  A new generation of radio telescopes are currently being built with the goal
of tracing the cosmic distribution of atomic hydrogen at redshifts 6-15 through
its 21-cm line. The observations will probe the large-scale brightness
fluctuations sourced by ionization fluctuations during cosmic reionization.
Since detailed maps will be difficult to extract due to noise and foreground
emission, efforts have focused on a statistical detection of the 21-cm
fluctuations. During cosmic reionization, these fluctuations are highly
non-Gaussian and thus more information can be extracted than just the
one-dimensional function that is usually considered, i.e., the correlation
function. We calculate a two-dimensional function that if measured
observationally would allow a more thorough investigation of the properties of
the underlying ionizing sources. This function is the probability distribution
function (PDF) of the difference in the 21-cm brightness temperature between
two points, as a function of the separation between the points. While the
standard correlation function is determined by a complicated mixture of
contributions from density and ionization fluctuations, we show that the
difference PDF holds the key to separately measuring the statistical properties
of the ionized regions.
