We present the first measurement of the electron angular distribution parameter α2 in W → e ν events in proton-antiproton collisions as a function of the W boson transverse momentum. Our analysis is based on data collected using the DØ detector during the 1994–1995 Fermilab Tevatron run. We compare our results with next-to-leading order perturbative QCD, which predicts an angular distribution of (1 ± α1 cos θ* + α2 cos 2 θ*), where θ* is the polar angle of the electron in the Collins-Soper frame and α1 and α2 are functions of [Formula: see text], the W boson transverse momentum. This measurement provides a test of next-to-leading order QCD corrections which are a non-negligible contrbution to the W boson mass measurement.