Estimating Internal Consistency: Did We Choose the Right Coefficient?

Yıl 2026, Cilt: 4 Sayı: 1, 70 - 76, 28.02.2026

Néstor Montoro-pérez , Silvia Escribano

https://doi.org/10.62425/jopres.1789821

https://izlik.org/JA68ZZ56MH

Öz

Internal consistency is a concept extensively used in academic discourse, yet its definition remains debated. In the context of validation studies, it is noteworthy that, although internal consistency is commonly assessed, some studies could benefit from employing more accurate estimators that are better suited to the underlying factorial structure. These editorial addresses the various recommended estimators for calculating internal consistency based on the characteristics of the studied model. We explore one-dimensional measures, identifying when estimators such as α are suitable, particularly for tau-equivalent models. For congeneric measurement models, coefficient ω is recommended. We also discuss complex models incorporating multidimensional structures, including essential unidimensionality, scales with multiple correlated or uncorrelated factors, and higher-order models. Researchers should avoid reporting the total internal consistency of the instrument unless unidimensionality or a higher-order factor structure has been demonstrated. When data are approximately unidimensional, measures are congeneric with moderate factor loadings, and sample sizes are large, it is reasonable to report both α and ω.

Anahtar Kelimeler

Internal Consistency , Reliability , Psychometrics

Etik Beyan

As this manuscript constitutes a theoretical/editorial discussion and does not involve the collection of original data from human subjects, it is not necessary to report ethics committee approval.

Destekleyen Kurum

University of Alicante.

Teşekkür

We extend our sincere gratitude to Lidwine B. Mokkink, PhD, from the Department of Epidemiology and Data Science at Amsterdam UMC, Vrije Universiteit Amsterdam, and the Amsterdam Public Health Research Institute, for her valuable contribution in reviewing this editorial. Her expertise in measurement methodology and psychometrics has significantly enhanced the quality and rigour of our work.

İç Tutarlılığın Tahmini: Doğru Katsayıyı Seçtik mi?

https://izlik.org/JA68ZZ56MH

Öz

İç tutarlılık, akademik söylemde yaygın olarak kullanılan bir kavramdır ancak tanımı hâlâ tartışmalıdır. Geçerlilik çalışmaları bağlamında, iç tutarlılığın yaygın olarak değerlendirildiği, ancak bazı çalışmaların altta yatan faktör yapısına daha uygun ve daha doğru tahmin edicilerden faydalanabileceği dikkate değerdir. Bu editoryal, incelenen modelin özelliklerine göre iç tutarlılığın hesaplanması için önerilen çeşitli tahmin edicileri ele almaktadır. Tek boyutlu ölçümleri inceliyor, α gibi tahmin edicilerin özellikle tau-eşdeğer modeller için ne zaman uygun olduğunu belirtiyoruz. Kongenerik ölçüm modelleri için ω katsayısı önerilmektedir. Ayrıca, zorunlu tek boyutluluk, birden fazla ilişkili veya ilişkisiz faktöre sahip ölçekler ve üst düzey modeller dahil olmak üzere çok boyutlu yapıları içeren karmaşık modelleri de tartışıyoruz. Araştırmacılar, tek boyutluluk veya üst düzey faktör yapısı gösterilmedikçe aracın toplam iç tutarlılığını raporlamaktan kaçınmalıdır. Veriler yaklaşık olarak tek boyutlu olduğunda, ölçümler orta düzey faktör yüklerine sahip kongenerik ise ve örneklem büyüklüğü büyükse, hem α hem de ω’nun raporlanması makuldür.

Anahtar Kelimeler

İç Tutarlılık , Güvenilirlik , Psikometri

Etik Beyan

Bu makale teorik/editoriyal bir tartışma niteliğinde olup, insan katılımcılardan orijinal veri toplanmasını içermediği için etik kurul onayının bildirilmesi gerekli değildir.

Destekleyen Kurum

Alicante Üniversitesi.

Teşekkür

Amsterdam UMC, Vrije Universiteit Amsterdam Epidemiyoloji ve Veri Bilimi Bölümü ile Amsterdam Halk Sağlığı Araştırma Enstitüsü'nden Dr. Lidwine B. Mokkink'e bu editoryali değerlendirmeye katkılarından dolayı içten teşekkürlerimizi sunarız. Ölçme metodolojisi ve psikometri konusundaki uzmanlığı, çalışmamızın kalitesini ve titizliğini önemli ölçüde artırmıştır.

