Social Indicators Research

, Volume 137, Issue 3, pp 831–846 | Cite as

Subjective Indicators Construction by Distance Indices: An Application to Life Satisfaction Data

  • Sara Casacci
  • Adriano ParetoEmail author


The construction of subjective indicators for measuring phenomena expressed in an ordinal scale is a central issue in social sciences, particularly in sociology and psychology. In this paper, we propose the use of a subjective indicator by groups of units (for example, by geographical area) based on the ‘distance’ between the empirical cumulative distribution and a hypothetical cumulative distribution of reference. This approach allows to avoid the awkward question of the ‘quantification’ of an ordinal variable, i.e., the conversion of an ordinal variable into an interval variable. As an example of application, we consider life satisfaction data coming from the annual multipurpose survey on “Aspects of Daily Life”, carried out by the Italian National Institute of Statistics, and we present a comparison with some classical methods.


Ordinal data Quantification Subjective indicators 



The paper is the result of combined work of the authors: Sara Casacci has written Sects. 3 and 4; Adriano Pareto has written Sects. 1 and 2.


  1. Allen, M. P. (1976). Conventional and optimal interval scores for ordinal variables. Sociological Methods Research, 4, 475–494.CrossRefGoogle Scholar
  2. Andrews, F. M. (1974). Social indicators of perceived life quality. Social Indicators Research, 1, 279–299.CrossRefGoogle Scholar
  3. Bok, D. (2010). The politics of happiness: What government can learn from the new research on well-being. Princeton: Princeton University Press.CrossRefGoogle Scholar
  4. Bollen, K. A. (2002). Latent variables in psychology and the social sciences. Annual Review of Psychology, 53, 605–634.CrossRefGoogle Scholar
  5. Capursi, V., & Porcu, M. (2001). La didattica universitaria valutata dagli studenti: un indicatore basato su misure di distanza fra distribuzioni di giudizi. Atti del Convegno intermedio SIS su “Processi e Metodi Statistici di Valutazione”, 4–6 Giugno 2001. Roma: Università di Tor Vergata.Google Scholar
  6. Casacci, S., & Pareto, A. (2015). Methods for quantifying ordinal variables: A Comparative Study. Quality & Quantity, 49, 1859–1872.CrossRefGoogle Scholar
  7. Christoph, B., & Noll, H. H. (2003). Subjective well-being in the European Union during the 90′s. Social Indicators Research, 64, 521–546.CrossRefGoogle Scholar
  8. Diener, E., Inglehart, R., & Tay, L. (2013). Theory and validity of life satisfaction scales. Social Indicators Research, 112, 497–527.CrossRefGoogle Scholar
  9. Duncan, G. (2005). What do we mean by ‘happiness’? The relevance of subjective wellbeing to social policy. Social Policy Journal of New Zealand, 25, 16–31.Google Scholar
  10. Edwards, J. R., & Bagozzi, R. P. (2000). On the nature and direction of relationships between constructs and measures. Psychological Methods, 5, 155–174.CrossRefGoogle Scholar
  11. Fattore, M., Maggino, F., & Colombo, E. (2012). From composite indicators to partial orders: Evaluating socio-economic phenomena through ordinal data. In F. Maggino & G. Nuvolati (Eds.), Quality of life in Italy: Research and reflections (pp. 41–68). Dordrecht: Springer.CrossRefGoogle Scholar
  12. Fattore, M., Maggino, F., & Arcagni, A. (2015). Exploiting ordinal data for subjective well-being evaluation. Statistics in Transition new series, 16, 409–428.CrossRefGoogle Scholar
  13. Galtung, J. (1967). Theory and methods of social research. London: Allen & Unwin.Google Scholar
  14. Hensler, C., & Stipak, B. (1979). Estimating interval scale values for survey item response categories. American Journal of Political Science, 23, 627–648.CrossRefGoogle Scholar
