  Spatial dependence in the statistics of redshifted 21cm fluctuations promises
to provide the most powerful probe of the reionisation epoch. In this paper we
consider the second and third moments of the redshifted 21cm intensity
distribution using a simple model that accounts for galaxy bias during the
reionisation process. We demonstrate that skewness in redshifted 21cm maps
should be substantial throughout the reionisation epoch and on all angular
scales, owing to the effects of galaxy bias which leads to early reionisation
in over-dense regions of the IGM. The variance (or power-spectrum) of 21cm
fluctuations will exhibit a minimum in redshift part way through the
reionisation process, when the global ionisation fraction is around 50%. This
minimum is generic, and is due to the transition from 21cm intensity being
dominated by over-dense too under-dense regions as reionisation progresses. We
show that the details of the reionisation history, including the presence of
radiative feedback are encoded in the evolution of the auto-correlation and
skewness functions with redshift and mean IGM neutral fraction. We discuss the
detection of skewness by first generation instruments, and conclude that the
Mileura Widefield Array - Low Frequency Demonstrator will have sufficient
sensitivity to detect skewness on a range of angular scales at redshifts near
the end of reionisation, while a subsequent instrument of 10 times the
collecting area could map out the evolution of skewness in detail. The
observation of a minimum in variance during the reionisation history, and the
detection of skewness would both provide important confirmation of the
cosmological origin of redshifted 21cm intensity fluctuations.
