The 1.5 million figure is from 2011 Scottish Census data. [1]
[1] http://www.scotlandscensus.gov.uk/documents/censusresults/re...
[1] http://www.scotlandscensus.gov.uk/documents/censusresults/re...
I live in Aberdeen, and I'm pretty sure if I was to leave my flat and ask people I met in the street whether they spoke Scots or English, I'd get a disproportionate number of Scottish English speakers tell me they speak Scots; I'd also probably get some of the Doric-speaking locals tell me they speak English, even though Doric is actually a descendant of Scots.