The choice of normalization method and rankings of the set of  objects based on composite indicator values

Marek  Walesiak

doi:https://doi.org/10.21307/stattrans-2018-036

The choice of normalization method and rankings of the set of objects based on composite indicator values

Marek Walesiak Wroclaw University of Economics, Department of Econometrics and Computer Science, Jelenia Góra, Poland. Statistics in Transition new series, vol. 19, 2018, 4, pages: 693-710 Published online: 3 December 2018 https://doi.org/10.21307/stattrans-2018-036

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ARTICLE

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ABSTRACT

The choice of the normalization method is one of the steps for constructing a composite indicator for metric data (see, e.g. Nardo et al., 2008, pp. 19-21). Normalization methods lead to different rankings of the set of objects based on composite indicator values. In the article 18 normalization methods and 5 aggregation measures (composite indicators) were taken into account. In the first step the groups of normalization methods, leading to identical rankings of the set of objects, were identified. The considerations included in Table 3 reduce this number to 10 normalization methods. Next, the article discusses the procedure which allows separating groups of normalization methods leading to similar rankings of the set of objects separately for each composite indicator formula. The proposal, based on Kendall’s tau correlation coefficient (Kendall, 1955) and cluster analysis, can reduce the problem of choosing the normalization method. Based on the suggested research procedure the simulation results for five composite indicators and ten normalization methods were presented. Moreover, the proposed approach was illustrated by an empirical example. Based on the analysis of the dendrograms three groups of normalization methods were separated. The biggest differences in the results of linear ordering refer to methods n2, n9a against the other normalization methods.

KEYWORDS

variables normalization, rankings, composite indicators, Kendall’s tau correlation coefficient, cluster analysis.

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