  A proposed method for dealing with foreground emission in upcoming 21-cm
observations from the epoch of reionization is to limit observations to an
uncontaminated window in Fourier space. Foreground emission can be avoided in
this way, since it is limited to a wedge-shaped region in $k_{\parallel},
k_{\perp}$ space. However, the power spectrum is anisotropic owing to
redshift-space distortions from peculiar velocities. Consequently, the 21-cm
power spectrum measured in the foreground avoidance window---which samples only
a limited range of angles close to the line-of-sight direction---differs from
the full spherically-averaged power spectrum which requires an average over
\emph{all} angles. In this paper, we calculate the magnitude of this "wedge
bias" for the first time. We find that the bias is strongest at high redshifts,
where measurements using foreground avoidance will over-estimate the power
spectrum by around 100 per cent, possibly obscuring the distinctive rise and
fall signature that is anticipated for the spherically-averaged 21-cm power
spectrum. In the later stages of reionization, the bias becomes negative, and
smaller in magnitude ($\lesssim 20$ per cent). The effect shows only a weak
dependence on spatial scale and reionization topology.
