Recordings of electrical brain activity carry information about a person's cognitive health. For recording EEG signals, a very common setting is for a subject to be at rest with its eyes closed. Analysis of these recordings often involve a dimensionality reduction step in which electrodes are grouped into 10 or more regions (depending on the number of electrodes available). Then an average over each group is taken which serves as a feature in subsequent evaluation. Currently, the most prominent features used in clinical practice are based on spectral power densities. In our work we consider a simplified grouping of electrodes into two regions only. In addition to spectral features we introduce a secondary, non-redundant view on brain activity through the lens of Tsallis Entropy $S_{q=2}$. We further take EEG measurements not only in an eyes closed (ec) but also in an eyes open (eo) state. For our cohort of healthy controls (HC) and individuals suffering from Parkinson's disease (PD), the question we are asking is the following: How well can one discriminate between HC and PD within this simplified, binary grouping? This question is motivated by the commercial availability of inexpensive and easy to use portable EEG devices. If enough information is retained in this binary grouping, then such simple devices could potentially be used as personal monitoring tools, as standard screening tools by general practitioners or as digital biomarkers for easy long term monitoring during neurological studies.