Thanks coefficient alpha, We'll take it from here

Psychological Methods

Volumn 23, Issue 3, 2018, Pages 412-433

  McNeish, Daniel ^a,b  

^a UTRECHT UNIVERSITY   (Netherlands)

^b UNIVERSITY OF NORTH CAROLINA   (United States)

Author keywords

Cronbach's alpha; Internal consistency; Psychometrics; Reliability

Indexed keywords

HUMAN; PROCEDURES; PSYCHOMETRY; REPRODUCIBILITY; STANDARDS; STATISTICAL ANALYSIS;

DATA INTERPRETATION, STATISTICAL; HUMANS; PSYCHOMETRICS; REPRODUCIBILITY OF RESULTS;

EID: 85047268244     PISSN: 1082989X     EISSN: None     Source Type: Journal    
DOI: 10.1037/met0000144     Document Type: Article

References (93)

1. Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84, 191-215. http://dx.doi.org/10.1037/ 0033-295X.84.2.191
2. Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173-1182. http://dx.doi.org/10.1037/0022-3514.51.6.1173
3. Barrett, P. (2007). Structural equation modelling: Adjudging model fit. Personality and Individual Differences, 42, 815-824. http://dx.doi.org/ 10.1016/j.paid.2006.09.018
4. Becker, G. (2000). How important is transient error in estimating reliability? Going beyond simulation studies. Psychological Methods, 5, 370-379. http://dx.doi.org/10.1037/1082-989X.5.3.370
5. Bentler, P. M. (1968). Alpha-maximized factor analysis (alphamax): Its relation to alpha and canonical factor analysis. Psychometrika, 33, 335-345. http://dx.doi.org/10.1007/BF02289328
6. Bentler, P. M. (2007). Covariance structure models for maximal reliability of unit-weighted composites. In S. Lee (Ed.), Handbook of computing and statistics with applications: Vol. 1. (pp. 1-19). New York, NY: Elsevier
7. Bentler, P. M. (2009). Alpha, dimension-free, and model-based internal consistency reliability. Psychometrika, 74, 137-143. http://dx.doi.org/10.1007/s11336-008-9100-1
8. Carroll, J. B. (1961). The nature of the data, or how to choose a correlation coefficient. Psychometrika, 26, 347-372. http://dx.doi.org/10.1007/ BF02289768
9. Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling, 14, 464-504. http://dx.doi.org/10.1080/10705510701301834
10. Cheung, G. W., & Rensvold, R. B. (2002). Evaluating goodness-of-fit indexes for testing measurement invariance. Structural Equation Modeling, 9, 233-255. http://dx.doi.org/10.1207/S15328007SEM0902_5
11. Cole, D. A., Ciesla, J. A., & Steiger, J. H. (2007). The insidious effects of failing to include design-driven correlated residuals in latent-variable covariance structure analysis. Psychological Methods, 12, 381-398. http://dx.doi.org/10.1037/1082-989X.12.4.381
12. Cortina, J. M. (1993). What is coefficient alpha? An examination of theory and applications. Journal of Applied Psychology, 78, 98-104. http://dx.doi.org/10.1037/0021-9010.78.1.98
13. Crocker, L., & Algina, J. (2008). Introduction to classical and modern test theory. New York, NY: Holt
14. Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334. http://dx.doi.org/10.1007/BF02310555
15. Cronbach, L. J., & Shavelson, R. J. (2004). My current thoughts on coefficient alpha and successor procedures. Educational and Psychological Measurement, 64, 391-418. http://dx.doi.org/10.1177/ 0013164404266386
16. Crutzen, R. (2007). Time is a jailer: What do alpha and its alternatives tell us about reliability? European Health Psychologist, 16, 70-74
17. Crutzen, R., & Peters, G. J. Y. (2015). Scale quality: Alpha is an inadequate estimate and factor-analytic evidence is needed first of all. Health Psychology Review. Advance online publication. http://dx.doi.org/10.1080/17437199.2015.1124240
18. Curran, F. C., & Kellogg, A. T. (2016). Understanding science achievement gaps by race/ethnicity and gender in kindergarten and first grade. Educational Researcher, 45, 273-282. http://dx.doi.org/10.3102/ 0013189X16656611
19. DeVellis, R. F. (1991). Scale development. London, UK: Sage
20. Dunn, T. J., Baguley, T., & Brunsden, V. (2014). From alpha to omega: A practical solution to the pervasive problem of internal consistency estimation. British Journal of Psychology, 105, 399-412. http://dx.doi.org/ 10.1111/bjop.12046
21. Flora, D. B., & Curran, P. J. (2004). An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. Psychological Methods, 9, 466-491. http://dx.doi.org/10.1037/1082-989X.9.4.466
22. 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, 1-13
