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Firstly, this paper reviews Hall’s theory of bootstrap critical points (Hall, 1988) and the Edgeworth expansion for the mean direction φ = μ(Fn) of directional data (Wu & Deng, 1996), and then applies Hall’s results to study six bootstrap confidence intervals for circular mean direction μ. = μ(F). Our results show that STUD-interval and ABC-interval are both second-order correct. For von Mises...