  We present a new experimental design procedure that divides a set of
experimental units into two groups so that the two groups are balanced on a
prespecified set of covariates and being almost as random as complete
randomization. Under complete randomization, the difference in covariate
balance as measured by the standardized average between treatment and control
will be $O_p(n^{-1/2})$. If the sample size is not too large this may be
material. In this article, we present an algorithm which greedily switches
assignment pairs. Resultant designs produce balance of the much lower order
$O_p(n^{-3})$ for one covariate. However, our algorithm creates assignments
which are, strictly speaking, non-random. We introduce two metrics which
capture departures from randomization: one in the style of entropy and one in
the style of standard error and demonstrate our assignments are nearly as
random as complete randomization in terms of both measures. The results are
extended to more than one covariate, simulations are provided to illustrate the
results and statistical inference under our design is discussed. We provide an
open source R package available on CRAN called GreedyExperimentalDesign which
generates designs according to our algorithm.
