What did the 2016 Brexit referendum data really say?
  The Brexit referendum took place in the UK in June, 2016. The unweighted percentage of leavers over the whole population was 51.9%. In this paper, first, we demonstrate that a 52%-48% split represents only a difference that is not sufficiently different from a 50-50 split to claim a majority for either side. Second, and most important, on this basis of the unweighted percentage, statement like: The country voted to leave the EU, were made. When a statement about a population is made based on a subset of it (the turnout rate for Brexit was only 72% and therefore 37% of the eligible population voted Leave), it comes with an element of uncertainty that should not be ignored. The unweighted average disregards, not only between-region heterogeneity but also within-region variability. Our analysis, controlling for both, finds that the split of the Brexit is of negligible material significance and do not indicate majority for either side. 
Nicholas Donaldson, Nora Donaldson and Grace Yang
stat.AP