23. Geldhof, G. J., Preacher, K. J., & Zyphur, M. J. (2014). Reliability estimation in a multilevel confirmatory factor analysis framework. Psychological Methods, 19, 72-91. http://dx.doi.org/10.1037/a0032138
24. Gessaroli, M. E., & Folske, J. C. (2002). Generalizing the reliability of tests comprised of testlets. International Journal of Testing, 2, 277-295. http://dx.doi.org/10.1080/15305058.2002.9669496
25. Gignac, G. E., Bates, T. C., & Jang, K. (2007). Implications relevant to CFA model misfit, reliability, and the five factor model as measured by the NEO-FFI. Personality and Individual Differences, 43, 1051-1062. http://dx.doi.org/10.1016/j.paid.2007.02.024
26. Graham, J. M. (2006). Congeneric and (essentially) tau-equivalent estimates of score reliability what they are and how to use them. Educational and Psychological Measurement, 66, 930-944. http://dx.doi.org/ 10.1177/0013164406288165
27. Green, S. B. (2003). A coefficient alpha for test-retest data. Psychological Methods, 8, 88-101. http://dx.doi.org/10.1037/1082-989X.8.1.88
28. Green, S. B., & Hershberger, S. L. (2000). Correlated errors in true score models and their effect on coefficient alpha. Structural Equation Modeling, 7, 251-270. http://dx.doi.org/10.1207/S15328007SEM0702_6
29. Green, S. B., Lissitz, R. W., & Mulaik, S. A. (1977). Limitations of coefficient alpha as an index of test unidimensionality. Educational and Psychological Measurement, 37, 827-838. http://dx.doi.org/10.1177/ 001316447703700403
30. Green, S. B., & Yang, Y. (2009a). Commentary on coefficient alpha: A cautionary tale. Psychometrika, 74, 121-135. http://dx.doi.org/10.1007/ s11336-008-9098-4
31. Green, S. B., & Yang, Y. (2009b). Reliability of summed item scores using structural equation modeling: An alternative to coefficient alpha. Psychometrika, 74, 155-167. http://dx.doi.org/10.1007/s11336-008-9099-3
32. Hancock, G. R., & Mueller, R. O. (2001). Rethinking construct reliability within latent variable systems. In R. Cudeck, S. du Toit, & D. Sörbom (Eds.), Structural equation modeling: Present and future-A festschrift in honor of Karl Jöreskog (pp. 195-216). Lincolnwood, IL: Scientific Software International
33. Hancock, G. R., & Mueller, R. O. (2011). The reliability paradox in assessing structural relations within covariance structure models. Educational and Psychological Measurement, 71, 306-324. http://dx.doi.org/10.1177/0013164410384856
34. Hattie, J. (1985). Methodology review: Assessing unidimensionality of tests and items. Applied Psychological Measurement, 9, 139-164. http:// dx.doi.org/10.1177/014662168500900204
35. Hogan, T. P., Benjamin, A., & Brezinski, K. L. (2000). Reliability methods: A note on the frequency of use of various types. Educational and Psychological Measurement, 60, 523-531. http://dx.doi.org/10.1177/ 00131640021970691
36. Hu, L. T., & Bentler, P. M. (1998). Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification. Psychological Methods, 3, 424-453. http://dx.doi.org/10.1037/1082-989X.3.4.424
37. Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1-55. http://dx.doi.org/10.1080/ 10705519909540118
38. Jackson, P. H., & Agunwamba, C. C. (1977). Lower bounds for the reliability of the total score on a test composed of non-homogeneous items: I: Algebraic lower bounds. Psychometrika, 42, 567-578. http:// dx.doi.org/10.1007/BF02295979
39. Kelley, K. (2007). Methods for the behavioral, educational, and social sciences: An R package. Behavior Research Methods, 39, 979-984. http://dx.doi.org/10.3758/BF03192993
40. Kelley, K., & Cheng, Y. (2012). Estimation of and confidence interval formation for reliability coefficients of homogeneous measurement instruments. Methodology, 8, 39-50. http://dx.doi.org/10.1027/1614-2241/a000036
41. Kelley, K., & Pornprasertmanit, S. (2016). Confidence intervals for population reliability coefficients: Evaluation of methods, recommendations, and software for composite measures. Psychological Methods, 21, 69-92. http://dx.doi.org/10.1037/a0040086
42. Kenny, D. A., Kaniskan, B., & McCoach, D. B. (2015). The performance of RMSEA in models with small degrees of freedom. Sociological Methods & Research, 44, 486-507. http://dx.doi.org/10.1177/ 0049124114543236
43. Kline, P. (1986). A handbook of test construction: Introduction to psychometric design. London, UK: Methuen
