IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v97y2006i7p1660-1674.html
   My bibliography  Save this article

Robust estimation of Cronbach's alpha

Author

Listed:
  • Christmann, A.
  • Van Aelst, S.

Abstract

Cronbach's alpha is a popular method to measure reliability, e.g. in quantifying the reliability of a score to summarize the information of several items in questionnaires. The alpha coefficient is known to be non-robust. We study the behavior of this coefficient in different settings to identify situations where Cronbach's alpha is extremely sensitive to violations of the classical model assumptions. Furthermore, we construct a robust version of Cronbach's alpha which is insensitive to a small proportion of data that belong to a different source. The idea is that the robust Cronbach's alpha reflects the reliability of the bulk of the data. For example, it should not be possible that some small amount of outliers makes a score look reliable if it is not.

Suggested Citation

  • Christmann, A. & Van Aelst, S., 2006. "Robust estimation of Cronbach's alpha," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1660-1674, August.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:7:p:1660-1674
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(05)00089-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lee Cronbach, 1951. "Coefficient alpha and the internal structure of tests," Psychometrika, Springer;The Psychometric Society, vol. 16(3), pages 297-334, September.
    2. D. M. Rocke & D. L. Woodruff, 1993. "Computation of robust estimates of multivariate location and shape," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 47(1), pages 27-42, March.
    3. G. Kuder & M. Richardson, 1937. "The theory of the estimation of test reliability," Psychometrika, Springer;The Psychometric Society, vol. 2(3), pages 151-160, September.
    4. Louis Guttman, 1953. "Reliability formulas that do not assume experimental independence," Psychometrika, Springer;The Psychometric Society, vol. 18(3), pages 225-239, September.
    5. Pison, Greet & Rousseeuw, Peter J. & Filzmoser, Peter & Croux, Christophe, 2003. "Robust factor analysis," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 145-172, January.
    6. Helena Kraemer, 1981. "Extension of Feldt's approach to testing homogeneity of coefficients of reliability," Psychometrika, Springer;The Psychometric Society, vol. 46(1), pages 41-45, March.
    7. Leonard Feldt, 1965. "The approximate sampling distribution of Kuder-Richardson reliability coefficient twenty," Psychometrika, Springer;The Psychometric Society, vol. 30(3), pages 357-370, September.
    8. Croux, Christophe & Haesbroeck, Gentiane, 1999. "Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 161-190, November.
    9. J. Berge & Frits Zegers, 1978. "A series of lower bounds to the reliability of a test," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 575-579, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Otilia Vanessa Cordero-Ahiman & Jorge Leonardo Vanegas & Pablo Beltrán-Romero & María Elena Quinde-Lituma, 2020. "Determinants of Food Insecurity in Rural Households: The Case of the Paute River Basin of Azuay Province, Ecuador," Sustainability, MDPI, vol. 12(3), pages 1-18, January.
    2. Marcus Selart & Svein Johansen, 2011. "Ethical Decision Making in Organizations: The Role of Leadership Stress," Journal of Business Ethics, Springer, vol. 99(2), pages 129-143, March.
    3. Alexandra Bertschi-Michel & Philipp Sieger & Nadine Kammerlander, 2021. "Succession in family-owned SMEs: the impact of advisors," Small Business Economics, Springer, vol. 56(4), pages 1531-1551, April.
    4. Tabassum Ali & Aftab Alam & Jabir Ali, 2021. "Factors Affecting Consumers’ Purchase Behaviour for Health and Wellness Food Products in an Emerging Market," Global Business Review, International Management Institute, vol. 22(1), pages 151-168, February.
