Neutrosophic Statistical Approach to Multiple Comparison Analysis

Abstract

Objective: This study investigates the implementations of neutrosophic statistics in multiple comparison tests in situations with uncertain data, which commonly arise in real-world settings. Methods: This study proposed four post-hoc tests viz. Tukey-Kramer (𝑇 𝐾𝐾𝑅𝑁), Dunnet (𝐷𝑁𝑇 𝑁), Tamhane’s (𝑇 2𝑁), and Dunn (𝐷𝑁) tests in undetermined situations with simulation work. The empirical levels and power calculations through simulation studies are used in a one-way design framework at a 5% significance level. Findings: The study reveals that Tamhane’s (𝑇 2𝑁) and Dunn (𝐷𝑁) test satisfied the empirical level and performed well, including indeterminacy 𝐼𝑁 ∈ [0, .05] in neutrosophic multiple comparison analysis for the above four tests. Thus, an attempt is made to apply neutrosophic statistics to the suggested multiple comparison tests in a health-related application. Novelty: We have introduced neutrosophic statistics with simulation work for the above post hoc tests for small to medium sample sizes in uncertain situations.

Keywords: Multiple comparisons; Neutrosophic Statistics; Tukey-Kramer; Dunnet; Tamhane’s (T2); Dunn tests