  We give some useful decompositions of sum-of-powers statistics, leading to
decompositions for the sample mean, sample variance, sample skewness and sample
kurtosis. We solve two related problems: computing these sample moments for a
pooled sample composed of subgroups with known moments; and computing these
sample moments for a subgroup using known moments from other subgroups and the
overall pooled sample. Each task is accomplished via decompositions of the
sums-of-squares, sums-of-cubes and sums-of-quads from which the sample central
moments (up to fourth order) are formed. We give decomposition results and we
implement these in a user-friendly R function.