44. Lubienski, S., & Crane, C. C. (2010). Beyond free lunch: Which family background measures matter? Education Policy Analysis Archives, 18, 11. http://dx.doi.org/10.14507/epaa.v18n11.2010
45. Mansolf, M., & Reise, S. P. (2016). Exploratory bifactor analysis: The Schmid-Leiman orthogonalization and Jennrich-Bentler analytic rotations. Multivariate Behavioral Research, 51, 698-717. http://dx.doi.org/ 10.1080/00273171.2016.1215898
46. Marsh, H. W., Hau, K. T., & Wen, Z. (2004). In search of golden rules: Comment on hypothesis-testing approaches to setting cutoff values for fit indexes and dangers in overgeneralizing Hu and Bentler's (1999) findings. Structural Equation Modeling, 11, 320-341. http://dx.doi.org/ 10.1207/s15328007sem1103_2
47. McDonald, R. P. (1970). The theoretical foundations of principal factor analysis, canonical factor analysis, and alpha factor analysis. British Journal of Mathematical & Statistical Psychology, 23, 1-21. http://dx.doi.org/10.1111/j.2044-8317.1970.tb00432.x
48. McDonald, R. P. (1999). Test theory: A unified approach. Mahwah, NJ: Erlbaum
49. Miller, M. B. (1995). Coefficient alpha: A basic introduction from the perspectives of classical test theory and structural equation modeling. Structural Equation Modeling, 2, 255-273. http://dx.doi.org/10.1080/ 10705519509540013
50. Moltner, A., & Revelle, W. (2015). Find the greatest lower bound to reliability. Retrieved from http://personality-project.org/r/psych/help/ glb.algebraic
51. Novick, M. R., & Lewis, C. (1967). Coefficient alpha and the reliability of composite measurements. Psychometrika, 32, 1-13. http://dx.doi.org/10.1007/BF02289400
52. Nunnally, J. C., & Bernstein, R. H. (Eds.). (1994). The assessment of reliability. Psychometric theory (pp. 248-292). New York, NY: McGraw-Hill
53. Pedhazur, E. J., & Schmelkin, L. P. (1991). Measurement, design, and analysis: An integrated approach. Hillsdale, NJ: Erlbaum
54. Peters, G. J. Y. (2014). The alpha and the omega of scale reliability and validity: Why and how to abandon Cronbach's alpha and the route towards more comprehensive assessment of scale quality. European Health Psychologist, 16, 56-69
55. Peterson, R. A., & Kim, Y. (2013). On the relationship between coefficient alpha and composite reliability. Journal of Applied Psychology, 98, 194-198
56. Raykov, T. (1997a). Estimation of composite reliability for congeneric measures. Applied Psychological Measurement, 21, 173-184
57. Raykov, T. (1997b). Scale reliability, Cronbach's coefficient alpha, and violations of essential tau-equivalence with fixed congeneric components. Multivariate Behavioral Research, 32, 329-353
58. Raykov, T. (1998). Coefficient alpha and composite reliability with interrelated nonhomogeneous items. Applied Psychological Measurement, 22, 375-385
59. Raykov, T. (2004). Behavioral scale reliability and measurement invariance evaluation using latent variable modeling. Behavior Therapy, 35, 299-331
60. Raykov, T., & Shrout, P. E. (2002). Reliability of scales with general structure: Point and interval estimation using a structural equation modeling approach. Structural Equation Modeling, 9, 195-212
61. Reise, S. P. (2012). The rediscovery of bifactor measurement models. Multivariate Behavioral Research, 47, 667-696
62. Reise, S. P., Bonifay, W. E., & Haviland, M. G. (2013). Scoring and modeling psychological measures in the presence of multidimensionality. Journal of Personality Assessment, 95, 129-140
63. Reise, S. P., Morizot, J., & Hays, R. D. (2007). The role of the bifactor model in resolving dimensionality issues in health outcomes measures. Quality of Life Research, 16, 19-31
64. Revelle, W. (1979). Hierarchical cluster analysis and the internal structure of tests. Multivariate Behavioral Research, 14, 57-74
65. Revelle, W. (2008). psych: Procedures for personality and psychological research (R package version 1.0-51)
66. Revelle, W. (2016, May). Using R and the psych package to find ω. Retrieved from http://personality-project.org/r/psych/HowTo/omega.pdf
67. Revelle, W., Wilt, J., & Rosenthal, A. (2010). Individual differences in cognition: New methods for examining the personality-cognition link. In A. Gruszka, G. Matthews, & B. Szymura (Eds.), Handbook of individual differences in cognition: Attention, memory and executive control (pp. 27-49). New York, NY: Springer
