Analyzing data from a fuzzy rating scale-based questionnaire: a case study

• María Angeles Gil Alvarez ^[1] ; María Asunción Lubiano Gómez ^[1] ; Sara de la Rosa de Sáa ^[1] ; Beatriz Sinova Fernández ^[1]
  1. [1] Universidad de Oviedo

     Universidad de Oviedo

     Oviedo, España

     
• Localización: Psicothema, ISSN-e 1886-144X, ISSN 0214-9915, Vol. 27, Nº. 2, 2015, págs. 182-191
• Idioma: inglés
• Títulos paralelos:
  • Análisis de datos de un cuestionario basado en la escala de valoración fuzzy: estudio de caso
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    Antecedentes: la escala de valoración difusa se introdujo para abordar la imprecisión inherente al pensamiento humano y la experiencia al medir actitudes en muchos campos de la Psicología. La flexibilidad y expresividad de esta escala permiten describir apropiadamente las respuestas a la mayoría de las cuestiones que involucran mediciones psicológicas. Método: analizar las respuestas a cuestionarios basados en dicha escala supone un problema crítico. No obstante, en los últimos años se está desarrollando una metodología específica para el análisis estadístico de datos difusos que explota toda la información disponible. En este trabajo se recoge un resumen de los procedimientos más relevantes. Resultados: los métodos se ilustrarán mediante su aplicación a los datos de un estudio realizado con niños de nueve años. En él, los niños han respondido a algunas cuestiones del conocido cuestionario TIMSS/PIRLS recurriendo a un formulario basado en la escala de valoración difusa y en formato impreso o digital. Conclusiones: en primer lugar, el estudio muestra que los requisitos previos de formación y entrenamiento para cumplimentar tal formulario son poco exigentes. En segundo lugar, se verifica que a menudo las conclusiones estadísticas difieren sustancialmente dependiendo de que las respuestas se den según escala Likert o de valoración difusa.

  • English

    Background: The fuzzy rating scale was introduced to cope with the imprecision of human thought and experience in measuring attitudes in many fields of Psychology. The flexibility and expressiveness of this scale allow us to properly describe the answers to many questions involving psychological measurement. Method: Analyzing the responses to a fuzzy rating scale-based questionnaire is indeed a critical problem. Nevertheless, over the last years, a methodology is being developed to analyze statistically fuzzy data in such a way that the information they contain is fully exploited. In this paper, a summary review of the main procedures is given. Results: The methods are illustrated by their application on the dataset obtained from a case study with nine-year-old children. In this study, children replied to some questions from the well-known TIMSS/PIRLS questionnaire by using a fuzzy rating scale. The form could be filled in either on the computer or by hand. Conclusions: The study indicates that the requirements of background and training underlying the fuzzy rating scale are not too demanding. Moreover, it is clearly shown that statistical conclusions substantially often differ depending on the responses being given in accordance with either a Likert scale or a fuzzy rating scale.

