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Uncertainty in the Hot Hand Fallacy: Detecting Streaky Alternatives to Random Bernoulli Sequences

David M. Ritzwoller, Joseph P. Romano

arXiv 4 Aug 2019 · Econometrics · publishedThe Review of Economic Studies (2021) · 3 citations (OpenAlex)

arXiv:1908.01406 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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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60
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Miller, J. B. and Sanjurjo, A (2018) A cold shower for the hot hand fallacy: Robust evidence that belief in the hot hand is justified1.000143100%
2Miller, J. B. and Sanjurjo, A (2019) Is it a fallacy to believe in the hot hand in the nba three-point contest?0.874122100%
3Lehmann, E. L. and Romano, J. P (2005) Testing Statistical Hypotheses self0.87452100%
4Bocskocsky, A., Ezekowitz, J., and Stein, C (2014) The hot hand: A new approach to an old `fallacy'0.73732100%
5Gilovich, T., Vallone, R., and Tversky, A (1985) The hot hand in basketball: On the misperception of random sequences0.73732100%
6Lantis, R. M. and Nesson, E. T (2019) Hot shots: An analysis of the `hot hand' in nba field goal and free throw shooting0.73732100%
7Jagacinski, R. J., Newel, K. M., and Isaac, P. D (1979) Predicting the success of a basketball shot at various stages of execution0.69351100%
8Künsch, H. R (1989) The jackknife and the bootstrap for general stationary observations0.64422100%
9Lahiri, S. N (2013) Resampling Methods for Dependent Data0.64422100%
10Liu, R. Y. and Singh, K (1992) Moving blocks jackknife and bootstrap capture weak dependence0.64422100%

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Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Randomization Inference: Theory and Applications0.58531