  15. Herzel, A. (1974). Un criterio di quantificazione. Aspetti statistici. Metron, 32, 3–54.Google Scholar
  16. Istat. (2006). Il sistema di indagini sociali multiscopo. Contenuti e metodologia delle indagini. Metodi e norme.Google Scholar
  17. Jahedi, S., & Méndez, F. (2014). On the advantages and disadvantages of subjective measures. Journal of Economic Behavior & Organization, 98, 97–114.CrossRefGoogle Scholar
  18. Labovitz, S. (1970). The assignment of numbers to rank order categories. American Sociological Review, 35, 515–524.CrossRefGoogle Scholar
  19. Lantz, B. (2013). Equidistance of Likert-type scales and validation of inferential methods using experiments and simulations. The Electronic Journal of Business Research Methods, 11, 16–28.Google Scholar
  20. Leti, G. (1983). Statistica descrittiva. Bologna: Il Mulino.Google Scholar
  21. Likert, R. (1932). A technique for the measurement of attitudes. Archives of Psychology, 140, 1–55.Google Scholar
  22. Maggino, F. (2009). Methodological aspects and technical approaches in measuring subjective well-being. Firenze: Firenze University Press.Google Scholar
  23. Marradi, A., & Macrì, E. (2012). Sono equidistanti le categorie di una scala Likert? Alcune risultanze di ricerca. Cambio. Rivista sulle Trasformazioni Sociali, 3, 171–188.Google Scholar
  24. Michalos, A. C. (2014). Encyclopedia of quality of life and well-being research. Dordrecht: Springer.CrossRefGoogle Scholar
  25. Montecolle, S., & Orsini, S. (2012). Satisfied or dissatisfied? an analysis of the results of ‘aspects of daily life’ Italian survey on households. In F. Maggino & G. Nuvolati (Eds.), Quality of life in Italy: Research and reflections (pp. 115–133). Dordrecht: Springer.CrossRefGoogle Scholar
  26. Noll, H. H. (2013). Subjective social indicators: Benefits and limitations for policy making—an introduction to this special issue. Social Indicators Research, 114, 1–11.CrossRefGoogle Scholar
  27. O’Brien, R. M. (1981). Using rank category variables to represent continuous variables: Defects of common practice. Social Forces, 59, 1149–1162.CrossRefGoogle Scholar
  28. OECD. (2013). OECD guidelines on measuring subjective well-being. Paris: OECD Publishing. doi: 10.1787/9789264191655-en.Google Scholar
  29. Powers, D. A., & Xie, Y. (2000). Statistical methods for categorical data analysis. San Diego: Academic Press.Google Scholar
  30. Preston, C. C., & Colman, A. M. (2000). Optimal number of response categories in rating scales: reliability, validity, discriminating power, and respondent preferences. Acta Psychologica, 104, 1–15.CrossRefGoogle Scholar
  31. Rammstedt, B. (2009). Subjective indicators. German council for social and economic data (RatSWD), Working Paper Series, 119.Google Scholar
  32. Stevens, S. S. (1946). On the theory of scales of measurement. Science, 103, 677–680.CrossRefGoogle Scholar
  33. Stiglitz, J. E., Sen, A., Fitoussi, J. P. (2009). Report by the commission on the measurement of economic performance and social progress.
  34. Veenhoven, R. (1991). Is happiness relative? Social Indicators Research, 24, 1–34.CrossRefGoogle Scholar
  35. Veenhoven, R. (2002). Why social policy needs subjective indicators. Social Indicators Research, 58, 33–45.CrossRefGoogle Scholar
  36. Young, F. W. (1981). Quantitative analysis of qualitative data. Psychometrika, 46, 357–388.CrossRefGoogle Scholar
  37. Zanarotti, M. C. (2012). Scelta della distribuzione di riferimento nell’uso degli indici di dissomiglianza per la valutazione con dati ordinali. Dipartimento di Scienze Statistiche: Università Cattolica del Sacro Cuore di Milano, Serie EP.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Italian National Institute of StatisticsRomeItaly

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