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.
翻译:许多真实生活状况要求按随机顺序反复排列一系列物品,在这种情况下,往往有必要检验这种随机化是否确实得到,但这个问题在文献中受到的关注非常有限,本文件阐述了这一问题的关键特征,并提出了三次“非目标”测试,不需要分析员事先提供信息。这些方法用来分析彩票的抽奖顺序、美国偶像比赛的顺序以及得克萨斯州和西弗吉尼亚州初选选票的候选人顺序。在最后一项应用中,发现了与完全随机化的多重偏差,可能产生严重的政治和法律后果。这些偏差的形式各不相同,取决于体制因素,有时需要使用交换权力的测试来提高稳健性。