68. Revelle, W., & Zinbarg, R. E. (2009). Coefficients alpha, beta, omega, and the glb: Comments on Sijtsma. Psychometrika, 74, 145-154
69. 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, 354-373
70. Rozeboom, W. W. (1966). Scaling theory and the nature of measurement. Synthese, 16, 170-233
71. Schmid, J., & Leiman, J. M. (1957). The development of hierarchical factor solutions. Psychometrika, 22, 53-61
72. Schmitt, N. (1996). Uses and abuses of coefficient alpha. Psychological Assessment, 8, 350-353
73. Shapiro, A., & ten Berge, J. M. (2000). The asymptotic bias of minimum trace factor analysis, with applications to the greatest lower bound to reliability. Psychometrika, 65, 413-425
74. Sharpe, D. (2013). Why the resistance to statistical innovations? Bridging the communication gap. Psychological Methods, 18, 572-582
75. Sheng, Y., & Sheng, Z. (2012). Is coefficient alpha robust to non-normal data? Frontiers in Psychology, 3, 34
76. Sijtsma, K. (2009). On the use, the misuse, and the very limited usefulness of Cronbach's alpha. Psychometrika, 74, 107-120
77. Sočan, G. (2000). Assessment of reliability when test items are not essentially-equivalent. Developments in Survey Methodology, 15, 23-35
78. Steinberg, L., & Thissen, D. (1996). Uses of item response theory and the testlet concept in the measurement of psychopathology. Psychological Methods, 1, 81-97
79. ten Berge, J. M., & Kiers, H. A. (1991). A numerical approach to the approximate and the exact minimum rank of a covariance matrix. Psychometrika, 56, 309-315
80. ten Berge, J. M., & Sočan, G. (2004). The greatest lower bound to the reliability of a test and the hypothesis of unidimensionality. Psychometrika, 69, 613-625
81. Teo, T., & Fan, X. (2013). Coefficient alpha and beyond: Issues and alternatives for educational research. The Asia-Pacific Education Researcher, 22, 209-213
82. Terry, L., & Kelley, K. (2012). Sample size planning for composite reliability coefficients: Accuracy in parameter estimation via narrow confidence intervals. British Journal of Mathematical and Statistical Psychology, 65, 371-401
83. Trizano-Hermosilla, I., & Alvarado, J. M. (2016). Best alternatives to Cronbach's alpha reliability in realistic conditions: Congeneric and asymmetrical measurements. Frontiers in Psychology, 7, 769
84. van Noorden, R., Maher, B., & Nuzzo, R. (2014). The top 100 papers. Nature, 514, 550-553
85. van Zyl, J. M., Neudecker, H., & Nel, D. G. (2000). On the distribution of the maximum likelihood estimator of Cronbach's alpha. Psychometrika, 65, 271-280
86. Wolff, H. G., & Preising, K. (2005). Exploring item and higher order factor structure with the Schmid-Leiman solution: Syntax codes for SPSS and SAS. Behavior Research Methods, 37, 48-58
87. Yang, Y., & Green, S. B. (2011). Coefficient alpha: A reliability coefficient for the 21st century? Journal of Psychoeducational Assessment, 29, 377-392
88. Zhang, Z., & Yuan, K. H. (2016). Robust coefficients alpha and omega and confidence intervals with outlying observations and missing data: Methods and software. Educational and Psychological Measurement, 76, 387-411
89. Zimmerman, D. W., Zumbo, B. D., & Lalonde, C. (1993). Coefficient alpha as an estimate of test reliability under violation of two assumptions. Educational and Psychological Measurement, 53, 33-49
90. Zinbarg, R. E., Revelle, W., & Yovel, I. (2007). Estimating α h for structures containing two group factors: Perils and prospects. Applied Psychological Measurement, 31, 135-157
91. Zinbarg, R. E., Revelle, W., Yovel, I., & Li, W. (2005). Cronbach's α, Revelle's β, and McDonald's ω H: Their relations with each other and two alternative conceptualizations of reliability. Psychometrika, 70, 123-133
92. Zinbarg, R. E., Yovel, I., Revelle, W., & McDonald, R. P. (2006). Estimating generalizability to a latent variable common to all of a scale's indicators: A comparison of estimators for ωh. Applied Psychological Measurement, 30, 121-144
93. Zumbo, B. D., & Rupp, A. A. (2004). Responsible modeling of measurement data for appropriate inferences: Important advances in reliability and validity theory. In D. Kaplan (Ed.), The SAGE handbook of quantitative methodology for the social sciences (pp. 73-92). Thousand Oaks, CA: Sage