College of Statistical and Actuarial Sciences, University of the Punjab Lahore, Lahore, Pakistan.
Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, 21551, Saudi Arabia.
BMC Med Res Methodol. 2021 Oct 17;21(1):215. doi: 10.1186/s12874-021-01410-x.
Kruskal-Wallis H test from the bank of classical statistics tests is a well-known nonparametric alternative to a one-way analysis of variance. The test is extensively used in decision-making problems where one has to compare the equality of several means when the observations are in exact form. The test is helpless when the data is in an interval form and has some indeterminacy.
The interval-valued data often contain uncertainty and imprecision and often arise from situations that contain vagueness and ambiguity. In this research, a modified form of the Kruskal-Wallis H test has been proposed for indeterminacy data. A comprehensive theoretical methodology with an application and implementation of the test has been proposed in the research.
The proposed test is applied on a Covid-19 data set for application purposes. The study results suggested that the proposed modified Kruskal-Wallis H test is more suitable in interval-valued data situations. The application of this new neutrosophic Kruskal-Wallis test on the Covid-19 data set showed that the proposed test provides more relevant and adequate results. The data representing the daily ICU occupancy by the Covid-19 patients were recorded for both determinate and indeterminate parts. The existing nonparametric Kruskal-Wallis H test under Classical Statistics would have given misleading results. The proposed test showed that at a 1% level of significance, there is a statistically significant difference among the average daily ICU occupancy by corona-positive patients of different age groups.
The findings of the results suggested that our proposed modified form of the Kruskal-Wallis is appropriate in place of the classical form of the test in the presence of the neutrosophic environment.
经典统计学检验库中的 Kruskal-Wallis H 检验是一种广为人知的、用于方差分析的非参数替代方法。该检验广泛应用于决策问题中，当观测值以精确形式出现时，需要比较几个平均值是否相等。当数据为区间形式且存在某些不确定性时，该检验就无能为力了。
区间值数据通常包含不确定性和不精确性，并且经常出现在包含模糊性和歧义性的情况下。在这项研究中，针对不确定数据提出了一种修正形式的 Kruskal-Wallis H 检验。研究中提出了一种全面的理论方法，并对该检验进行了应用和实施。
将所提出的检验应用于新冠疫情数据集以进行应用研究。研究结果表明，所提出的修正 Kruskal-Wallis H 检验更适用于区间值数据情况。在新冠疫情数据集上应用这种新的中立型 Kruskal-Wallis 检验表明，该检验提供了更相关和充分的结果。记录了新冠病毒患者每日 ICU 占用情况的确定性和不确定性部分的数据。在经典统计学下的现有非参数 Kruskal-Wallis H 检验会给出误导性的结果。该检验表明，在 1%的显著性水平上，不同年龄组的新冠病毒阳性患者的平均每日 ICU 占用率存在统计学上的显著差异。
结果表明，在存在中立型环境的情况下，我们提出的 Kruskal-Wallis 修正形式适合替代经典形式的检验。
