Confidence intervals for seroprevalence
Confidence intervals for seroprevalence
复制标题
血清阳性率的置信区间
DOI：
10.1093/restud/rdab020
复制
发表时间：
2022
影响因子：
5.7
通讯作者：
Shaikh, A.
中科院分区：
文献类型：
--
作者：
DiCiccio, T;Ritzwoller, D;Romano, J;Shaikh, A.
我们研究了一组Bernoulli序列的随机性的一类置换检验，以及它们在分析人类倾向于将连续的成功序列感知为过度代表正相关性的倾向--热手谬误--中的应用。特别是，我们研究了随机性零假设(即试验是I.I.D.)的排列检验。基于测试统计，该测试统计将紧跟在连续成功之后的成功比例与紧跟在连续失败之后的成功的总比例进行比较。我们刻画了这些检验统计量在随机性、一组一般平稳过程和一类马尔可夫链备选方案下的渐近分布及其置换分布，从而得到了它们的局部渐近幂。研究结果被用来评估四个受控篮球投篮实验对热手谬误的实证支持。我们确定，需要更大的数据集来得出篮球投篮中偏离随机性的信息性测量。在我们能够获得数据的一个实验中，多个测试程序显示，一个射手的投篮模式与随机性显著不一致--这提供了强有力的证据，表明篮球投篮并不总是对所有射手都是随机的。然而，我们发现，在这项实验中反对随机性的证据仅限于这名枪手。我们的结果为设计和验证实验提供了数学和统计基础，这些实验直接比较偏离随机性的偏差与人类关于偏离随机性的信念，从而构成对热手谬误的直接测试。
We study a class of permutation tests of the randomness of a collection of Bernoulli sequences and their application to analyses of the human tendency to perceive streaks of consecutive successes as overly representative of positive dependence—the hot hand fallacy. In particular, we study permutation tests of the null hypothesis of randomness (i.e.that trials are i.i.d.) based on test statistics that compare the proportion of successes that directly followconsecutive successes with either the overall proportion of successes or the proportion of successes that directly followconsecutive failures. We characterize the asymptotic distributions of these test statistics and their permutation distributions under randomness, under a set of general stationary processes, and under a class of Markov chain alternatives, which allow us to derive their local asymptotic power. The results are applied to evaluate the empirical support for the hot hand fallacy provided by four controlled basketball shooting experiments. We establish that substantially larger data sets are required to derive an informative measurement of the deviation from randomness in basketball shooting. In one experiment, for which we were able to obtain data, multiple testing procedures reveal that one shooter exhibits a shooting pattern significantly inconsistent with randomness—supplying strong evidence that basketball shooting is not random for all shooters all of the time. However, we find that the evidence against randomness in this experiment is limited to this shooter. Our results provide a mathematical and statistical foundation for the design and validation of experiments that directly compare deviations from randomness with human beliefs about deviations from randomness and thereby constitute a direct test of the hot hand fallacy.