In applied psychological, behavioral and sociological research the majority of data are typically mixed (continuous and discrete) or, if continuous, they violate the normality condition. Given a dependent and an independent variables: (a) both the variables may appear with distinct values (continuous variables); (b) the dependent variable may present distinct values (continuous variable) and the independent variable tied values (discrete variable); (c) the dependent variable may present tied values (discrete variable) and the independent variable distinct values (continuous variable). The dependence relationship between the variables could be assessed through the common correlation coefficients, i.e., the Pearson’s, Spearman’s and Kendall’s coefficients, jointly with a recently revisited monotonic dependence coefficient, called “Monotonic Dependence Coefficient”. But, the choice of the most suitable dependence measure in different scenarios may become problematic. The aim of the paper is to show which dependence measure to use to discover dependence relationships. A flow tree displaying how to find the best dependence measures is proposed by means of a Monte Carlo simulation study. Both Normal and non-Normal distributions producing continuous and discrete data, together with the possibility of transforming discrete data into continuous ones, are considered. Finally, validation of simulation findings on real data is also introduced.

A dependence measure flow tree through Monte Carlo simulations / E. Raffinetti, P.A. Ferrari. - In: QUALITY AND QUANTITY. - ISSN 1573-7845. - (2020 Jul 07). [Epub ahead of print] [10.1007/s11135-020-01010-9]

A dependence measure flow tree through Monte Carlo simulations

E. Raffinetti
Primo
;
P.A. Ferrari
Ultimo
2020

Abstract

In applied psychological, behavioral and sociological research the majority of data are typically mixed (continuous and discrete) or, if continuous, they violate the normality condition. Given a dependent and an independent variables: (a) both the variables may appear with distinct values (continuous variables); (b) the dependent variable may present distinct values (continuous variable) and the independent variable tied values (discrete variable); (c) the dependent variable may present tied values (discrete variable) and the independent variable distinct values (continuous variable). The dependence relationship between the variables could be assessed through the common correlation coefficients, i.e., the Pearson’s, Spearman’s and Kendall’s coefficients, jointly with a recently revisited monotonic dependence coefficient, called “Monotonic Dependence Coefficient”. But, the choice of the most suitable dependence measure in different scenarios may become problematic. The aim of the paper is to show which dependence measure to use to discover dependence relationships. A flow tree displaying how to find the best dependence measures is proposed by means of a Monte Carlo simulation study. Both Normal and non-Normal distributions producing continuous and discrete data, together with the possibility of transforming discrete data into continuous ones, are considered. Finally, validation of simulation findings on real data is also introduced.
Normal and non-normal distributed data; Mixed data; Dependence coefficient; “Continuous-ation” approach;
Settore SECS-S/01 - Statistica
7-lug-2020
Article (author)
File in questo prodotto:
File Dimensione Formato  
PAPER_QUALITY_AND_QUANTITY_RAFFINETTI_FERRARI_ARIEL.pdf

accesso aperto

Tipologia: Pre-print (manoscritto inviato all'editore)
Dimensione 9.32 MB
Formato Adobe PDF
9.32 MB Adobe PDF Visualizza/Apri
Raffinetti-Ferrari2020_Article_ADependenceMeasureFlowTreeThro.pdf

accesso riservato

Descrizione: e-pub ahead of print
Tipologia: Publisher's version/PDF
Dimensione 41.5 MB
Formato Adobe PDF
41.5 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/748930
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? ND
social impact