The last decade has seen the development of a range of new statistical and computational techniques for analysing large collections of radiocarbon (14C) dates, often but not exclusively to make inferences about human population change in the past. Here we introduce rcarbon, an open-source software package for the R statistical computing language which implements many of these techniques and looks to foster transparent future study of their strengths and weaknesses. In this paper, we review the key assumptions, limitations and potentials behind statistical analyses of summed probability distribution of 14C dates, including Monte-Carlo simulation-based tests, permutation tests, and spatial analyses. Supplementary material provides a fully reproducible analysis with further details not covered in the main paper.