midrangeMCP: The R Package for multiple comparisons based on the Range and Midrange distributions
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Abstract
This paper introduces four new types of multiple comparison procedures. Their performance was evaluated in large experimental scenarios using Monte Carlo simulations, with a focus on comparing experimentwise error rates and statistical power against those of the traditional Tukey, Student-Newman-Keuls (SNK), and Scott-Knott tests. To facilitate the practical application of these methods, we developed the R package midrangeMCP. The proposed procedures are: the Midrange Tukey test (TM), the Midrange Student-Newman-Keuls test (SNKM), the Mean Grouping based on the Midrange (MGM), and the Mean Grouping based on the Range (MGR). The TM, MGM, and MGR tests outperformed their classical counterparts (Tukey and Scott-Knott), except under scenarios with partially true null hypotheses. The SNKM test was the only one that consistently underperformed compared to its original version (the SNK test) across all evaluated scenarios. Among the proposed methods, the MGM test stood out for its superior performance and its additional advantage of avoiding ambiguity in group assignments.
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References
1. Batista, B. D. O. & Ferreira, D. F. Alternative to Tukey test. Ciênc. agrotec. 44, 1–10. https://doi.org/10.1590/1413-7054202044008020 (2020).
2. Batista, B. D. O. & Ferreira, D. F. The Externally StudentizedNormal Midrange Distribution. Ciência e Agrotecnologia 41, 378–389. https://doi.org/10.1590/1413-70542017414047716 (2017).
3. Batista, B. D. O. & Ferreira, D. F. SMR. An R Package for Computing the Externally Studentized Normal Midrange Distribution. The R Journal 6, 123–136. https://doi.org/10.32614/RJ-2014-029 (Dec. 2014).
4. Batista, B. D. O. & Ferreira, D. F. SMR. Externally Studentized Midrange Distribution R package version 2.1.0 (Vienna, Austria, 2023). https://cloud.r-project.org/web/packages/SMR/index.html.
5. Batista, B. D. O., Ferreira, D. F., Santos, M. F. R. & Alves, H. J. d. P. Means Grouping based on Studentized Midrange. Brazilian Journal of Biometrics 41, 361–397. https://doi.org/10.28951/ bjb.v41i4.640 (2023).
6. Bogaert, I. Iteration-Free Computation of Gauss–Legendre Quadrature Nodes and Weights. SIAM Journal on Scientific Computing 36, A1008–A1026. https://doi.org/10.1137/140954969 (2014).
7. Borges, L. C. & Ferreira, D. F. Poder e taxas de erro tipo I dos tetes Scott-Knott, Tukey e Student-Newman-Keuls sob Distribuições normal e não normais dos resíduos. Revista Matemática e Estatística 21. (Portuguese), 67–83. https://dialnet.unirioja.es/servlet/articulo?codigo=665113 (2003).
8. Carmer, S. G. & Swanson, M. R. An Evaluation of Ten Pairwise Multiple Comparison Procedures by Monte Carlo Methods. Journal of the American Statistical Association 68, 66–74. https:
//doi.org/10.2307/2284140 (1973).
9. Conrado, T. V., Ferreira, D. F., Scapim, C. A. & Maluf, W. R. Adjusting the Scott-Knott cluster analyses for unbalanced designs. Crop Breeding and Applied Biotechnology 17, 1–9. https:
//doi.org/10.1590/1984-70332017v17n1a1 (2017).
10. Dahl, D. B., Scott, D., Roosen, C., Magnusson, A. & Swinton, J. xtable. Export tables to LaTeX or HTML R package version 1.8-4 (Vienna, Austria, 2019). http://CRAN.R- project .org/package=xtable.
11. David, H. A., Hartley, H. O. & Pearson, E. S. The Distribution of the Ratio, in a SingleNormal Sample, of Range to Standard Deviation. English. Biometrika 41, 482–493. https://doi.org/10.2307/2332728 (1954).
12. Duncan, D. B. Multiple range and multiple F tests. Biometrics 11, 1–42. https://doi.org/10.2307/3001478 (1955).
13. Graybill, F. An introduction to linear statistical models 1, 463 (McGraw-Hill, New York, 1961).
14. Hartley, H. O. The Range in Random Samples. English. Biometrika 32, 334–348. https://doi.org/10.2307/2332137 (1942).
15. Keuls, M. The use of the “studentized range” in connection with an analysis of variance. Euphytica 1, 112–122. https://link.springer.com/article/10.1007/BF01908269 (1952).
16. Newman, D. The Distribution of Range in Samples from a Normal Population, Expressed in Terms of an Independent Estimate of Standard Deviation. Biometrika 31, 20–30. https://doi.org/10.2307/2334973 (1939).
17. Pearson, E. S. & Haines, J. The Use of Range in Place of Standard Deviation in Small Samples. Supplement to the Journal of the Royal Statistical Society 2, 83–98. https://doi.org/10.2307/2983588 (1935).
18. Pearson, E. S. & Hartley, H. O. Tables of the Probability Integral of the Studentized Range. English. Biometrika 33, 89–99. https://doi.org/10.2307/2333622 (1943).
19. Pearson, E. S. & Hartley, H. O. The Probability Integral of the Range in Samples of n Observations
From a Normal Population. Biometrika 32, 301–310. https://doi.org/10.2307/2332134 (1942).
20. Pearson, E. S. A Further Note on the Distribution of Range in Samples Taken from a Normal Population. Biometrika 18, 173–194. https://doi.org/10.2307/2332501 (1926).
21. Pearson, E. S. The Percentage Limits for the Distribution of Range in Samples from a Normal Population. Biometrika 24, 404–417. https://doi.org/10.2307/2331974 (1932).
22. Perecin, D. & Malheiros, E. B. Uma avaliação de seis procedimentos para comparações múltiplas in
3o Simpósio de Estatística aplicada à Experimentação Agonômica (Portuguese) (Lavras, MG, 1989), 66.
23. Schwartz, M. WriteXLS. Cross-Platform Perl Based R Function to Create Excel 2003 (XLS) and Excel 2007 (XLSX) Files R package version 6.6.0 (Vienna, Austria, 2024). http://CRAN.Rproject. org/package=WriteXLS.
24. Searle, S. R. Linear models for unbalanced data 536 (Wiley, New York, 1987).
25. Silva, E. C. d., Ferreira, D. F. & Bearzoti, E. Avaliação do poder e taxas de erro tipo I do teste de Scott-Knott por meio do método de Monte Carlo. Ciência e Agrotecnologia 23. (Portuguese), 687–696 (1999).
26. Steel, R. & Torrie, J. Principles and Procedures of Statistics. A Biometrical Approach 2nd ed., 666
(McGraw-Hill, New York, 1980).
27. Student. Errors in routine analysis. Biometrika 19, 151–164. https://doi.org/10.2307/2332181 (1927).
28. Tukey, J. W. The problem of multiple comparisons. Mimeographed monograph. Unpublished memorandum in private circulation (1953).