Keywords
Reliability
Cronbach’s alpha
Omega
Software Consistencia interna
Fiabilidad
Alfa de Cronbach
Omega
Software
How to Cite
Abstract
Background: During the 20th century the alpha coefficient (α) was widely used in the estimation of the internal consistency reliability of test scores. After misuses were identified in the early 21st century alternatives became widespread, especially the omega coefficient (ω). Nowadays, α is re-emerging as an acceptable option for reliability estimation. Method: A review of the recent academic contributions, journal publication habits and recommendations from normative texts was carried out to identify good practices in estimation of internal consistency reliability. Results: To guide the analysis, we propose a three-phase decision diagram, which includes item description, fit of the measurement model for the test, and choice of the reliability coefficient for test score(s). We also provide recommendations on the use of R, Jamovi, JASP, Mplus, SPSS and Stata software to perform the analysis. Conclusions: Both α and ω are suitable for items with approximately normal distributions and approximately unidimensional and congeneric measures without extreme factor loadings. When items show non-normal distributions, strong specific components, or correlated errors, variants of ω are more appropriate. Some require specific data gathering designs. On a practical level we recommend a critical approach when using the software.
References
American Educational Research Association, American Psychological Association & National Council on Measurement in Education. (2014).
The Standards for Educational and Psychological Testing. American Educational Research Association.
Agresti, A. (1996). An introduction to categorical data analysis. Wiley. American Psychological Association. (2020). Publication manual of the
American Psychological Association (7th ed.). Author. https://doi.org/10.1037/000016S-000
Appelbaum, M., Cooper, H., Kline, R. B., Mayo-Wilson, E., Nezu, A. M., & Rao, S. M. (2018). Journal article reporting standards for quantitative
research in psychology: The APA publications and communications board task force report. American Psychologist, 73(1), 3–25. https://doi.org/10.1037/amp0000191
Arbuckle, J. L. (2014). Amos (Version 23.0) [Computer software]. IBM SPSS. Bandalos, D. L. (2021). Item meaning and order as causes of correlated residuals in confirmatory factor analysis. Structural Equation Modeling, 28(6), 903–913. https://doi.org/10.1080/10705511.2021.1916395
Béland, S., & Falk, C. F. (2022). A comparison of modern and popular approaches to calculating reliability for dichotomously scored items.
Applied Psychological Measurement, 46(4), 321–337. https://doi.org/10.1177/01466216221084210
Bentler, P. M. (2009). Alpha, dimension-free, and model-based internal consistency reliability. Psychometrika, 74(1), 137–143. https://doi.org/10.1007/s11336-008-9100-1
Bentler, P. M. (2017). Specificity-enhanced reliability coefficients. Psychological Methods, 22(3), 527–540. https://doi.org/10.1037/met0000092
Bentler, P. M. (2021). Alpha, FACTT, and beyond. Psychometrika, 86(4), 861– 868. https://doi.org/10.1007/s11336-021-09797-8
Bovaird, J. A., & Koziol, N. A. (2012). Measurement models for orderedcategorical indicators. In R. H. Hoyle (Ed.), Handbook of Structural
Equation Modeling (pp. 495–511). Guilford.
Brennan, R. L. (2001). Generalizability theory. Springer.
Brown, T. A. (2015). Confirmatory factor analysis for applied research. Guilford.
