  We present the first measurement of the electron angular distribution
parameter alpha_2 in W to e nu events produced in proton-antiproton collisions
as a function of the W boson transverse momentum. Our analysis is based on data
collected using the D0 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 +/- alpha_1 cos theta* + alpha_2 cos^2 theta*),
where theta* is the polar angle of the electron in the Collins-Soper frame. In
the presence of QCD corrections, the parameters alpha_1 and alpha_2 become
functions of p_T^W, 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.
