Abstract
Nowadays, new types of data are emerging from lots of distinct real-life experiments and statistical researchers need to develop new tools to deal with them. For instance, interval-valued responses arise as an alternative to Likert-type responses in questionnaires measuring people’s behavior (their attitudes, opinions, perceptions, feelings, etc.). In order to facilitate the comparison of different analysis involving several rating scales and with the aim of studying the effect size measure for difference between two independent groups, in this paper we extend the concept of Cohen’s d index established for real numbers to the interval-valued data context. Finally, a real-life example has been included to motivate and illustrate the problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
American Psychological Association: Publication Manual of the American Psychological Association, 6th edn. APA, Washington, D.C. (2010)
Aumann, R.J.: Integrals of set-valued functions. J. Math. Anal. Appl. 12, 1–12 (1965)
Bertoluzza, C., Corral, N., Salas, A.: On a new class of distances between fuzzy numbers. Mathware Soft Comput. 2, 71–84 (1995)
Castaño, A.M., Lubiano, M.A., García-Izquierdo, A.L.: Gendered beliefs in STEM undergraduates: a comparative analysis of fuzzy rating versus likert scales. Sustainability 12, 6227 (2020)
Cohen, J.: Some statistical issues in psychological research. In: Wolman, B.B. (ed.) Handbook of Clinical Psychology, pp. 95–121. Academic Press, New York (1965)
Cohen, J.: Statistical Power Analysis for the Behavioral Sciences, 1st edn. Academic Press, New York (1969)
Cohen, J.: Statistical Power Analysis for the Behavioral Sciences, 2nd edn. L. Erlbaum Associates, Hillsdale (1988)
Ellerby, Z., Wagner, C., Broomell, S.B.: Capturing richer information: on establishing the validity of an interval-valued survey response mode. Beha. Res. Methods 54, 1240–1262 (2021). https://doi.org/10.3758/s13428-021-01635-0
Gil, M.Á., Lubiano, M.A., Montenegro, M., López, M.T.: Least squares fitting of an affine function and strength of association for interval-valued data. Metrika 56, 97–111 (2002)
Hays, W.L.: Statistics for Psychologists. Holt Rinehart and Winston, New York (1963)
Hedges, L.V.: Distribution theory for Glass’s estimator of effect size and related estimators. J. Educ. Stat. 6(2), 106–128 (1981)
Körner, R.: On the variance of fuzzy random variables. Fuzzy Sets Syst. 92(1), 83–93 (1997)
Likert, R.: A technique for the measurement of attitudes. Arch. Psychol. 22, 140–155 (1932)
Lubiano, M.A., Gil, M.Á., López-Díaz, M., López, M.T.: The \(\overrightarrow{\lambda }\)-mean squared dispersion associated with a fuzzy random variable. Fuzzy Sets Syst. 111, 307–317 (2000)
Lubiano, M.A., Montenegro, M., Sinova, B., de la Rosa de Sáa, S., Gil, M.Á.: Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications. Eur. J. Oper. Res. 251, 918–929 (2016)
Matheron, G.: Random Sets and Integral Geometry. Wiley, New York (1975)
Minkowski, H.: Vorlumen und Oberflache. Math. Ann. 57, 447–495 (1903)
Themistocleous, C., Pagiaslis, A., Smith, A., Wagner, C.: A comparison of scale attributes between interval-valued and semantic differential scales. Int. J. Mark. Res. 61(4), 394–407 (2019)
Vitale, R.A.: \(L_p\) metrics for compact, convex sets. J. Approx. Theory 45(3), 280–287 (1985)
Wagner, C., Miller, S., Garibaldi, J.M., Anderson, D.T., Havens, T.C.: From interval-valued data to general type-2 fuzzy sets. IEEE Trans. Fuzzy Syst. 23, 248–269 (2015)
Weinert, C., Maier, C., Laumer, S.: Why are teleworkers stressed? An empirical analysis of the causes of telework-enabled stress. In: Thomas, O., Teuteberg, F. (eds.) 12th International Conference on Wirtschaftsinformatik, pp. 1407–1421 (2015). aisel.aisnet.org/wi2015/94
Wilkinson, L.: Task force on statistical inference, American Psychological Association, Science Directorate: statistical methods in psychology journals: guidelines and explanations. Am. Psychol. 54, 594–604 (1999)
Acknowledgement
The research in this paper has been partially supported by from Principality of Asturias Grant AYUD/2021/50897, and the Spanish Ministry of Economy and Business Grant PID2019-104486GB-I00. Their financial support is gratefully acknowledged. The authors would like to the reviewers for valuable and helpful comments to improve the quality of this work.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Lubiano, M.A., García-García, J., García-Izquierdo, A.L., Castaño, A.M. (2023). The Extended Version of Cohen’s d Index for Interval-Valued Data. In: García-Escudero, L.A., et al. Building Bridges between Soft and Statistical Methodologies for Data Science . SMPS 2022. Advances in Intelligent Systems and Computing, vol 1433. Springer, Cham. https://doi.org/10.1007/978-3-031-15509-3_35
Download citation
DOI: https://doi.org/10.1007/978-3-031-15509-3_35
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-15508-6
Online ISBN: 978-3-031-15509-3
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)