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif";
color:black'><o:p> </o:p></span></p>

<pre><span style='font-size:12.0pt;font-family:"Times New Roman","serif";
color:black'>Alpha = the confidence interval desired (where 0.05 is generally used)<o:p></o:p></span></pre><pre><span
style='font-size:12.0pt;font-family:"Times New Roman","serif";color:black'>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.)) <o:p></o:p></span></pre><pre><span
style='font-size:12.0pt;font-family:"Times New Roman","serif";color:black'>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)<o:p></o:p></span></pre><pre><span
style='font-size:12.0pt;font-family:"Times New Roman","serif";color:black'><o:p> </o:p></span></pre><pre><span
style='font-size:12.0pt;font-family:"Times New Roman","serif";color:black'>Then, “if the </span><span
style='font-size:12.0pt;font-family:"Times New Roman","serif";color:black'>probability of F less than 5%, these would be the components that you would retain.”<o:p></o:p></span></pre><pre><span
style='font-size:12.0pt;font-family:"Times New Roman","serif";color:black'><o:p> </o:p></span></pre>

<p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif";
color:black'>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?<o:p></o:p></span></p>

<p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif";
color:black'><o:p> </o:p></span></p>

<p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif";
color:black'>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.<o:p></o:p></span></p>

<p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif";
color:black'>Andrew<o:p></o:p></span></p>

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