Chalmers, R. P. (2018). On misconceptions and the limited usefulness of ordinal alpha. Educational and Psychological Measurement, 78(6), 1056–1071. https://doi.org/10.1177/0013164417727036
Cho, E. (2022). The accuracy of reliability coefficients: A reanalysis of existing simulations. Psychological Methods. Advance online publication.
https://doi.org/10.1037/met0000475
Cho, S. J., Shen, J., & Naveiras, M. (2019). Multilevel reliability measures of latent scores within an item response theory framework. Multivariate
Behavioral Research, 54(6), 856–881. https://doi.org/10.1080/00273171.2019.1596780
Christensen, W. F., Wall, M. M., & Moustaki, I. (2022). Assessing dimensionality in dichotomous items when many subjects have all-zero responses: An example from psychiatry and a solution using mixture models. Applied Psychological Measurement, 46(3), 167–184.
https://doi.org/10.1177/01466216211066602
Cortina, J. M. (1993). What is coefficient alpha? An examination of theory and applications. Journal of Applied Psychology, 78(1), 98–104.
https://doi.org/10.1037/0021-9010.78.1.98
Cortina, J. M., Sheng, Z., Keener, S. K., Keeler, K. R., Grubb, L. K., Schmitt, N., Tonidandel, S., Summerville, K. M., Heggestad, E. D., & Banks, G.
C. (2020). From alpha to omega and beyond! A look at the past, present, and (possible) future of psychometric soundness in the Journal of Applied Psychology. Journal of Applied Psychology, 105(12), 1351–1381. https://doi.org/10.1037/apl0000815
Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297-334.
Cronbach, L. J., Nageswari, R., & Gleser, G. C. (1963). Theory of generalizability: A liberation of reliability theory. The British Journal of
Statistical Psychology, 16(2), 137–163. https://doi.org/10.1111/j.2044-8317.1963.tb00206.x
Culpepper, S. A. (2013). The reliability and precision of total scores and IRT estimates as a function of polytomous IRT parameters and latent trait distribution. Applied Psychological Measurement, 37(3), 201–225. https://doi.org/10.1177/0146621612470210
Davenport, E. C., Davison, M. L., Liou, P-Y., & Love, Q. U. (2016). Easier said than done: Rejoinder on Sijtsma and on Green and Yang. Educational Measurement: Issues and Practice, 35(1), 6–10. https://doi.org/10.1111/emip.12106
Deng, L., & Chan, W. (2017). Testing the difference between reliability coefficients alpha and omega. Educational and Psychological Measurement, 77(2), 185–203. https://doi.org/10.1177/0013164416658325
DeVellis, R. F. (2003). Scale development. Theory and applications. Sage.
DiStefano, C., Shi, D., & Morgan, G. B. (2020). Collapsing categories is often more advantageous than modeling sparse data: Investigations in the CFA framework. Structural Equation Modeling, 28(2), 237–249. https://doi.org/10.1080/10705511.2020.1803073
Edwards, A. A., Joyner, K. J., & Schatschneider, C. (2021). A simulation study on the performance of different reliability estimation methods. Educational and Psychological Measurement, 81(6), 1–29. https://doi.org/10.1177/0013164421994184
Ellis, J. L. (2021). A test can have multiple reliabilities. Psychometrika, 86(4), 869–876. https://doi.org/10.1007/s11336-021-09800-2
Elosua, P., & Zumbo, B. D. (2008). Reliability coefficients for ordinal response scales. Psicothema, 20(4), 896–901.
Enders, C. K. (2010). Applied missing data analysis. Guilford.
Evers, A., Lucassen, W., Meijer, R., & Sijtsma, K. (2015). COTAN Review System for Evaluating Test Quality. https://psynip.nl/wp-content/uploads/2022/05/COTAN-review-system-forevaluating-test-quality.pdf
Evers, A., Muñiz, J., Hagemeister, C., Hstmælingen, A., Lindley, P., Sjöberg, A., & Bartram, D. (2013). Assessing the quality of tests: Revision of the EFPA review model. Psicothema, 25(3), 283–291. https://doi.org/10.7334/psicothema2013.97
Ferrando, P. J., & Lorenzo-seva, U. (2016). A note on improving EAP trait estimation in oblique factor-analytic and item response theory models. Psicológica, 37, 235–247.
