  When estimating the abundances which result from a given star formation
event, it is customary to treat the IMF as a series of weight factors to be
applied to the stellar yields, as a function of mass, implicitly assuming one
is dealing with an infinite population. However, when the stellar population is
small, the standard procedure would imply the inclusion of fractional numbers
of stars at certain masses. We study the effects of small number statistics on
the resulting abundances by performing an statistical sampling of the IMF to
form a stellar population out of discrete numbers of stars. A chemical
evolution code then follows the evolution of the population, and traces the
resulting abundances. The process is repeated to obtain an statistical
distribution of the resulting abundances and their evolution. We explore the
manner in which different elements are affected, and how different abundances
converge to the infinite population limit as the total mass increases. We
include a discussion of our results in the context of dwarf spheroidal galaxies
and show the recently reported internal dispersions in abundance ratios for
dSph galaxies might be partly explained through the stochastic effects
introduced by a low star formation rate, which can account for dispersions of
over 2 dex in [C/O], [N/O], [C/Fe], [N/Fe] and [O/Fe].
