  In order to examine the validity of Wandzura-Wilczek relation for the
polarized DIS structure function $g_2(x,Q^2)$, we use the light-front
time-ordering pQCD to calculate $g_2(x,Q^2)$ at order $\alpha_s$ on a quark
target. We find that the study of the transverse polarized structure function
in pQCD is only meaningful if we begin with massive quarks. The result shows
that the Wandzura-Wilczek relation for $g_2(x,Q^2)$ is strongly violated by the
quark mass in pQCD.