Ferrando, P. J., & Lorenzo-Seva, U. (2018). Assessing the quality and appropriateness of factor solutions and factor score estimates in exploratory item factor analysis. Educational and Psychological Measurement, 78(5), 762–780. https://doi.org/10.1177/0013164417719308
Ferrando, P. J., Lorenzo-seva, U., Hernández-Dorado, A., & Muñiz, J. (2022).
Decalogue for the factor analysis of test items. Psicothema, 34(1), 7–17.
https://doi.org/10.7334/psicothema2021.456
Ferrando, P. J., & Navarro-González, D. (2021). Reliability and external validity of personality test scores: The role of person and item error. Psicothema, 33(2), 259–267. https://doi.org/10.7334/psicothema2020.346
Flake, J. K., Pek, J., & Hehman, E. (2017). Construct validation in social and personality research: Current practice and recommendations. Social
Psychological and Personality Science, 8(4), 370–378. https://doi.org/10.1177/1948550617693063
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
Foldnes, N., & Grønneberg, S. (2020). Pernicious polychorics: The impact and detection of underlying non-normality. Structural Equation Modeling, 27(4), 525–543. https://doi.org/10.1080/10705511.2019.1673168
Forero, C. G., Maydeu-Olivares, A., & Gallardo-Pujol, D. (2009). Factor analysis with ordinal indicators: A Monte Carlo study comparing DWLS
and ULS estimation. Structural Equation Modeling, 16(4), 625–641. https://doi.org/10.1080/10705510903203573
Foster, R. C. (2020). A generalized framework for classical test theory. Journal of Mathematical Psychology, 96, Article 102330.
https://doi.org/10.1016/j.jmp.2020.102330
Foster, R. C. (2021). KR20 and KR21 for some nondichotomous data (It’s not just Cronbach’s alpha). Educational and Psychological Measurement, 81(6), 1172–1202. https://doi.org/10.1177/0013164421992535
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 and Evaluation, 17(3), 1–13.
Gallucci, M., & Jentschke, S. (2021). Semlj: Jamovi SEM Analysis [Computer software]. https://semlj.github.io
García-Garzón, E., Nieto, M. D., Garrido, L. E., & Abad, F. J. (2020). Bi-factor exploratory structural equation modeling done right: using the slidapp application. Psicothema, 32(4), 607–614. https://doi.org/10.7334/psicothema2020.179
Golino, H. F., & Epskamp, S. (2017). Exploratory graph analysis: A new approach for estimating the number of dimensions in psychological research. PLoS ONE, 12(6), 1–26. https://doi.org/10.1371/journal.pone.0174035
Goodboy, A. K., & Martin, M. M. (2020). Omega over alpha for reliability estimation of unidimensional communication measures. Annals of the
International Communication Association, 44(4), 422–439. https://doi.org/10.1080/23808985.2020.1846135
Graham, J. (2006). Congeneric and (essentially) tau-equivalent estimates of score reliability. What they are and how to use them. 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, 7(2), 251–270. https://doi.org/10.1207/S15328007SEM0702_6
Green, S. B., & Yang, Y. (2009). Reliability of summed item scores using structural equation modeling: An alternative to coefficient alpha. Psychometrika, 74(1), 155–167. https://doi.org/10.1007/s11336-008-9099-3
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
Greenacre, M. (2017). Correspondence analysis in practice (3rd ed.). Chapman & Hall. https://doi.org/10.1201/9781315369983
Gu, F., Little, T. D., & Kingston, N. M. (2013). 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
Gulliksen, H. (1950). Theory of mental tests. Wiley. Hallquist, M., Willey, J., van Lissa, C., & Morillo, D. (2022). MplusAutomation:
an R package for facilitating large-scale latent variable analyses in Mplus (1.1.0) [Computer software].
https://michaelhallquist.github.io/MplusAutomation/
Hayes, A. F., & Coutts, J. J. (2020). Use omega rather than Cronbach’s alpha for estimating reliability. But… Communication Methods and Measures, 14(1), 1–24. https://doi.org/10.1080/19312458.2020.1718629
Hernández, A., Ponsoda, V., Muñiz, J., Prieto, G., & Elosua, P. (2016). Revisión del modelo para evaluar la calidad de los tests utilizados en España [Assessing the quality of tests in spain: revision of the spanish test review model]. Papeles Del Psicólogo, 37(3), 192–197.