• Referencias bibliográficas
  • Agarwal, S., & Agarwal, P. (2005). A Fuzzy Logic approach to search results’ personalization by tracking user’s web navigation pattern...
  • Ávila-Muñoz, A.M., & Sánchez-Sáez, J.M. (2014). Fuzzy sets and prototype theory representational model of cognitive community structures...
  • Bělohlávek, R., & Klir, G.J. (Eds.) (2011). Concepts and Fuzzy Logic. Cambridge, USA: The MIT Press.
  • Bělohlávek, R., Klir, G.J., Lewis III, H.W., & Way, E. (2002). On the capability of Fuzzy Set Theory to represent concepts. International...
  • Bělohlávek, R., Klir, G.J., Lewis III, H.W., & Way, E. (2009). Concepts and fuzzy sets: Misunderstandings, misconceptions, and oversights....
  • Bertoluzza, C., Corral, N., & Salas, A. (1995). On a new class of distances between fuzzy numbers. Mathware & Soft Computing, 2, 71-84.
  • Blanco-Fernández, A., Casals, M.R., Colubi, A., Corral, N., García- Bárzana, M., Gil, M.A., González-Rodríguez, G., López, M.T., Lubiano,...
  • Castillo, I., Tomás, I., Ntoumanis, N., Bartholomew, K., Duda, J.L., & Balaguer, I. (2014). Psychometric properties of the Spanish version...
  • Coppi, R., Giordani, P., & D’Urso, P. (2006). Component models for fuzzy data. Psychometrika, 71, 733-761.
  • Corral-Blanco, N., Zurbano-Fernández, E., Blanco-Fernández, A., García- Honrado, I., & Ramos-Guajardo, A.B. (2013). Structure of the family...
  • De la Rosade Sáa, S., Gil, M.A., González-Rodríguez, G., López, M.T., & Lubiano, M.A. (2015). Fuzzy rating scale-based questionnaires...
  • Diamond, P., & Kloeden, P. (1990). Metric spaces of fuzzy sets. Fuzzy Sets and Systems, 35, 241-249.
  • Dubois, D., & Prade, H. (1979). Fuzzy real algebra: Some results. Fuzzy Sets and Systems, 2, 327-348.
  • Garriga Trillo, A.J., & Dorn, T. (1991). Medición de la borrosidad: modalidades cruzadas. Psicothema, 3, 423-432.
  • Giné, E., & Zinn, J. (1990). Bootstrapping general empirical measures. Annals of Probability, 18, 851-869.
  • González-Rodríguez, G., Colubi, A., & Gil, M.A. (2012). Fuzzy data treated as functional data. A one-way ANOVA test approach. Computational...
  • González-Rodríguez, G., Montenegro, M., Colubi, A., & Gil, M.A. (2006). Bootstrap techniques and fuzzy random variables: Synergy in hypothesis...
  • Ghneim, J. (Ed.) (2013). Fuzzy concept. In Encyclopedia of Psychometrics, pp. 61-68 - Wikipedia. October 27, 2014, URL: http://en.wikipedia.org/...
  • Hesketh, B., Griffi n, B., & Loh, V. (2011). A future-oriented retirement transition adjustment framework. Journal of Vocational Behavior,...
  • Hesketh, B., Hesketh, T., Hansen, J.-I., & Goranson, D. (1995). Use of fuzzy variables in developing new scales from the strong interest...
  • Hesketh, T., & Hesketh, B. (1994). Computerized fuzzy ratings: The concept of a fuzzy class. Behavior Research Methods, Instruments &...
  • Hesketh, T., Pryor, R., & Hesketh, B. (1988). An application of a computerized fuzzy graphic rating scale to the psychological measurement...
  • Horowitz, L.M., & Malle, B.M. (1993). Fuzzy concepts in psychotherapy research. Psychotherapy Research, 3, 131-148.
  • Horvath, J.M. (1988). A fuzzy set model of learning disability: identifi cation from clinical data. In T. Zétényi (Ed.), Fuzzy Sets in Psychology....
  • Leding, J.K. (2013). Need for cognition is related to the rejection (but not the acceptance) of false memories. American Journal of Psychology,...
  • Lozano, L.M., García-Cueto, E., & Muñiz, J. (2008). Effect of the number of response categories on the reliability and validity of rating...
  • Lubiano, M.A., & Gil, M.A. (1999). Estimating the expected value of fuzzy random variables in random samplings from finite populations....
  • Lubiano, M.A., Gil, M.A., López-Díaz, M., & López, M.T. (2000). The lambda-mean squared dispersion associated with a fuzzy random variable....
  • Montenegro, M., Casals, M.R., Lubiano, M.A., & Gil, M.A. (2001). Two-sample hypothesis tests of means of a fuzzy random variable. Information...
  • Montenegro, M., Colubi, A., Casals, M.R., & Gil, M.A. (2004). Asymptotic and Bootstrap techniques for testing the expected value of a...
  • Montenegro, M., López-García, M.T., Lubiano, M.A., & González- Rodríguez, G. (2009). A dependent multi-sample test for fuzzy means. In...
  • Nakama, T., Colubi, A., & Lubiano, M.A. (2010). Factorial analysis of variance for fuzzy data. In Abstracts 3rd Workshop ERCIM WG Computing...
  • Osherson, D.N., & Smith, E.E. (1981). On the adequacy of prototype theory as a theory of concepts. Cognition, 9, 35-58.
  • Osherson, D.N., & Smith, E.E. (1982). Gradedness and conceptual combination. Cognition, 12, 299-318.
  • Peña-Suárez, E., Muñiz, J., Campillo-Álvarez, Á., Fonseca-Pedrero, E., & García-Cueto, E. (2013). Assessing organizational climate: Psychometric...
  • Puri, M.L., & Ralescu, D.A. (1986). Fuzzy random variables. Journal of Mathematical Analysis and Applications, 114, 409-422.
  • Ramos-Guajardo, A.B., & Lubiano, M.A. (2012). K-sample tests for equality of variances of random fuzzy sets. Computational Statistics...
  • Sinova, B., Gil, M.A., Colubi, A., & Van Aelst, S. (2012). The median of a random fuzzy number. The 1-norm distance approach. Fuzzy Sets...
  • Smithson, M., & Oden, G.C. (1999). Fuzzy set theory and applications in Psychology. In H.-J. Zimmermann (Ed.), Practical Applications...
  • Sowa, J.F. (2013). What is the source of fuzziness? In R. Seising, E. Trillas, C. Moraga & S. Termini (Eds.), On Fuzziness. A Homage to...
  • Stoklasa, J., Talášek, T., & Musilová, J. (2014). Fuzzy approach - a new chapter in the methodology of Psychology? Human Affairs, 24,...
  • Szalma, J.L., & Hancock, P.A. (2013). A signal improvement to signal detection analysis: Fuzzy sdt on the ROCs. Journal of Experimental...
  • Takemura, K. (1999). A fuzzy linear regression analysis for fuzzy inputoutput data using the least squares method under linear constraints...
  • Takemura, K. (2007). Ambiguous comparative judgment: fuzzy set model and data analysis. Japanese Psychological Research, 49, 148-156.
  • Tomás, J.M., & Oliver, A. (1988). Efectos de formato de respuesta y método de estimación en análisis factorial confi rmatorio. Psicothema,...
  • Van Dijk, M., & Van Geert, P. (2009). The application of Fuzzy Logic principles to Developmental Psychology. In R.E. Vargas (Ed.), Fuzzy...
  • Walsh, R.T.G., Teo, T., & Baydala, A. (2014). A Critical History and Philosophy of Psychology. Cambridge UK: Cambridge University Press.
  • Wierman, M.J. (2013). Psychologists: Are they logically fuzzy? In Joint IFSA World Conference and NAFIPS Annual Meeting (pp. 854-859).
  • Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8, 338-353.
  • Zadeh, L.A. (1975). The concept of a linguistic variable and its application to approximate reasoning. Part 1. Information Sciences, 8, 199-249;...
  • Zadeh, L.A. (2008). Is there a need for fuzzy logic? Information Sciences, 178, 2751-2779.
  • Zétényi, T. (Ed.) (1988). Fuzzy Sets in Psychology. Series: Advances in Psychology, Vol. 56. Amsterdam: North-Holland, Elsevier.