A Study of Multiple Comparison Tests with Imprecise and Uncertain Information

Objectives: This study aims to demonstrate the application of multiple comparison tests in situations involving imprecise, incomplete, and uncertain observations. Such data arises in many practical situations. Methods: Five post hoc multiple comparison tests viz. Fisher’s LSD test, Tukey’s HSD, Bonferroni (𝐵𝑇 𝑁), Scheffe, and Hochberg (𝐻𝐵𝑁) method is utilized within a one-way design framework, with a significance level of 5%. Simulation studies are applied to the empirical level and power calculation. Findings: The study shows that Tukey’s HSD (𝑇 𝐾𝑁) shows the highest power in the determinant part, not the indeterminant part, compared to other tests. For, e.g., For (5, 5, 5, 5) with location parameter (0, .5, 1, 0), the power interval shows [.3953, .3584] where 𝐼𝑁 ∈ [0, .05]. Overall, 𝐵𝑇 𝑁 and 𝐻𝐵𝑁 shows a prominent result and are preferable compared to other tests. From application, NANOVA provided the P-value is [<.001, <.001], i.e., tests are statistically significant. The P-value of the tests for pairs [1, 1] and [2, 2] accepted (greater than .05) means the average daily ICU occupancy of corona patients of more than 55 years and between 35 and 55 age groups are not equal. Similarly, other tests also show the same. Novelty: Neutrosophic Multiple comparisons are still developing, and computer programs are still unavailable to support them. We have applied a simulation study to check the performance of the tests. Keywords: Multiple comparisons; NANOVA; Neutrosophic Statistics; Indeterminacy; Covid-19