Hoekstra, R., Vugteveen, J., Warrens, M. J., & Kruyen, P. M. (2019). An empirical analysis of alleged misunderstandings of coefficient alpha.
International Journal of Social Research Methodology, 22(4), 351–364. https://doi.org/10.1080/13645579.2018.1547523
Hox, J., Moerbeek, M., & van de Schoot, R. (2018). Multilevel analysis: Techniques and applications. Routledge.
Hussey, I., & Hughes, S. (2020). Hidden invalidity among 15 commonly used measures in social and personality psychology. Advances in Methods and Practices in Psychological Science, 3(2), 166–184. https://doi.org/10.1177/2515245919882903
IBM Corp. (2021). IBM SPSS Statistics for Windows, Version 28.0 (28.0) [Computer software]. IBM Corp. JASP Team. (2022). JASP (Jeffreys’s Amazing Statistics Program) (0.16.2) [Computer software]. https://jasp-stats.org/
Kalkbrenner, M. T. (2021). Alpha, omega, and H internal consistency reliability estimates: Reviewing these options and when to use them. Counseling Outcome Research and Evaluation, Published. Advance online publication, 1–12. https://doi.org/10.1080/21501378.2021.1940118
Kim, S., Lu, Z., & Cohen, A. S. (2020). Reliability for tests with items having different numbers of ordered categories. Applied Psychological
Measurement, 44(2), 137–149. https://doi.org/10.1177/0146621619835498
Kim, Seonghoon, & Feldt, L. S. (2010). The estimation of the IRT reliability coefficient and its lower and upper bounds, with comparisons to CTT
reliability statistics. Asia Pacific Education Review, 11(2), 179–188. https://doi.org/10.1007/s12564-009-9062-8
Komperda, R., Pentecost, T. C., & Barbera, J. (2018). Moving beyond alpha: A primer on alternative sources of single-administration reliability evidence for quantitative chemistry education research. Journal of Chemical Education, 95(9), 1477–1491. https://doi.org/10.1021/acs.jchemed.8b00220
Lai, M. H. C. (2021). Composite reliability of multilevel data: It’s about observed scores and construct meanings. Psychological Methods, 26(1),
–102. https://doi.org/10.1037/met0000287
Lance, C., Butts, M. M., & Michels, L. C. (2006). The sources of four commonly reported cutoff criteria: What did they really say? Organizational Research Methods, 9(2), 202–220. https://doi.org/10.1177/1094428105284919
Liddell, T. M., & Kruschke, J. K. (2018). Analyzing ordinal data with metric models: What could possibly go wrong? Journal of Experimental Social Psychology, 79, 328–348. https://doi.org/10.1016/j.jesp.2018.08.009
Lloret-Segura, S., Ferreres-Traver, A., Hernández-Baeza, A., & Tomás-Marco, I. (2014). El análisis factorial exploratorio de los ítems: una guía práctica, revisada y actualizada [The exploratory factor analysis of the items: a practical guide, revised and updated]. Anales de Psicología, 30(3), 1151–1169. https://doi.org/10.6018/analesps.30.3.199361
Lord, F. M., & Novick, M. R. (1968). Statistical theories of mental test scores. Addison Wesley.
