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摘要翻译：
我们研究了伯努利序列集合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成功的条纹视为正依赖的过度代表--热手谬误中的应用。特别地，我们研究了随机零假设（即试验是I.I.D.）的置换检验基于测试统计数据，将直接跟随k个连续成功的成功比例与总体成功比例或直接跟随k个连续失败的成功比例进行比较。我们刻划了这些检验统计量及其置换分布在随机性下、在一组一般平稳过程下和在一类马尔可夫链方案下的渐近分布，从而使我们可以得到它们的局部渐近幂。结果被应用于评价四个控制篮球投篮实验提供的热手谬误的经验支持。我们确定，需要大量的数据集来导出篮球投篮中偏离随机性的信息测量。在我们能够获得数据的一个实验中，多个测试程序揭示了一个射手表现出与随机性明显不一致的投篮模式--提供了强有力的证据，证明篮球投篮不是所有射手在任何时候都是随机的。然而，我们发现在这个实验中反对随机性的证据仅限于这个射手。我们的结果为设计和验证实验提供了数学和统计基础，这些实验直接比较了对随机性的偏离与人类对随机性偏离的信念，从而构成了对热手谬误的直接检验。
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英文标题：
《Uncertainty in the Hot Hand Fallacy: Detecting Streaky Alternatives to
Random Bernoulli Sequences》
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作者：
David M. Ritzwoller and Joseph P. Romano
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最新提交年份：
2021
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分类信息：
一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics 统计学
二级分类：Applications 应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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英文摘要：
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 follow k consecutive successes with either the overall proportion of successes or the proportion of successes that directly follow k consecutive 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.
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PDF链接：
https://arxiv.org/pdf/1908.01406
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