<p></p>
<p>Spectral power is an often used measure in qEEG studies. The amount of power for each frequency or frequency band for a given electrode is computed and compared to the database mean value. The results are often represented as z-scores, that is the difference
    between the mean score of a population and the patient’s individual score divided by the standard deviation of the population. Z-scores detect and characterize potential abnormalities from the tested individual, relative to the normative population
    within his/her own age range. It is not strictly the number of deviations, rather the pattern of deviations that is most relevant. The use of parametric statistics assumes a normal (Gaussian) distribution of the variable(s) in question. </p>

<p>The&nbsp;Gaussian&nbsp;distribution&nbsp;is&nbsp;a&nbsp;fundamental&nbsp;distribution&nbsp;that&nbsp;is&nbsp;used&nbsp;throughout&nbsp;science,&nbsp;for&nbsp;example,&nbsp;the&nbsp;Schrodinger&nbsp;wave&nbsp;equation&nbsp;in&nbsp;Quantum&nbsp;mechanics&nbsp;uses&nbsp;the&nbsp;Gaussian&nbsp;distribution&nbsp;
    <span style="font-size: 1rem;">as&nbsp;basis&nbsp;functions&nbsp;(Robinett,&nbsp;1997).&nbsp;&nbsp;The&nbsp;application&nbsp;of&nbsp;the&nbsp;EEG&nbsp;to&nbsp;the&nbsp;concept&nbsp;of&nbsp;the
Gaussian&nbsp;distribution&nbsp;requires&nbsp;the&nbsp;use&nbsp;of&nbsp;standard&nbsp;mathematical&nbsp;transforms&nbsp;by&nbsp;which
all
statistical&nbsp;distributions&nbsp;can&nbsp;be&nbsp;transformed&nbsp;to&nbsp;a&nbsp;Gaussian&nbsp;distribution&nbsp;(Box&nbsp;and&nbsp;Cox,&nbsp;1964).
Quantitative EEG uses transforms that are applied to the power spectrum of the
digital time series in order to approximate a normal distribution.</span></p>
<h2><a name="_Toc35342987">Gaussian distribution</a></h2>
<p style="text-align: center;"><span style="font-size: 1rem;">&nbsp;</span><img src="@@PLUGINFILE@@/Gaussian%20Distribution.png" alt="Gaussian Distribution" width="500" height="364" class="img-responsive atto_image_button_middle" style="font-size: 1rem; text-align: center;"></p>
<p></p>
<p style="text-align: center; "><br></p>
<p style="text-align: center; "><br></p>
<p style="text-align: center; "><br></p>
<p style="text-align: left;">Here is a video describing Gaussianity:&nbsp;<a href="https://www.youtube.com/watch?v=IIuXF5QRBTY">Gaussianity</a></p>
<p></p>
<p style="text-align: left;">The next two figures are representations of raw, un-normed data, and Z-score data, respectively, in spectral graphs. The raw image shows the absolute power of the EEG in microvolts squared. We see that 10Hz shows up at approximately 16mV<sup>2
</sup>. The second image shows the data in Z-scores, or how deviant from the norm these frequencies are. We can see that the purple line (representing one electrode) is 3+ standard deviations above the norm between 14 – 16 Hz, and 4+ standard deviations
    above the norm at 28 Hz. Both of these findings are potentially artifactual, but this cannot be determined without an analysis of the raw EEG.</p>
<h2 style="text-align: left;"><a name="_Toc35342988" style="color: rgb(55, 71, 79); font-size: 2.143rem; background-color: rgb(255, 255, 255);">Spectral Power in Microvolts squared
(y-axis) and hertz (x-axis)</a><br></h2>
<p style="text-align: left;"><span style="font-size: 1rem;">&nbsp;&nbsp;</span></p>
<p style="text-align: center;"><span style="font-size: 1rem;">&nbsp;</span><img src="@@PLUGINFILE@@/Spectral%20Power.png" alt="Spectral Power" width="599" height="553" class="img-responsive atto_image_button_middle" style="font-size: 1rem; text-align: center;"></p>
<p></p>
<p style="text-align: center; "><br></p>
<p></p>
<h2 style="text-align: left;"><a name="_Toc35342989">Spectral Power in Z-Scores (y-axis) and
hertz (x-axis)</a></h2>
<p style="text-align: center;"><span style="font-size: 1rem;">&nbsp;</span><img src="@@PLUGINFILE@@/Z-Score%20Spectral%20Power.png" alt="Z-Score Spectral Power" width="595" height="541" class="img-responsive atto_image_button_middle" style="font-size: 1rem; text-align: center;"></p>
<p></p>
<p style="text-align: center; "><br></p>
<p></p>
<p style="text-align: left;">The next figure we see is showing, one graph per electrode channel, the raw data in the EEG on a spectral display. This imagery is from WinEEG. Each peak represents a rhythm in the data, showing kurtosis, or the expected bell shape that indicates it is
    a frequency range.</p>
<p style="text-align: left;"><br></p>
<h2 style="text-align: left;"><a name="_Toc35342990">Spectra of Raw EEG (not norm referenced)
as seen at each electrode in WinEEG</a></h2>
<p style="text-align: center;"><span style="font-size: 1rem;">&nbsp;</span><img src="@@PLUGINFILE@@/WinEEG%20Spectra.png" alt="WinEEG Spectra" width="1000" height="636" style="font-size: 1rem; text-align: center;" class="img-responsive atto_image_button_middle"></p>
<p></p>
<p style="text-align: center; "><br></p>
<p></p>
<p style="text-align: left;">The figure below illustrates a common modern quantitative EEG analysis where EEG traces are viewed and examined at the same time that quantitative analyses are displayed so as to facilitate and extend analytical power.</p>
<p style="text-align: left;"><br></p>
<p></p>
<p></p>
<h3 style="text-align: left;"><a name="_Toc35342991">Raw EEG and Quantitative EEG</a></h3>
<p></p>
<p style="text-align: center;"><a name="_Toc35342991" style="background-color: rgb(255, 255, 255); color: rgb(82, 96, 105); font-size: 1rem;"><img src="@@PLUGINFILE@@/Raw%20vs.%20Quantitative.png" alt="Raw EEG vs. Quantitative EEG" width="1000" height="604" class="img-responsive atto_image_button_middle"></a></p>
<a name="_Toc35342991">
    <p style="text-align: center;"><br></p>
    </a>
    <p></p>
    <p style="text-align: center; "><a name="_Toc35342991"><br></a></p>