Lorenzo-Seva, U., & Ferrando, P. J. (2012). TETRA-COM: A comprehensive SPSS program for estimating the tetrachoric correlation. Behavior Research Methods, 44(4), 1191–1196. https://doi.org/10.3758/s13428-012-0200-6
Lorenzo-Seva, U., & Ferrando, P. J. (2015). POLYMAT-C: A comprehensive SPSS program for computing the polychoric correlation matrix. Behavior Research Methods, 47(3), 884–889. https://doi.org/10.3758/s13428-014-0511-x
McCrae, R. R. (2015). A more nuanced view of reliability: specificity in the trait hierarchy. Personality and Social Psychology Review, 19(2), 97–112. https://doi.org/10.1177/1088868314541857
McDonald, R. P. (1999). Test theory: a unified treatment. Lawrence Erlbaum Associates.
McNeish, D. (2018). Thanks coefficient alpha, we’ll take it from here. Psychological Methods, 23(3), 412–433. https://dx.doi.org/10.1037/met0000144
Muñiz, J. (2018). Introducción a las Teorías Psicométricas [Introduction to Psychometric Theories]. Pirámide.
Muñiz, J., & Fonseca-Pedrero, E. (2019). Ten steps for test development. Psicothema, 31(1), 7–16. https://doi.org/10.7334/psicothema2018.291
Muthén, B. O., Muthén, L. K., & Asparouhov, T. (2016). Regression and mediation analysis using Mplus. Muthén & Muthén.
Muthén, L. K., & Muthén, B. O. (2017). Mplus User’s Guide (8th edition).
Muthén & Muthén. Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric theory. McGraw-Hill. Olvera, O. L., Kroc, E., & Zumbo, B. D. (2020). The role of item distributions on reliability estimation: the case of Cronbach’s coefficient alpha. Educational and Psychological Measurement, 80(5), 825–846. https://doi.org/10.1177/0013164420903770
Oosterwijk, P. R., van der Ark, L. A., & Sijtsma, K. (2019). Using confidence intervals for assessing reliability of real tests. Assessment, 26(7), 1207–1216. https://doi.org/10.1177/1073191117737375
Pfadt, J. M., van den Bergh, D., Klaas, S., Moshagen, M., & Wagenmakers, E.-J. (2022). Bayesian estimation of single-test reliability coefficients
bayesian estimation of single-test reliability coefficients. 57(4), 620–641.
Multivariate Behavioural Research, 57(4). https://doi.org/10.1080/00273171.2021.1891855
Pons, J., Viladrich, C., & Ramis, Y. (2017). Examining the big three of coping in adolescent athletes using network analysis. Revista de Psicologia Del Deporte, 26, 68–74.
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
R Core Team. (2021). R: A language and environment for statistical computing [Computer software]. R Foundation for Statistical Computing.
Raykov, T. (1997a). Estimation of composite reliability for congeneric measures. Applied Psychological Measurement, 21(2), 173–184.
Raykov, T. (1997b). Scale reliability, Cronbach’s coefficient alpha, and violations of essential tau-equivalence with fixed congeneric components. Multivariate Behavioral Research, 32(4), 329–353. https://doi.org/10.1207/s15327906mbr3204_2
Raykov, T. (2001). Bias of coefficient alpha for fixed congeneric measures with correlated errors. Applied Psychological Measurement, 25(1), 69–76. https://doi.org/10.1177/01466216010251005
Raykov, T. (2004). Point and interval estimation of reliability for multiplecomponent measuring instruments via linear constraint covariance structure modeling. Structural Equation Modeling, 11(3), 452–483. https://doi.org/10.1207/s15328007sem1103
Raykov, T. (2007). Reliability of multiple-component measuring instruments: Improved evaluation in repeated measure designs. British Journal of Mathematical and Statistical Psychology, 60(1), 119–136. https://doi.org/10.1348/000711006X100464
Raykov, T., Anthony, J. C., & Menold, N. (2022). On the importance of coefficient alpha for measurement research: loading equality is not necessary for alpha’s utility as a scale reliability index. Educational and Psychological Measurement. Advance online publication.
https://doi.org/10.1177/00131644221104972
Raykov, T., Dimitrov, D. M., & Asparouhov, T. (2010). Evaluation of scale reliability with binary measures using latent variable modeling. Structural Equation Modeling: A Multidisciplinary Journal, 17(2), 265–279. https://doi.org/10.1080/10705511003659417
Raykov, T., & Marcoulides, G. A. (2015). A direct latent variable modeling based method for point and interval estimation of coefficient alpha.
