<p>John and colleques expanded on the use of the Z score for clinical evaluation including the use of multivariate measures such as the Mahalanobis distance metric.A direct normalization of the Gaussian distribution using Z scores is useful in comparing&nbsp; individuals to a QEEG normative database. That is, the standard score form of the&nbsp;</p><p>Gaussian is where the mean = 0 and standard deviation = 1 or, by substitution into the&nbsp;</p><p>Gaussian equation for a bell shaped curve, then&nbsp;</p><p style="text-align: center;"><img src="@@PLUGINFILE@@/shaped-curve.png" alt="" width="120" height="79" role="presentation" class="img-responsive atto_image_button_text-bottom"><br></p><p>, where Y = Gaussian distribution and the Z score is a deviation in&nbsp;</p><p>standard deviation units measured along the baseline of the Gaussian curve from a mean of 0 and a standard deviation = 1 and deviations to the right of the mean being&nbsp;</p><p>positive and those to the left negative.&nbsp; By substituting different values of Z then different values of Y can be calculated.&nbsp; &nbsp;For example, when Z = 0, Y = 0.3989 or, in other words, the height of the curve at the mean of the normal distribution in standard score form is given by the number 0.3989.&nbsp; For purposes of assessing deviation from&nbsp;</p><p>normal, the values of Z above and below the mean, which include 95% of the area of the Gaussian is often used as a level of confidence necessary to minimize Type I and&nbsp;<span style="font-size: 1rem;">Type II errors.</span></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).&nbsp;</p><p style="text-align: center;"><img src="@@PLUGINFILE@@/gaussian-distribution-across-metrics.png" alt="Gaussian Distribution across metrics" width="587" height="461" class="img-responsive atto_image_button_text-bottom"><br></p><p style="text-align: center;">Figure #2 - Gaussian Distribution across metrics<br></p><p style="text-align: center;"><br></p><p style="text-align: left;">Figure #5 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.&nbsp;<br></p><p style="text-align: left;"><img src="@@PLUGINFILE@@/statistical-considerations-databases.png" alt="Statistical considerations in databases" width="587" height="628" role="presentation" class="img-responsive atto_image_button_text-bottom"><br></p><p style="text-align: center;">Figure #5: Statistical considerations in databases<br></p><p style="text-align: center;"><br></p><p style="text-align: left;">Figure #6 below is a list of the Gold Standards of a QEEG Normative Database, as developed by Robert Thatcher.<br></p><p style="text-align: center;"><img src="@@PLUGINFILE@@/QEEG-Normative-Databases.png" alt="Gold Standards of QEEG Normative Databases, from Thatcher" width="528" height="288" role="presentation" class="img-responsive atto_image_button_text-bottom"><br></p><p style="text-align: center;">Figure #6: Gold Standards of QEEG Normative Databases, from Thatcher<br></p>