<p></p><p>Here is a quick video on how EEG became QEEG:&nbsp;<a href="https://vimeo.com/429326339">QEEG VIdeo</a></p><p>The earliest
quantitative EEG (QEEG) reference normative database was developed in the 1950s
at UCLA as part of the NASA study and selection of astronauts for purposes of
space travel (Adey et al, 1961; 1964a; 1964b). Clinical inclusion and exclusion
criteria were not used because there was no intended clinical application of
this early QEEG reference normative database. However, the essential
quantitative foundations of QEEG normative databases were tested such as the
calculation of means and standard deviations and measures of Gaussianity,
complex demodulation, fourier spectral analysis and basic statistical
parameters necessary for any reference normative database.</p><h2><a name="_Toc35342993">History of Sample Size per Age Group</a> </h2>

<p>There is no
absolute sample size that is best for a QEEG database because statistically
sample size is related to the “effect size” and “power” (Hayes, 1973; Winer,
1971). The smaller the effect size then the larger the sample size necessary to
detect that effect. The power of a statistical measure varies as a function of
sample size and the effect size (Cohen, 1977). Another issue related to sample
size is the degree to which a sample approximates a Gaussian distribution. Increased
sample size is often necessary in order to achieve closer approximations to
Gaussian which in turn is related to the accuracy of cross-validation. Thus,
the sample size is one of several inter-related issues in all normative
databases and the sample size should not be singled out as being the most
important factor in a QEEG normative database.</p>

<p>In regard to
pediatric EEGs, there are rapid changes in EEG measures during early childhood.
For this reason, a relatively large sample sizes is required during the period
of time when the brain is changing most rapidly, as well as during old age when
potential rapid declines in neural function may occur.<b></b></p><h2><a name="_Toc35342994">History of Gaussian Distribution Approximation and
Cross-Validation</a></h2><h3>Dr. Frank Duffy</h3><br><span style="font-size: 1rem;"><img src="@@PLUGINFILE@@/Dr.%20Frank%20Duffy.png" alt="Dr. Frank Duffy" width="175" height="251" class="img-responsive atto_image_button_left"></span><p>The statistics of replication and independent cross-validation of normative QEEG databases was first applied by E. Roy John and collaborators in 1974 to 1977 (John, 1977; John et al, 1977; 1987). The importance of approximation to a Gaussian distribution was emphasized by both Dr. E. Roy John and Dr. Frank Duffy a Harvard Neurologist in the 1970s and 1980s. In 1994 the American EEG Association produced a position paper in which the statistical standards of replication, cross-validation, reliability and Gaussian approximation were iterated as&nbsp;<span>acceptable basic standards to be met by any normative QEEG database (Duffy, 1994). The American EEG Society included the same standards.&nbsp;</span><br><br><br></p><h3><br></h3><h3><br></h3><h3>E. Roy John</h3><p><img src="@@PLUGINFILE@@/E.%20Roy%20John.gif" alt="E. Roy John" width="150" height="200" class="img-responsive atto_image_button_left"></p><p><span style="font-size: 1rem;"><br></span></p><p><span style="font-size: 1rem;"><br></span></p><p><span style="font-size: 1rem;"><br></span></p><p><span style="font-size: 1rem;"><br></span></p><p><span style="font-size: 1rem;"><br></span></p><p><span style="font-size: 1rem;"><br></span></p><p><span style="font-size: 1rem;">Milos Matousek&nbsp;and Ingemar Petersen&nbsp;(1973)&nbsp;computed&nbsp;means&nbsp;and&nbsp;standard&nbsp;deviations&nbsp;in&nbsp;one-year&nbsp;age&nbsp;groups&nbsp;and&nbsp;were&nbsp;the&nbsp;first&nbsp;to&nbsp;use&nbsp;Z&nbsp;scores&nbsp;to&nbsp;compare&nbsp;an&nbsp;individual&nbsp;to&nbsp;the&nbsp;normative&nbsp;</span><span style="font-size: 1rem;">database&nbsp;means&nbsp;and&nbsp;standard&nbsp;deviations.&nbsp;&nbsp;&nbsp;The&nbsp;Z&nbsp;score&nbsp;is&nbsp;an&nbsp;excellent&nbsp;statistic&nbsp;defined&nbsp;as</span><br></p>

