  This paper provides a statistical method to test whether a system that
performs a binary sequential hypothesis test is optimal in the sense of
minimizing the average decision times while taking decisions with given
reliabilities. The proposed method requires samples of the decision times, the
decision outcomes, and the true hypotheses, but does not require knowledge on
the statistics of the observations or the properties of the decision-making
system. The method is based on fluctuation relations for decision time
distributions which are proved for sequential probability ratio tests. These
relations follow from the martingale property of probability ratios and hold
under fairly general conditions. We illustrate these tests with numerical
experiments and discuss potential applications.
