  Fisher (1934) argued that certain ancillary statistics form a relevant
subset, a subset of the sample space on which inference should be restricted,
and showed that conditioning on their observed value reduces the dimension of
the data without a loss of information. The use of ancillary statistics in
post-data inference has received significant attention; however, their role in
the design of the experiment has not been well characterized. Ancillary
statistics are unknown prior to data collection and as a result cannot be
incorporated into the design a priori. However, if the data are observed
sequentially then the ancillary statistics based on the data from the preceding
observations can be used to determine the design assignment for the current
observation. The main results of this work describe the benefits of
incorporating ancillary statistics, specifically, the ancillary statistic that
constitutes a relevant subset, into an adaptive design.