<p>the&nbsp;difference&nbsp;between&nbsp;the&nbsp;value&nbsp;from&nbsp;an&nbsp;individual&nbsp;and&nbsp;the&nbsp;mean&nbsp;of&nbsp;the&nbsp;population&nbsp;<span style="font-size: 1rem;">divided&nbsp;by&nbsp;the&nbsp;standard&nbsp;deviation&nbsp;of
the&nbsp;population&nbsp;or&nbsp;</span></p><img src="@@PLUGINFILE@@/Equation%201.png" alt="Equation 1" width="102" height="65" class="img-responsive atto_image_button_left"><br><p></p><p><br></p><p></p><h2><a name="_Toc35342995"></a><a name="_Toc3535217">Inclusion and exclusion criteria for normative databases</a>
</h2>

<p>John&nbsp;and&nbsp;colleagues&nbsp;expanded&nbsp;on&nbsp;the&nbsp;use&nbsp;of&nbsp;the&nbsp;Z-score&nbsp;for&nbsp;clinical&nbsp;evaluation&nbsp;including&nbsp;</p>

<p>the&nbsp;use&nbsp;of&nbsp;multivariate&nbsp;measures&nbsp;such&nbsp;as&nbsp;the&nbsp;Mahalanobis&nbsp;distance&nbsp;metric,&nbsp; a direct&nbsp;</p>

<p>normalization&nbsp;of&nbsp;the&nbsp;Gaussian&nbsp;distribution&nbsp;using&nbsp;Z&nbsp;scores&nbsp;is&nbsp;useful&nbsp;in&nbsp;comparing&nbsp;</p>

<p>individuals&nbsp;to&nbsp;a&nbsp;QEEG&nbsp;normative&nbsp;database.&nbsp;That&nbsp;is,&nbsp;the&nbsp;standard&nbsp;score&nbsp;form&nbsp;of&nbsp;the&nbsp;</p>

<p>Gaussian&nbsp;is&nbsp;where&nbsp;the&nbsp;mean&nbsp;=&nbsp;0&nbsp;and&nbsp;standard&nbsp;deviation&nbsp;=&nbsp;1&nbsp;or,&nbsp;by&nbsp;substitution&nbsp;into&nbsp;the&nbsp;</p>

<p>Gaussian&nbsp;equation&nbsp;for&nbsp;a&nbsp;bell&nbsp;shaped&nbsp;curve,&nbsp;then&nbsp;</p><img src="@@PLUGINFILE@@/Equation%202.png" alt="Equation 2" width="120" height="79" class="img-responsive atto_image_button_left"><br><p></p><p><br></p><p><br></p><p></p><p>where&nbsp;Y&nbsp;=&nbsp;Gaussian&nbsp;distribution&nbsp;and&nbsp;the&nbsp;Z&nbsp;score&nbsp;is&nbsp;a&nbsp;deviation&nbsp;in&nbsp;</p>

<p>standard&nbsp;deviation&nbsp;units&nbsp;measured&nbsp;along&nbsp;the&nbsp;baseline&nbsp;of&nbsp;the&nbsp;Gaussian&nbsp;curve&nbsp;from&nbsp;a&nbsp;mean&nbsp;</p>

<p>of&nbsp;0&nbsp;and&nbsp;a&nbsp;standard&nbsp;deviation&nbsp;=&nbsp;1&nbsp;and&nbsp;deviations&nbsp;to&nbsp;the&nbsp;right&nbsp;of&nbsp;the&nbsp;mean&nbsp;being&nbsp;positive&nbsp;</p>

<p>and&nbsp;those&nbsp;to&nbsp;the&nbsp;left&nbsp;negative.&nbsp;&nbsp;By&nbsp;substituting&nbsp;different&nbsp;values&nbsp;of&nbsp;Z&nbsp;then&nbsp;different&nbsp;values&nbsp;</p>

