The sign test is one of the most popular nonparametric tests for location problems and allows testing for any quantile of a population. However, the common sign test has serious drawbacks such as loss of information by considering solely signs of observations but not their magnitudes, various problems related to handling of ties in the data, and the lack of embedding uncertainty regarding the fraction of underlying quantile. To address these issues, we present an extended sign test based on fuzzy categories and fuzzy formulated hypotheses that improves the generality, versatility, and practicability of the common sign test. This generalized test procedure is neat in theory and practice and avoids disadvantages that are often associated with fuzzy tests (e.g., a considerably higher complexity of the underlying model, a fuzzy test decision, and a possibilistic instead of a probabilistic interpretation of test results). In addition, we perform a comprehensive case study on COVID‐19 in HIV‐infected individuals with a focus on human body temperature and related measurement problems. The results of the study clearly indicate that fuzzy categories and fuzzy hypotheses improve the performance of the sign test.

中文翻译：

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适用于 COVID-19 临床特征的分位数非参数模糊假设检验


符号检验是最流行的位置问题非参数检验之一，允许对总体的任何分位数进行测试。然而，常见的符号检验具有严重的缺点，例如仅考虑观察的符号而不考虑其大小而导致信息丢失，与处理数据中的联系相关的各种问题，以及缺乏关于基础分位数分数的嵌入不确定性。为了解决这些问题，我们提出了一种基于模糊类别和模糊假设的扩展符号测试，提高了通用符号测试的通用性、多功能性和实用性。这种广义的测试过程在理论和实践上都很简洁，并且避免了通常与模糊测试相关的缺点（例如，基础模型的复杂性相当高、模糊测试决策以及测试结果的可能性解释而不是概率解释）。此外，我们还对 HIV 感染者的 COVID-19 进行了全面的案例研究，重点关注人体体温和相关测量问题。研究结果清楚地表明，模糊类别和模糊假设提高了符号检验的性能。