Electroencephalography (EEG) is used to measure brain activity through summing the electrical activity of the neurons under each electrode. Different frequencies of waves recorded correspond to different cognitive states. EEG power refers to the amplitude of an oscillatory signal squared, an indicator of brain functioning across each frequency band. Prior research has shown significant variability in evoked potentials within 30-minute segments in patients. The shortest time segment (epoch) needed for a reliable measurement of EEG power has not been established through research. Statistical analysis using Engle’s ARCH Test for conditional heteroscedasticity was computed using variances of power data for 10 child subjects with Rett Syndrome who were given a placebo and 10 neurotypical controls of the same age. The median number of trials until stability of variance is reached per frequency band of each subject patient indicates that children with Rett syndrome probably have a longer minimum time necessary (up to 30 seconds) for a stable measure of power than neurotypical children, whose variances of power data stabilize almost immediately.