<p>of&nbsp;Y&nbsp;can&nbsp;be&nbsp;calculated.&nbsp;&nbsp;&nbsp;For&nbsp;example,&nbsp;when&nbsp;Z&nbsp;=&nbsp;0,&nbsp;Y&nbsp;=&nbsp;0.3989&nbsp;or,&nbsp;in&nbsp;other&nbsp;words,&nbsp;the&nbsp;</p>

<p>height&nbsp;of&nbsp;the&nbsp;curve&nbsp;at&nbsp;the&nbsp;mean&nbsp;of&nbsp;the&nbsp;normal&nbsp;distribution&nbsp;in&nbsp;standard ­score&nbsp;form&nbsp;is&nbsp;given&nbsp;</p>

<p>by&nbsp;the&nbsp;number&nbsp;0.3989.&nbsp;&nbsp;For&nbsp;purposes&nbsp;of&nbsp;assessing&nbsp;deviation&nbsp;from&nbsp;normal,&nbsp;the&nbsp;values&nbsp;of&nbsp;Z&nbsp;</p>

<p>above&nbsp;and&nbsp;below&nbsp;the&nbsp;mean,&nbsp;which&nbsp;include&nbsp;95%&nbsp;of&nbsp;the&nbsp;area&nbsp;of&nbsp;the&nbsp;Gaussian&nbsp; curve is&nbsp;often&nbsp;used&nbsp;</p>

<p>as&nbsp;a&nbsp;level&nbsp;of&nbsp;confidence&nbsp;necessary&nbsp;to&nbsp;minimize&nbsp;Type&nbsp;I&nbsp;and&nbsp;Type&nbsp;II&nbsp;errors.</p><br><p></p><p></p><p>The Gaussian
distribution is a fundamental distribution that is used throughout science. The
application of EEG to Gaussian distribution requires the use of standard
mathematical transforms by which all statistical distributions can be
transformed into Gaussian distributions. The pyramidal neurons exhibit rhythmic
bursts and periods of asynchrony in a non-Gaussian distribution as a function
of time. In order to run Z-score analysis or Z-score neurofeedback, it is
mandatory to transform EEG digital data to approximate a Gaussian shape (a bell
curve). </p><h2><a name="_Toc35342996">Gaussian Distribution across metrics</a></h2><p></p><p style="text-align: center;"><a name="_Toc35342996" style="background-color: rgb(255, 255, 255); color: rgb(82, 96, 105); font-size: 1rem;">&nbsp;<img src="@@PLUGINFILE@@/Gaussian%20Dist.png" alt="Gaussian Dist" width="500" height="393" style="text-align: center; " class="img-responsive atto_image_button_middle"></a></p><p style="text-align: center;"><a name="_Toc35342996" style="background-color: rgb(255, 255, 255); color: rgb(82, 96, 105); font-size: 1rem;"><br></a></p><p></p><p><br></p><p></p><p>The figure below is
a summary and overview of the procedures that are used to eliminate artifact,
maximize reliability, approximate Gaussian distributions, cross-validate and
compute clinical correlations as a standard set of procedures and sequences to
make normative database creation more easy. </p><a name="_Toc35342997"></a><br><p></p><p></p><p style="text-align: center;"><a name="_Toc3535218" style="background-color: rgb(255, 255, 255); color: rgb(82, 96, 105); font-size: 1rem;">&nbsp;&nbsp;<img src="@@PLUGINFILE@@/Validation%20Steps.png" alt="Validation Steps" width="500" height="535" style="text-align: center; " class="img-responsive atto_image_button_middle"></a></p><p><a name="_Toc3535218"><br></a></p><p><a name="_Toc3535218"><br></a></p><p><a name="_Toc3535218"></a></p><p><a name="_Toc3535218">The figure below is
a list of the Gold Standards of a QEEG Normative Database, as developed by
Robert Thatcher.</a></p><a name="_Toc3535218">

</a><h2><a name="_Toc3535218"></a><a name="_Toc35342998">Gold Standards of QEEG Normative
Databases, from Thatcher</a> </h2><p style="text-align: center;"><img src="@@PLUGINFILE@@/Gold%20Standards.png" alt="Gold Standards" width="501" height="273" class="img-responsive atto_image_button_text-bottom" style="font-size: 1rem;"></p><p></p><p><a name="_Toc3535218"></a></p><h2><a name="_Toc35342999"></a><a name="_Toc3535219">Basic statistical analysis</a></h2>

