Goodness and lack of fit tests to pretest normality when comparing means

• Autorzy: Flores, Pablo , Lourdes Palacios, de, Maria
• Języki publikacji: EN

Abstrakty

EN

Previous studies show that processes related to traditional pretests to prove the perfect fulfillment of assumptions in comparison means tests lead to severe alterations in the overall Type I error probability and power. These problems seem to be overcome when pretests based on an equivalence approach are used. The paper proposes a lack of fit tests based on equivalence to pretest normality on homoscedastic samples with measurable departures from normality. The Type I error probability and power produced by this equivalence pretest are compared with two traditional goodness of fit pretests and with the direct use of the t-Student and Wilcoxon test of means comparison. Furthermore, since the irrelevance limit for the lack of fit test is an arbitrary value, we propose a non-subjective methodology to find it. Results show that this proposed equivalence test controls the overall Type I Error Probability and produces adequate power; therefore, its use is recommended.

Słowa kluczowe

EN

normality; lack of fit; goodness of fit; equivalence; assumptions; Type I error probability

• Czasopismo: Operations Research and Decisions
• Rocznik: 2024
• Tom: Vol. 34, No. 1
• Strony: 119--129
• Opis fizyczny: Bibliogr. 27 poz., rys.

Twórcy

autor

Flores, Pablo

• Grupo de Investigación en Ciencia de Datos CIDED, Facultad de Ciencias, Escuela Superior Politécnica de Chimborazo (ESPOCH), Riobamba, Ecuador,

autor

Lourdes Palacios, de, Maria

• Carrera de Matemáticas, Facultad de Ciencias, Escuela Superior Politécnica de Chimborazo (ESPOCH), Riobamba, Ecuador

Bibliografia

• [1] Altman, D. G., and Bland, J. M. Statistics notes: Absence of evidence is not evidence of absence. BMJ 311, 7003 (1995), 485.
• [2] Bishop, Y. M. M., Fienberg, S. E., Holland, P. W. Discrete Multivariate Analysis: Theory and Practice. The MIT Press, 1977.
• [3] Blanca, M. J., Arnau, J., López-Montiel, D., Bono, R., and Bendayan, R. Skewness and kurtosis in real data samples. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences 9, 2 (2013), 78–84.
• [4] Box, G. E. P. Science and statistics. Journal of the American Statistical Association 71, 356 (1976), 791–799.
• [5] Cochran, W. G. The χ2correction for continuity. Iowa State College Journal of Science 16, 1 (1942), 421–436.
• [6] Doob, J. L. The limiting distributions of certain statistics. 2007em The Annals of Mathematical Statistics 6, 3 (1935), 160–169.
• [7] Fleishman, A. I. A method for simulating non-normal distributions. Psychometrika 43, 4 (1978), 521–532.
• [8] Flores Muñoz, P., Muñoz Escobar, L., and Sánchez Acalo, T. Study of the power of test for normality using unknown distributions with different levels of non normality. Revista Perfiles 21, 1 (2019), 4–11.
• [9] Flores, P., and Ocaña, J. Heteroscedasticity irrelevance when testing means difference. SORT-Statistics and Operations Research Transactions 42, 1 (2018), 59–72.
• [10] Flores, P., and Ocaña, J. Pretesting strategies for homoscedasticity when comparing means their robustness facing nonnormality. Communications in Statistics - Simulation and Computation 51, 1 (2022), 280–292.
• [11] Flores, P., Salicrú, M., Sánchez-Pla, A., and Ocaña, J. An equivalence test between features lists, based on the Sorensen–Dice index and the joint frequencies of GO term enrichment. BMC Bioinformatics 23, 207 (2022), 1–21.
• [12] Hsu, P. Contribution to the theory of “student’s” t-test as applied to the problem of two samples. Statistical Research Memoirs 2 (1938), 1–24.
• [13] Inan, G., Demirtas, H., and Gao, R. BinNonNor: Data Generation with Binary and Continuous Non-Normal Components, 2021. R package version 1.5.3.
• [14] Mann, H. B., and Whitney, D. R. On a test of whether one of two random variables is stochastically larger than the other. The Annals of Mathematical Statistics 18, 1 (1947), 50–60.
• [15] Montilla, J.-M., and Kromrey, J. Robustness of the t tests in comparison of means, under violation of normality and homoscedasticity assumptions. Ciencia e Ingeniería 31, 2 (2010), 101–107, (in Spanish).
• [16] Pearson, K. X. on the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 50, 302 (1900), 157–175.
• [17] Rasch, D., and Guiard, V. The robustness of parametric statistical methods. Psychology Science 46, 2 (2004), 175–208.
• [18] Rasch, D., Kubinger, K. D., and Moder, K. The two-sample t test: pre-testing its assumptions does not pay off. Statistical Papers 52, 1 (2011), 219–231.
• [19] Sánchez-Pla, A., Salicrú, M., and Ocaña, J. An equivalence approach to the integrative analysis of feature lists. BMC Bioinformatics 20, (2019), 441.
• [20] Scheffé, H. Practical solutions of the Behrens-Fisher problem. Journal of the American Statistical Association 65, 332 (1970), 1501–1508.
• [21] Shapiro, S. S., and Wilk, M. B. An analysis of variance test for normality (complete samples). Biometrika 52, 3/4 (1965), 591–611.
• [22] Student. The probable error of a mean. Biometrika 6, 1 (1908), 1–25.
• [23] Sullivan, L. M., and D’Agostino, R. B. Robustness of the t test applied to data distorted from normality by floor effects. Journal of Dental Research 71, 12 (1992), 1938–1943.
• [24] Welch, B. L. On the comparison of several mean values: an alternative approach. Biometrika 38, 3/4 (1951), 330–336.
• [25] Wellek, S. Testing Statistical Hypotheses of Equivalence and Noninferiority. CRC Press, 2010.
• [26] Wilcoxon, F. Individual comparisons by ranking methods. Biometrics Bulletin 1, 6 (1945), 80–83.
• [27] Zimmerman, D. W. A note on preliminary tests of equality of variances. British Journal of Mathematical and Statistical Psychology 57, 1 (2004), 173–181.

Identyfikatory

DOI

10.37190/ord240106