    5. Marc Dressler & Ivan Paunovic, 2021. "Not All Wine Businesses Are the Same: Examining the Impact of Winery Business Model Extensions on the Size of Its Core Business," Sustainability, MDPI, vol. 13(18), pages 1-16, September.
    6. Ofori, Elvis Kwame & Aram, Simon Appah & Saalidong, Benjamin M. & Gyimah, Justice & Niyonzima, Patrick & Mintah, Clement & Ahakwa, Isaac, 2023. "Exploring new antecedent metrics for safety performance in Ghana’s oil and gas industry using partial least squares structural equation modelling (PLS-SEM)," Resources Policy, Elsevier, vol. 81(C).
    7. Ricci, Elena Claire & Banterle, Alessandro, 2020. "Do major climate change-related public events have an impact on consumer choices?," Renewable and Sustainable Energy Reviews, Elsevier, vol. 126(C).
    8. Chen, Hong Long, 2023. "Influence of supply chain risks on project financial performance," International Journal of Production Economics, Elsevier, vol. 260(C).
    9. Hasan, A S M Monjurul & Tuhin, Rashedul Amin & Ullah, Mahfuz & Sakib, Taiyeb Hasan & Thollander, Patrik & Trianni, Andrea, 2021. "A comprehensive investigation of energy management practices within energy intensive industries in Bangladesh," Energy, Elsevier, vol. 232(C).
    10. George-Laurentiu Serban-Oprescu & Liana Badea & Isabel Novo-Corti & Mihaela Roberta Stanef & Silvia Elena Iacob & Grigore Ioan Pirosca, 2021. "Socio-Psychological Dimensions of Students Migration. A Pilot Study," The AMFITEATRU ECONOMIC journal, Academy of Economic Studies - Bucharest, Romania, vol. 23(Special15), pages 1015-1015, November.
    11. Huakang Liang & Tianhong Liu & Wenqian Yang & Fan Xia, 2022. "Impact of COVID-19 Pandemic Perception on Job Stress of Construction Workers," IJERPH, MDPI, vol. 19(16), pages 1-14, August.
    12. Vitor William Batista Martins & Denilson Ricardo de Lucena Nunes & André Cristiano Silva Melo & Rayra Brandão & Antônio Erlindo Braga Júnior & Verônica de Menezes Nascimento Nagata, 2022. "Analysis of the Activities That Make Up the Reverse Logistics Processes and Their Importance for the Future of Logistics Networks: An Exploratory Study Using the TOPSIS Technique," Logistics, MDPI, vol. 6(3), pages 1-17, August.
    13. Leontitsis, Alexandros & Pagge, Jenny, 2007. "A simulation approach on Cronbach's alpha statistical significance," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(5), pages 336-340.
    14. Hong-Long Chen, 2021. "Impact of Communication on Capital Project Performance: A Mediated Moderation Model," Sustainability, MDPI, vol. 13(20), pages 1-19, October.
    15. Wobbe P. Zijlstra & L. Andries van der Ark & Klaas Sijtsma, 2011. "Outliers in Questionnaire Data," Journal of Educational and Behavioral Statistics, , vol. 36(2), pages 186-212, April.
    16. Stefan Schmid & Sebastian Baldermann, 2021. "CEOs’ International Work Experience and Compensation," Management International Review, Springer, vol. 61(3), pages 313-364, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Klaas Sijtsma & Julius M. Pfadt, 2021. "Part II: On the Use, the Misuse, and the Very Limited Usefulness of Cronbach’s Alpha: Discussing Lower Bounds and Correlated Errors," Psychometrika, Springer;The Psychometric Society, vol. 86(4), pages 843-860, December.
    2. David Woodruff & Leonard Feldt, 1986. "Tests for equality of several alpha coefficients when their sample estimates are dependent," Psychometrika, Springer;The Psychometric Society, vol. 51(3), pages 393-413, September.
    3. Donald W. Zimmerman, 2011. "Sampling Variability and Axioms of Classical Test Theory," Journal of Educational and Behavioral Statistics, , vol. 36(5), pages 586-615, October.
