  Randomization tests allow simple and unambiguous tests of null hypotheses, by
comparing observed data to a null ensemble in which experimentally-controlled
variables are randomly resampled. In behavioral and neuroscience experiments,
however, the stimuli presented often depend on the subject's previous actions,
so simple randomization tests are not possible. We describe how conditional
randomization can be used to perform exact hypothesis tests in this situation,
and illustrate it with two examples. We contrast conditional randomization with
a related approach of tangent randomization, in which stimuli are resampled
based only on events occurring in the past, which is not valid for all choices
of test statistic. We discuss how to design experiments that allow conditional
randomization tests to be used.