<p>The&nbsp;selected&nbsp;normal&nbsp;subjects&nbsp;are&nbsp;grouped&nbsp;by&nbsp;age&nbsp;with
sufficiently&nbsp;large&nbsp;sample&nbsp;size&nbsp;and&nbsp;</p>

<p>the&nbsp;means&nbsp;and&nbsp;standard&nbsp;deviations&nbsp;of&nbsp;the&nbsp;EEG&nbsp;time&nbsp;series&nbsp;and/or&nbsp;Frequency&nbsp;domain&nbsp;</p>

<p>analyses&nbsp;are&nbsp;computed&nbsp;for&nbsp;each&nbsp;age&nbsp;group.&nbsp;&nbsp;&nbsp;Transforms&nbsp;are&nbsp;applied&nbsp;to&nbsp;approximate&nbsp;a&nbsp;</p>

<p>Gaussian&nbsp;distribution&nbsp;of&nbsp;the&nbsp;EEG&nbsp;measures&nbsp;that&nbsp;comprise&nbsp;the&nbsp;means.&nbsp;&nbsp;&nbsp;Once&nbsp;</p>

<p>approximation&nbsp;to&nbsp;Gaussian&nbsp;is&nbsp;completed,&nbsp;then&nbsp;Z&nbsp;scores&nbsp;are&nbsp;computed&nbsp;for&nbsp;each&nbsp;subject&nbsp;in&nbsp;</p>

<p>the&nbsp;database&nbsp;and&nbsp;leave&nbsp;one&nbsp;out&nbsp;Gaussian&nbsp;Cross ­Validation&nbsp;is&nbsp;computed&nbsp;in&nbsp;order&nbsp;to&nbsp;arrive&nbsp;</p>

<p>at&nbsp;an&nbsp;optimum&nbsp;Gaussian&nbsp;Cross ­validation&nbsp;sensitivity.&nbsp;&nbsp;&nbsp;&nbsp;Finally,
the&nbsp;Gaussian&nbsp;validated&nbsp;</p>

<p>norms&nbsp;are&nbsp;subjected&nbsp;to&nbsp;content&nbsp;and&nbsp;predictive&nbsp;validation&nbsp;procedures&nbsp;such&nbsp;as&nbsp;correlation&nbsp;</p>

<p>with&nbsp;neuropsychological&nbsp;test&nbsp;scores&nbsp;and&nbsp;intelligence,&nbsp;etc.&nbsp;and&nbsp;also&nbsp;discriminant&nbsp;analyses&nbsp;</p>

<p>and&nbsp;neural&nbsp;networks&nbsp;and&nbsp;outcome&nbsp;statistics,&nbsp;etc.&nbsp;&nbsp;&nbsp;The&nbsp;content&nbsp;validations&nbsp;are&nbsp;with&nbsp;respect&nbsp;</p>

<p>to&nbsp;clinical&nbsp;measures&nbsp;such&nbsp;as&nbsp;intelligence,&nbsp;neuropsychological&nbsp;test&nbsp;scores,&nbsp;school&nbsp;</p>

<p>achievement,&nbsp;clinical&nbsp;outcomes,&nbsp;etc.&nbsp;&nbsp;The&nbsp;predictive&nbsp;validations&nbsp;are&nbsp;with&nbsp;respect&nbsp;to&nbsp;the&nbsp;</p>

<p>discriminative,&nbsp;statistical&nbsp;or&nbsp;neural&nbsp;network&nbsp;clinical&nbsp;classification&nbsp;accuracy.&nbsp;&nbsp;Both&nbsp;</p>

<p>parametric&nbsp;and&nbsp;non­parametric&nbsp;statistics&nbsp;are&nbsp;used&nbsp;to&nbsp;determine&nbsp;the&nbsp;content&nbsp;and&nbsp;predictive&nbsp;</p>

<p>validity&nbsp;of&nbsp;a&nbsp;normative&nbsp;EEG&nbsp;database.&nbsp;</p><br><p></p><p><a name="_Toc3535218"><br></a></p>