Educational and Psychological Measurement, 75(1), 146–156. https://doi.org/10.1177/0013164414526039
Raykov, T., & Marcoulides, G. A. (2016). Scale reliability evaluation under multiple assumption violations. Structural Equation Modeling: A
Multidisciplinary Journal, 23(2), 302–313. https://doi.org/10.1080/10705511.2014.938597
Raykov, T., & Marcoulides, G. A. (2019). Thanks coefficient alpha, we still need you! Educational and Psychological Measurement, 79(1), 200–210. https://doi.org/10.1177/0013164417725127
Raykov, T., Marcoulides, G. A., Harrison, M., & Menold, N. (2019). Multiplecomponent measurement instruments in heterogeneous populations: Is there a single coefficient alpha? Educational and Psychological Measurement, 79(2), 399–412. https://doi.org/10.1177/0013164417733305
Revelle, W. (2022). psych: Procedures for personality and pscychological research (2.2.5) [Computer software]. https://personality-project.org/r/psych/
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
Revelle, W., & Zinbarg, R. E. (2009). Coefficient alpha, beta, omega, and the GLB: Comment on Sitjsma. Psychometrika, 74(1), 145–154.
Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3), 354–373. https://doi.org/10.1037/a0029315
Rodriguez, A., Reise, S. P., & Haviland, M. G. (2016a). Applying bifactor statistical indices in the evaluation of psychological measures. Journal of Personality Assessment, 98(3), 223–237. https://doi.org/10.1080/00223891.2015.1089249
Rodriguez, A., Reise, S. P., & Haviland, M. G. (2016b). Evaluating bifactor models: Calculating and interpreting statistical indices. Psychological
Methods, 21(2), 137–150. https://doi.org/10.1037/met0000045
Sánchez-Meca, J. (2022, July 20). Meta-análisis de generalización de la fiabilidad [Reliability generalization Meta-analysis][Simposium]. XVII
Congreso de Metodología de Las Ciencias Sociales y de La Salud.
Sánchez-Meca, Julio, Marín-Martínez, F., López-López, J. A., Núñez- Núñez, R. M., Rubio-Aparicio, M., López-García, J. J., López-Pina, J. A.,
Blázquez-Rincón, D. M., López-Ibáñez, C., & López-Nicolás, R. (2021). Improving the reporting quality of reliability generalization meta-analyses: The REGEMA checklist. Research Synthesis Methods, 12(4), 516–536. https://doi.org/10.1002/jrsm.1487
Savalei, V., & Reise, S. P. (2019). Don’t forget the model in your model-based reliability coefficients: A reply to McNeish (2018). Collabra: Psychology, 5(1), 36. https://doi.org/10.1525/collabra.247
Savalei, V., & Rhemtulla, M. (2013). The performance of robust test statistics with categorical data. British Journal of Mathematical and Statistical Psychology, 66(2), 201–223. https://doi.org/10.1111/j.2044-8317.2012.02049.x
Scherer, R., & Teo, T. (2020). A tutorial on the meta-analytic structural equation modeling of reliability coefficients. Psychologycal Methods, 25(6), 747–775. https://doi.org/10.1037/14262-002
Schmitt, N. (1996). Uses and abuses of coefficient alpha. Psychological Assessment, 8(4), 350–353.
