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Kind of a bummer that they didn't provider their own estimates, but the way they found the discrepancy is interesting:
How exactly do you test the accuracy of global datasets used to derive population totals in the first place? Well, with a background in water resource management, Láng-Ritter looked at a different kind of population data gathered from rural dam projects—300 such projects across 35 countries, to be precise. This data focused on the years 1975 to 2010, and these population tallies provided a significant dataset to check against other population totals calculated by organizations like WorldPop, GWP, GRUMP, LandScan, and GHS-POP (which were also analyzed in this study).