Abstract
BackgroundKruskal-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.MethodsThe 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.ResultsThe 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.ConclusionsThe 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.
Highlights
Hypothesis testing is a scientific process used to investigate the acceptance or rejection of a proposition under consideration
Smarandache introduced Neutrosophic Statistics as a generalization of classical statistics applied when the data under consideration is in neutrosophic numbers [6]
The objectives of this article are (1) to introduce the modified neutrosophic Kruskal Wallis test; (2) to define the methodology of the neutrosophic Kruskal Wallis test; and (3) to compare the performance of the existing Kruskal Wallis test with the proposed test through an application on Covid-19 data set under Neutrosophy
Summary
Hypothesis testing is a scientific process used to investigate the acceptance or rejection of a proposition under consideration. Two approaches are used in statistics to verify a hypothesis: 1) Parametric approach 2) Nonparametric approach. [5] generalized the fuzzy logic in the neutrosophic sense by considering the interval-valued data and the measure of indeterminacy or falseness. Smarandache introduced Neutrosophic Statistics as a generalization of classical statistics applied when the data under consideration is in neutrosophic numbers [6]. Smarandache and Khalid [6] verified the efficiency of neutrosophic logic. Several authors have implemented neutrosophic logic for data containing uncertainty and vagueness; see ref [7,8,9,10,11]. The test is helpless when the data is in an interval form and has some indeterminacy
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