Shi, D., Lee, T., Fairchild, A. J., & Maydeu-Olivares, A. (2020). Fitting ordinal factor analysis models with missing data: A comparison between
pairwise deletion and multiple imputation. Educational and Psychological Measurement, 80(1), 41–66. https://doi.org/10.1177/0013164419845039
Sideridis, G. D., Tsaousis, I., & Al-Sadaawi, A. (2019). An application of reliability estimation in longitudinal designs through modeling item-specific error variance. Educational and Psychological Measurement, 79(6), 1038–1063. https://doi.org/10.1177/0013164419843162
Sijtsma, K. (2009). 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, 843–860. https://doi.org/10.1007/s11336-021-09789-8
Slaney, K. L., Tkatchouk, M., Gabriel, S. M., & Maraun, M. D. (2009). Psychometric assessment and reporting practices: Incongruence between
theory and practice. Journal of Psychoeducational Assessment, 27(6), 465–476. https://doi.org/10.1177/0734282909335781
StataCorp. (2021). Stata statistical software. (Release 17) [Computer software]. StataCorp LLC. https://www.stata.com/
Streiner, D. L. (2003). Starting at the beginning: An introduction to coefficient alpha and internal consistency. Journal of Personality Assessment, 80(1), 99–103. Taber, K. S. (2018). The use of Cronbach’s alpha when developing and reporting
research instruments in science education. Research in Science Education, 48(6), 1273–1296. https://doi.org/10.1007/s11165-016-9602-2
The jamovi project (2021). The jamovi project (v1.6) [Computer software]. https://www.jamovi.org
Thurstone, L. L. (1947). Multiple factor analysis. University of Chicago Press
Viladrich, C., y Angulo-Brunet, A. (2019). Reliability of Essentially Unidimensional Measures Derived From Bifactor Modeling With R, Mplus
and Stata. [Data set and syntax]. Universitat Autònoma de Barcelona. https://ddd.uab.cat/record/205936
Viladrich, C., Angulo-Brunet, A., & Doval, E. (2017). A journey around alpha and omega to estimate internal consistency reliability. Annals of Psychology, 33(3), 755–782. https://doi.org/10.6018/analesps.33.3.268401
Viladrich, C., Angulo-Brunet, A., & Doval, E. (2019). Mplus and stata tools to calculate the internal consistency reliability coefficients alpha and omega [Data set and syntax]. Universitat Autònoma de Barcelona. https://ddd.uab.cat/record/205870
Weijters, B., Geuens, M., & Schillewaert, N. (2009). The proximity effect: The role of inter-item distance on reverse-item bias. International Journal of Research in Marketing, 26(1), 2–12. https://doi.org/10.1016/j.ijresmar.2008.09.003
Xiao, L., & Hau, K.T. (2022). Performance of coefficient alpha and its alternatives: Effects of different types of non-normality. Educational and
Psychological Measurement. Advance online publication. https://doi.org/10.1177/00131644221088240
Yang, Y., & Green, S. B. (2011). Coefficient alpha: A reliability coefficient for the 21st Century? Journal of Psychoeducational Assessment, 29(4), 377–392. https://doi.org/10.1177/0734282911406668
Yang, Y., & Green, S. B. (2015). Evaluation of structural equation modeling estimates of reliability for scales with ordered categorical items.
Methodology, 11(1), 23–34. https://doi.org/10.1027/1614-2241/a000087
Yang, Y., & Xia, Y. (2019). Categorical omega with small sample sizes via bayesian estimation: An alternative to frequentist estimators. Educational and Psychological Measurement, 79(1), 19–39. https://doi.org/10.1177/0013164417752008
Ziegler, M. (2020). Psychological test adaptation and development – How papers are structured and why. Psychological Test Adaptation and Development. Advance online publication. https://doi.org/10.1027/2698-1866/a000002
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., Gadermann, A. M., & Zeisser, C. (2007). Ordinal versions of coefficients alpha and theta for Likert rating scales. Journal of Modern Applied Statistical Methods, 6(1), 21–29. https://doi.org/10.1107/S0907444909031205
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