标题： 使用多个安全置信区间进行视觉测试 显示英文标题

标题： Visual tests using several safe confidence intervals

摘要： 我们提出了一种新的统计假设检验框架，它通过使用置信区间来决定两个样本的均值是否相等，或者一个是否大于另一个。 使用我们的方法，用户可以同时可视化均值的置信区域，并通过观察两个置信区间是否重叠来判断两个总体的均值是否存在显著差异。 为了设计这个检验，我们使用了基于e-变量构造的置信区间，这为假设检验提供了一个证据度量。 我们提出了两种检验：一种是基于置信区间重叠的序贯检验，另一种是非序贯检验，并且对于这两种检验，我们都给出了误差概率在有限时间内的误差界。 我们还通过将其应用于顺序学习算法的比较，展示了我们方法的实际应用性。 显示英文摘要

摘要： We propose a new statistical hypothesis testing framework which decides visually, using confidence intervals, whether the means of two samples are equal or if one is larger than the other. With our method, the user can at the same time visualize the confidence region of the means and do a test to decide if the means of the two populations are significantly different or not by looking whether the two confidence intervals overlap. To design this test we use confidence intervals constructed using e-variables, which provide a measure of evidence in hypothesis testing. We propose both a sequential test and a non-sequential test based on the overlap of confidence intervals and for each of these tests we give finite-time error bounds on the probabilities of error. We also illustrate the practicality of our method by applying it to the comparison of sequential learning algorithms.