Squaring spectral means emphasizes extreme data points in a sample. It launches fringe events far away from the central tendency of a sample's distribution so that they can be easily identified and circled with red ink by the psychologist on duty. It is a technique to assist eyeballs, not computers. It is a geometric transformation that should not be embraced in the linear world of inferential statistics, but people continue to leave the welcome mat out. QEEG data, if anything, should be geometrically compressed or compacted in order to make it correspond readily with psychological phenomena.
Power geometrically expands it.
Let's take a fresh look at what we are doing when we convert magnitude values to power. Comparing squared values makes little sense in most endeavors. This adage is doubly appropriate when statistics are to be used, because statistics, as we all know, are the tools of the devil, a formalized scheme to confound and to confuse and occasionally illuminate. QEEG analysis includes a whole lot of averaging along the way. It's not always clear which average was squared to produce power values.