The use of a modified Chebyshev’s inequality for the statistical analysis of very small samples and for the application of non-robust test statistics

• Applicant: Professor Dr. Markus Neuhäuser
• Subject Area: Epidemiology and Medical Biometry/Statistics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 569634273

Beasley et al. (2004) introduced a two-sample test based on a modified Chebyshev´s inequality. This test procedure, useful in particular for small sample sizes and low significance levels, can be generalized beyond the two-sample problem. This has apparently not been done so far, even though the procedure is already 20 years old. Therefore, the procedure proposed by Beasley et al. (2004) will be generalized, namely the test based on a modified Chebyshev´s inequality (cf. Saw et al., 1984), both separately and as a maximum with the p-value of the respective classical procedure. Generalization here means considering other designs, endpoints with different levels of measurement, other test statistics, and other test problems. Both parametric and nonparametric test statistics, and especially non-robust tests, will be investigated. The test based on the modified Chebyshev´s inequality will be investigated in simulations and compared with alternative approaches such as permutation tests. To facilitate the application of the various methods, a freely available R package will be developed and made available. In addition, a Shiny app will be developed to make the application particularly user-friendly.

• DFG Programme: Research Grants