Nonparametric procedure for comparing the performance of divisions of a network organization
Abstract
To solve the problem of comparative efficiency analysis of branch operations for a small volume of randomly observed data, a non-parametric approach is relevant, since it does not require a probabilistic model of observations. Comparing the results of the non-parametric approach with the results obtained within the traditionally used Gaussian model is also relevant. Additionally, obtaining a consistent comparison of a group (of no less than three) branches is important. Currently, the non-parametric approach and the corresponding comparison with the known results of solving the problem considered in this work obtained within the framework of the normal model are absent. In addition, insufficient attention is paid to the search for methods of obtaining consistent solutions. This work to some extent fills these gaps. This work uses non-parametric statistical methods and theory of simultaneous hypothesis testing to address these problems. This paper proposes a procedure for comparative analysis of the efficiency of several units within a network organization with a small volume of observations based on the Mann–Whitney tests. We carry out a comparison of the results obtained from the proposed non-parametric procedure with results based on extensions of Student’s t-tests. We propose a method for reducing the number of compatibility problems based on the search for an appropriate significance level. We provide an example of a fully consistent comparison of the efficiency of branch operations.
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References
Aleskerov F.T., Belousova V. (2007) Effective development of the branch network of a commercial bank. Upravleniye v kreditnoy organizatsii (Management in a credit institution), no. 6, pp. 23–34 (in Russian).
Kryukov A.M. (2010) Efficiency analysis of branch and division activities is a prerequisite for business stability. Strategic decisions and risk management, vol. 4, pp. 84–87 (in Russian). https://doi.org/10.17747/2078-8886-2010-4-84-87
Myznikova M.A. (2022) Quality of strategic management under ambiguity: Assessment within the framework of sustainable development. Business Informatics, vol. 16, no. 3, pp. 36–52. https://doi.org/10.17323/2587-814X.2022.3.36.52
Koldanov А.P., Koldanov Р.A. (2012) Multiple decision procedures for the analysis of higher school entry selection results. Business Informatics (Biznes-informatika), vol. 19, no. 1, pp. 24–31 (in Russian).
Koldanov P.A. (2013) Efficiency analysis of branch network. Models, Algorithms, and Technologies for Network Analysis (eds. B.I. Goldengorin, V.A. Kalyagin, P.M. Pardalos). Springer Proceedings in Mathematics & Statistics, vol. 59, pp. 71–83. https://doi.org/10.1007/978-1-4614-8588-9_5
Hettmansperger T. (1987) Statistical Inference Based on Ranks. Moscow: Finance and Statistics (in Russian).
Kendall М. (1975) Rank correlations. Moscow: Statistics (in Russian).
Hollander М., Wolfe D. (1983) Nonparametric statistical methods. Moscow: Finance and Statistics (in Russian).
Lehmann E.L. (1975) Nonparametrics: Statistical methods based on ranks. San Francisco: Hoden-Day. https://doi.org/10.1002/zamm.19770570922
Kendall М., Stuart A. (1973) Statistical Inferences and relationships. Moscow: Science (in Russian).
Jordan M.I. (2004) Graphical models. Statistical Science, vol. 19, no. 1, pp. 140–155. https://doi.org/10.1214/088342304000000026
Newman M.E.J. (2010) Networks. An introduction. New York: Oxford University Press.
Opsahl T., Panzarasa P. (2009) Clustering in weighted networks. Social Networks, vol. 31, no. 2, pp. 155–163.
Horvath S. (2011) Weighted network analysis. Applications in genomics and systems biology. New York: Springer. https://doi.org/10.1007/978-1-4419-8819-5
Li S., He J., Zhuang Y. (2010) A network model of the interbank market. Physica A: Statistical Mechanics and its Applications, vol. 389, no. 24, pp. 5587–5593. https://doi.org/10.1016/j.physa.2010.08.057
Boginski V., Butenko S., Pardalos P.M. (2005) Statistical analysis of financial networks. Computational Statistics & Data Analysis, vol.48, no. 2, pp. 431–443. https://doi.org/10.1016/j.csda.2004.02.004
Lehmann E.L. (1957) A theory of some multiple decision problems, I. The Annals of Mathematical Statistics, vol. 28, no. 1, pp. 1–25. https://doi.org/10.1214/aoms/1177707034
Bretz F., Hothorn T., Westfall P. (2010) Multiple comparisons using R. New York: Chapman and Hall/CRC. https://doi.org/10.1201/9781420010909
Hochberg Y., Tamhane A.C. (1987) Multiple comparison procedures. New York: John Wiley & Sons. https://doi.org/10.1002/9780470316672
Handbook of Multiple Comparisons (2021) (eds. X. Cui, T. Dickhaus, Y. Ding, J.C. Hsu). New York: Chapman and Hall/CRC. https://doi.org/10.1201/9780429030888
Dickhaus T. (2014) Simultaneous statistical inference. With applications in the life sciences. Heidelberg: Springer Berlin. https://doi.org/10.1007/978-3-642-45182-9
Gabriel K.R. (1969) Simultaneous test procedures – some theory of multiple comparisons. The Annals of Mathematical Statistics, vol. 40, no. 1, pp. 224–250. https://doi.org/10.1214/aoms/1177697819
Cliff N. (1975) Complete orders from incomplete data: Interactive ordering and tailored testing. Psychological Bulletin, vol. 82, no. 2, pp. 289–302. https://doi.org/10.1037/h0076373
Cliff N. (1993) Dominance statistics: Ordinal analyses to answer ordinal questions. Psychological Bulletin, vol. 114, no. 3, pp. 494–509. https://doi.org/10.1037/0033-2909.114.3.494
Donoghue J.R. (2004) Implementing Shaffer's multiple comparison procedure for a large number of groups. Recent Developments in Multiple Comparison Procedures (Eds. Benjamini, Y., Bretz, F. and Sarkar, S.), Institute of Mathematical Statistics, Beachwood, Ohio, pp. 1–23.
