Check out this paper by Xiao-Li Meng on statistical paradoxes in which Meng poses the following question: “Which one should I trust more: a 1% survey with a 60% response rate or a self-reported administrative dataset covering 80% of the population?” Or to borrow Jason N. Doctor’s formulation via Twitter (@jasndoc):

“An urn contains 10K red & blue marbles of unknown proportion. Win $1M if you estimate the correct proportion. You can either: (1) sample 80%, or, (2) stir the marbles & sample 1%. Which do you do?”