  We present a randomization-based inferential framework for experiments
characterized by a strongly ignorable assignment mechanism where units have
independent probabilities of receiving treatment. Previous works on
randomization tests often assume these probabilities are equal within blocks of
units. We consider the general case where they differ across units and show how
to perform randomization tests and obtain point estimates and confidence
intervals. Furthermore, we develop a rejection-sampling algorithm to conduct
randomization-based inference conditional on ancillary statistics, covariate
balance, or other statistics of interest. Through simulation we demonstrate how
our algorithm can yield powerful randomization tests and thus precise
inference. Our work also has implications for observational studies, which
commonly assume a strongly ignorable assignment mechanism. Most methodologies
for observational studies make additional modeling or asymptotic assumptions,
while our framework only assumes the strongly ignorable assignment mechanism,
and thus can be considered a minimal-assumption approach.