    4. Eunseong Cho, 2021. "Neither Cronbach’s Alpha nor McDonald’s Omega: A Commentary on Sijtsma and Pfadt," Psychometrika, Springer;The Psychometric Society, vol. 86(4), pages 877-886, December.
    5. Tarkkonen, L. & Vehkalahti, K., 2005. "Measurement errors in multivariate measurement scales," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 172-189, September.
    6. Christmann, Andreas & Aelst, Stefan van, 2002. "Robust estimation of Cronbach's alpha," Technical Reports 2002,42, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    7. Metaxas, Theodore & Kallioras, Dimitris, 2013. "Small and medium-sized firms' competitiveness and territorial characteristics/assets: The cases of Bari, Varna and Thessaloniki," MPRA Paper 52446, University Library of Munich, Germany.
    8. Volker Seiler, 2013. "Comment on Ameriks, Caplin, Leahy & Tyler (2007): Measuring Self-Control Problems," Working Papers CIE 61, Paderborn University, CIE Center for International Economics.
    9. Theodore Metaxas, 2012. "Urban Advantages and Disadvantages in Southeastern Europe: An Appreciation of Industrial Firms by Using Exploratory Factor Analysis," European Research Studies Journal, European Research Studies Journal, vol. 0(2), pages 81-104.
    10. Kentaro Hayashi & Akihito Kamata, 2005. "A note on the estimator of the alpha coefficient for standardized variables under normality," Psychometrika, Springer;The Psychometric Society, vol. 70(3), pages 579-586, September.
    11. Kurtuluş, Ercan & Çetin, İsmail Bilge, 2020. "Analysis of modal shift potential towards intermodal transportation in short-distance inland container transport," Transport Policy, Elsevier, vol. 89(C), pages 24-37.
    12. Jiang, Jingxian & Ellis, Gary D. & Ettekal, Andrea V. & Nelson, Chad, 2022. "Situational engagement experiences: Measurement options and theory testing," Journal of Business Research, Elsevier, vol. 150(C), pages 223-236.
    13. Gilles E. Gignac & Elizabeth Ooi, 2022. "Measurement error in research on financial literacy: How much error is there and how does it influence effect size estimates?," Journal of Consumer Affairs, Wiley Blackwell, vol. 56(2), pages 938-956, June.
    14. María Vera & José A. Cortés, 2021. "Emotional and Cognitive Aptitudes and Successful Academic Performance: Using the ECCT," IJERPH, MDPI, vol. 18(24), pages 1-15, December.
    15. Klaas Sijtsma & Ivo Molenaar, 1987. "Reliability of test scores in nonparametric item response theory," Psychometrika, Springer;The Psychometric Society, vol. 52(1), pages 79-97, March.
    16. David J. Hessen, 2017. "Lower Bounds to the Reliabilities of Factor Score Estimators," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 648-659, September.
    17. Ronald Armstrong & Douglas Jones & Ing-Long Wu, 1992. "An automated test development of parallel tests from a seed test," Psychometrika, Springer;The Psychometric Society, vol. 57(2), pages 271-288, June.
    18. Emily Kistner & Keith Muller, 2004. "Exact distributions of intraclass correlation and Cronbach's alpha with Gaussian data and general covariance," Psychometrika, Springer;The Psychometric Society, vol. 69(3), pages 459-474, September.
    19. Wändi Bruine De Bruin & Ümit Güvenç & Baruch Fischhoff & Christopher M. Armstrong & Denise Caruso, 2009. "Communicating About Xenotransplantation: Models and Scenarios," Risk Analysis, John Wiley & Sons, vol. 29(8), pages 1105-1115, August.
    20. Avinash Advani & Shaista Tariq, 2014. "Causes and Identification of Employees’ Politics and its Impact on Performance of Banking Industry in Pakistan," KASBIT Business Journals (KBJ), Khadim Ali Shah Bukhari Institute of Technology (KASBIT), vol. 7(Special I), pages 75-92, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:97:y:2006:i:7:p:1660-1674. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.