  Threshold biasing of a Gaussian random field gives a linear amplification of
the reduced two point correlation function at large distances. We show that for
standard cosmological models this does not translate into a linear
amplification of the power spectrum (PS) at small k. For standard CDM type
models this means that the``turn-over'' at small k of the original PS
disappears in the PS of the biased field for the physically relevant range of
the threshold parameter. In real space this difference is manifest in the
asymptotic behaviour of the normalised mass variance in spheres of radius R,
which changes from the ``super-homogeneous'' behaviour to a Poisson-like
behaviour.This qualitative change results from the intrinsic stochasticity of
the threshold sampling. While our quantitative results are specific to the
simplest threshold biasing model, we argue that our qualitative conclusions
should be valid generically for any biasing mechanism involving a
scale-dependent amplification of the correlation function. One implication is
that the real-space correlation function will be a better instrument to probe
for the underlying Harrison Zeldovich spectrum in the distribution of visible
matter, as the characteristic asymptotic negative power-law \xi (r) \sim
-r^{-4} tail is undistorted by biasing.
