We present the first measurement of the electron angular distribution parameter α2 in −→Weν events produced 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±α1cosθ*+α2cos2θ*), where θ* is the polar angle of the electron in the Collins-Soper frame. In the presence of QCD corrections, the parameters α1 and α2 become functions of pWT, the W boson transverse momentum. This measurement provides a test of next-to-leading order QCD corrections which are a non-negligible contribution to the W boson mass measurement.Received 15 September 2000DOI:https://doi.org/10.1103/PhysRevD.63.072001©2001 American Physical Society