AStA Advances in Statistical Analysis

, Volume 103, Issue 4, pp 527–561 | Cite as

MDCgo takes up the association/correlation challenge for grouped ordinal data

  • Emanuela RaffinettiEmail author
  • Fabio Aimar
Original Paper


The subjective assessment of quality of life, personal skills and the agreement with a certain opinion are common issues in clinical, social, behavioral and marketing research. A wide set of surveys providing ordinal data arises. Beside such variables, other common surveys generate responses on a continuous scale, where the variable actual point value cannot be observed since data belong to certain groups. This paper introduces a re-formalization of the recent “Monotonic Dependence Coefficient” (MDC) suitable to all frameworks in which, given two variables, the independent variable is expressed in ordinal categories and the dependent variable is grouped. We denote this novel coefficient with \(\mathrm{MDC}\mathrm{go}\). The \(\mathrm{MDC}\mathrm{go}\) behavior and the scenarios in which it presents better performance with respect to the alternative correlation/association measures, such as Spearman’s \(r_\mathrm{S}\), Kendall’s \(\tau _b\) and Somers’ \(\varDelta \) coefficients, are explored through a Monte Carlo simulation study. Finally, to shed light on the usefulness of the proposal in real surveys, an application to drug-expenditure data is considered.


Grouped ordinal data Dependence Correlation coefficients Association coefficients Monte Carlo simulations 

Mathematics Subject Classification

62-07 62H20 62P25 



The authors gratefully acknowledge the ASL CN1 of Cuneo (Italy) for making available the dataset representing the case study illustrated and discussed in the paper. A special thanks goes to the Associate Editor and the two anonymous reviewers for their helpful comments and suggestions that allowed to improve the paper.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Economics, Management and Quantitative MethodsUniversità degli Studi di MilanoMilanItaly
  2. 2.School of Management and EconomicsUniversity of TurinTurinItaly
  3. 3.ASL CN1CuneoItaly

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