  Many real life situations require a set of items to be repeatedly placed in a
random sequence. In such circumstances, it is often desirable to test whether
such randomization indeed obtains, yet this problem has received very limited
attention in the literature. This paper articulates the key features of this
problem and presents three "untargeted" tests that require no a priori
information from the analyst. These methods are used to analyze the order in
which lottery numbers are drawn in Powerball, the order in which contestants
perform on American Idol, and the order of candidates on primary election
ballots in Texas and West Virginia. In this last application, multiple
deviations from full randomization are detected, with potentially serious
political and legal consequences. The form these deviations take varies,
depending on institutional factors, which sometimes necessitates the use of
tests that exchange power for increased robustness.
