This paper examines the assumption of stationarity used in EEG brain activity analyses, despite EEG data often being non-stationary. Transformations necessary to obtain stationary data from measured non-stationary EEG data and methods to assess non-stationarity are illustrated using eyes open (EO) and eyes closed (EC) data. The study shows that even short time EEG records of 10s duration exhibit non-stationary behavior. Examination of the change in variance when going from the EO to the EC state for both able bodied and spinal cord injured participants show that the difference in variance is consistently positive and statistically significant only when stationary data is used. This has implications for brain computer interfaces that utilizes changes in EO and EC EEG signals.