Department of Psychology, University of California, Berkeley.
J Exp Psychol Learn Mem Cogn. 2013 Sep;39(5):1473-90. doi: 10.1037/a0032397. Epub 2013 Apr 22.
Errors in detecting randomness are often explained in terms of biases and misconceptions. We propose and provide evidence for an account that characterizes the contribution of the inherent statistical difficulty of the task. Our account is based on a Bayesian statistical analysis, focusing on the fact that a random process is a special case of systematic processes, meaning that the hypothesis of randomness is nested within the hypothesis of systematicity. This analysis shows that randomly generated outcomes are still reasonably likely to have come from a systematic process and are thus only weakly diagnostic of a random process. We tested this account through 3 experiments. Experiments 1 and 2 showed that the low accuracy in judging whether a sequence of coin flips is random (or biased toward heads or tails) is due to the weak evidence provided by random sequences. While randomness judgments were less accurate than judgments involving non-nested hypotheses in the same task domain, this difference disappeared once the strength of the available evidence was equated. Experiment 3 extended this finding to assessing whether a sequence was random or exhibited sequential dependence, showing that the distribution of statistical evidence has an effect that complements known misconceptions.
检测随机性错误通常可以用偏见和误解来解释。我们提出并提供了一种解释，这种解释可以描述任务固有的统计难度的贡献。我们的解释是基于贝叶斯统计分析，重点是随机过程是系统过程的特殊情况，这意味着随机性假设嵌套在系统性假设中。这种分析表明，随机生成的结果仍然很有可能来自系统过程，因此对随机过程的诊断性很弱。我们通过 3 个实验来检验这个解释。实验 1 和实验 2 表明，判断硬币投掷序列是否随机（或偏向正面或反面）的准确性较低，是因为随机序列提供的证据较弱。虽然在同一任务领域中，随机判断的准确性低于涉及非嵌套假设的判断，但一旦可用证据的强度相等，这种差异就会消失。实验 3 将这一发现扩展到评估序列是否随机或表现出序列依赖性，表明统计证据的分布具有与已知误解互补的效果。