Kaynakça

• Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107(2), 238-246. https://doi.org/10.1037/0033-2909.107.2.238
• Bentler, P. M. (2021). Alpha, FACTT, and beyond. Psychometrika, 86(4), 861-868. https://doi.org/10.1007/s11336-021-09797-8
• Berge, J. M. F. T. (2014). Tau‐equivalent and congeneric measurements. Wiley StatsRef: Statistics Reference Online. https://doi.org/10.1002/9781118445112.stat06393
• Bollen, K. A. (1980). Issues in the comparative measurement of political democracy. American Sociological Review, 45(3), 370. https://doi.org/10.2307/2095172
• Cho, E., & Béland, S. (2025). Reliability in unidimensional ordinal data: A comparison of continuous and ordinal estimators. Psychological Methods. https://doi.org/10.1037/met0000739
• Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297-334. https://doi.org/10.1007/bf02310555
• Crutzen, R., & Peters, G. Y. (2015). Scale quality: Alpha is an inadequate estimate and factor-analytic evidence is needed first of all. Health Psychology Review, 11(3), 242-247. https://doi.org/10.1080/17437199.2015.1124240
• Doval, E., Viladrich, C., & Angulo-Brunet, A. (2023). Coefficient alpha: The resistance of a classic. Psicothema, 35(1), 5-20. https://doi.org/10.7334/psicothema2022.321
• Flora, D. B. (2020). Your coefficient alpha is probably wrong, but which coefficient omega is right? A tutorial on using r to obtain better reliability estimates. Advances in Methods and Practices in Psychological Science, 3(4), 484-501. https://doi.org/10.1177/2515245920951747
• Gadermann, A. M., Guhn, M., & Zumbo, B. D. (2012). Estimating ordinal reliability for likert-type and ordinal item response data: A conceptual, empirical, and practical guide. Practical Assessment, Research & Evaluation, 17(3), 1-13. https://doi.org/10.7275/n560-j767
• Graham, J. M. (2006). Congeneric and (essentially) tau-equivalent estimates of score reliability. Educational and Psychological Measurement, 66(6), 930-944. https://doi.org/10.1177/0013164406288165
• Green, S. B., & Hershberger, S. L. (2000). Correlated errors in true score models and their effect on coefficient alpha. Structural Equation Modeling A Multidisciplinary Journal, 7(2), 251-270. https://doi.org/10.1207/s15328007sem0702_6
• Green, S. B., & Yang, Y. (2015). Evaluation of dimensionality in the assessment of internal consistency reliability: Coefficient alpha and omega coefficients. Educational Measurement Issues And Practice, 34(4), 14-20. https://doi.org/10.1111/emip.12100
• Green, S. B., Lissitz, R. W., & Mulaik, S. A. (1977). Limitations of coefficient alpha as an index of test unidimensionality1. Educational And Psychological Measurement, 37(4), 827-838. https://doi.org/10.1177/001316447703700403
• Gu, F., Little, T. D., & Kingston, N. M. (2012). Misestimation of reliability using coefficient alpha and structural equation modeling when assumptions of tau-equivalence and uncorrelated errors are violated. Methodology, 9(1), 30-40. https://doi.org/10.1027/1614-2241/a000052
• Jarvis, C. B., MacKenzie, S. B., & Podsakoff, P. M. (2003). A critical review of construct indicators and measurement model misspecification in marketing and consumer research. Journal of Consumer Research, 30(2), 199-218. https://doi.org/10.1086/376806
• Jöreskog, K. G. (1971). Statistical analysis of sets of congeneric tests. Psychometrika, 36(2), 109-133. https://doi.org/10.1007/bf02291393
• Lord, F. M., & Novick, M. R. (1968). Statistical theories of mental test scores. Addison-Wesley.
• McDonald, R. P. (1981). The dimensionality of tests and items. British Journal of Mathematical and Statistical Psychology, 34(1), 100-117. https://doi.org/10.1111/j.2044-8317.1981.tb00621.x
• Miller, M. B. (1995). Coefficient alpha: A basic introduction from the perspectives of classical test theory and structural equation modeling. Structural Equation Modeling A Multidisciplinary Journal, 2(3), 255-273. https://doi.org/10.1080/10705519509540013
• Mokkink, L. B., Elsman, E. B., & Terwee, C. B. (2024). COSMIN guideline for systematic reviews of patient-reported outcome measures version 2.0. Quality of Life Research, 33(11), 2929-2939. https://doi.org/10.1007/s11136-024-03761-6
• Mokkink, L. B., Terwee, C. B., Patrick, D. L., Alonso, J., Stratford, P. W., Knol, D. L., Bouter, L. M., & de Vet, H. C. (2010). The COSMIN study reached international consensus on taxonomy, terminology, and definitions of measurement properties for health-related patient-reported outcomes. Journal of Clinical Epidemiology, 63(7), 737-745. https://doi.org/10.1016/j.jclinepi.2010.02.006
• Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric theory (3rd ed.). McGraw-Hill.
• Prinsen, C. A. C., Mokkink, L. B., Bouter, L. M., Alonso, J., Patrick, D. L., De Vet, H. C. W., & Terwee, C. B. (2018). COSMIN guideline for systematic reviews of patient-reported outcome measures. Quality of Life Research, 27(5), 1147-1157. https://doi.org/10.1007/s11136-018-1798-3
• Raykov, T. (1997). Estimation of composite reliability for congeneric measures. Applied Psychological Measurement, 21(2), 173-184. https://doi.org/10.1177/01466216970212006
• Raykov, T. (2004). Point and interval estimation of reliability for multiple-component measuring instruments via linear constraint covariance structure modeling. Structural Equation Modeling A Multidisciplinary Journal, 11(3), 342-356. https://doi.org/10.1207/s15328007sem1103_3
• Reise, S. P., Bonifay, W. E., & Haviland, M. G. (2012a). Scoring and modeling psychological measures in the presence of multidimensionality. Journal of Personality Assessment, 95(2), 129-140. https://doi.org/10.1080/00223891.2012.725437
• Reise, S. P. (2012b). The rediscovery of bifactor measurement models. Multivariate Behavioral Research, 47(5), 667-696. https://doi.org/10.1080/00273171.2012.715555
• Revelle, W. (1979). Hierarchical cluster analysis and the internal structure of tests. Multivariate Behavioral Research, 14(1), 57-74. https://doi.org/10.1207/s15327906mbr1401_4
• Revelle, W., & Condon, D. M. (2019). Reliability from α to ω: A tutorial. Psychological Assessment, 31(12), 1395-1411. https://doi.org/10.1037/pas0000754
• Rodriguez, A., Reise, S. P., & Haviland, M. G. (2015). Evaluating bifactor models: Calculating and interpreting statistical indices. Psychological Methods, 21(2), 137-150. https://doi.org/10.1037/met0000045
• Sijtsma, K. (2008). On the use, the misuse, and the very limited usefulness of cronbach’s alpha. Psychometrika, 74(1), 107-120. https://doi.org/10.1007/s11336-008-9101-0
• Sijtsma, K., & Pfadt, J. M. (2021). Part II: On the use, the misuse, and the very limited usefulness of cronbach’s alpha: Discussing lower bounds and correlated errors. Psychometrika, 86(4), 843-860. https://doi.org/10.1007/s11336-021-09789-8
• Stout, W. (1987). A nonparametric approach for assessing latent trait unidimensionality. Psychometrika, 52(4), 589-617. https://doi.org/10.1007/bf02294821
• Streiner, D. L. (2003). Starting at the beginning: An introduction to coefficient alpha and internal consistency. Journal of Personality Assessment, 80(1), 99-103. https://doi.org/10.1207/s15327752jpa8001_18
• Tang, W., Cui, Y., & Babenko, O. (2014). Internal consistency: Do we really know what it is and how to assess it? Journal of Psychology & Behavioral Science, 2(2), 205–220. https://jpbs.thebhprj.org/journals/jpbs/Vol_2_No_2_June_2014/13.pdf
• Thorndike, R. M. (1995). Book review: Psychometric Theory (3rd ed.) by Jum Nunnally and Ira Bernstein New York: McGraw-Hill, 1994, xxiv + 752 pp. Applied Psychological Measurement, 19(3), 303-305. https://doi.org/10.1177/014662169501900308
• Viladrich, C., Angulo-Brunet, A., & Doval, E. (2017). Un viaje alrededor de alfa y omega para estimar la fiabilidad de consistencia interna. Anales de Psicología, 33(3), 755 –782. https://doi.org/10.6018/analesps.33.3.268401
• Yung, Y., Thissen, D., & McLeod, L. D. (1999). On the relationship between the higher-order factor model and the hierarchical factor model. Psychometrika, 64(2), 113-128. https://doi.org/10.1007/bf02294531
• Zhang, Z., & Yuan, K. (2015). Robust coefficients alpha and omega and confidence intervals with outlying observations and missing data. Educational And Psychological Measurement, 76(3), 387-411. https://doi.org/10.1177/0013164415594658
• Zinbarg, R. E., Revelle, W., Yovel, I., & Li, W. (2005). Cronbach’s α, revelle’s β, and mcdonald’s ωh: their relations with each other and two alternative conceptualizations of reliability. Psychometrika, 70(1), 123-133. https://doi.org/10.1007/s11336-003-0974-7
• Zumbo, B. D., & Kroc, E. (2019). A measurement is a choice and stevens’ scales of measurement do not help make it: A response to chalmers. Educational And Psychological Measurement, 79(6), 1184-1197. https://doi.org/10.1177/0013164419844305