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What is coefficient alpha? An examination of theory and applications
Abstract
Psychological research involving scale construction has been hindered considerably by a wide-spread lack of understanding of coefficient alpha and reliability theory in general. A discussion of the assumptions and meaning of coefficient alpha is presented. This discussion is followed by a demonstration of the effects of test length and dimensionality on alpha by calculating the statistic for hypothetical tests with varying numbers of items, numbers of orthogonal dimensions, and average item intercorrelations. Recommendations for the proper use of coefficient alpha are of-fered. Coefficient alpha (Cronbach, 1951) is certainly one of the most important and pervasive statistics in research involving test construction and use. A review of the Social Sciences Cita-tions Index for the literature from 1966 to 1990 revealed that Cronbach's (1951) article had been cited approximately 60 times per year and in a total of 278 different journals. In addi-tion to the areas of psychology in which one may expect to see alpha used, such as educational, industrial, social, clinical, child, community, and abnormal psychology, this list of jour-nals included representatives from experimental psychology, so-ciology, statistics, medicine, counseling, nursing, economics,
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“The reliability of each scale was tested with the Cronbach's Alpha: all the values are over 0.7, which implies that there is an overall adequate internal consistency and that the measures could be considered reliable (Cortina, 1993;Taber, 2017).”
From The self-reinforcing effect of digital and social exclusion: The inequality loop (2022) · cites this paper as Cortina, 1993
In the citing paper
“Internal consistency reliability (Cronbach’s alpha) ranged from 0.70 to 0.79, which is within what is generally considered the acceptable range of 0.65–0.80 [47,48]”
From Gender Differences in Coping and Psychological Adaptation during the COVID-19 Pandemic (2023) · cites this paper as [47]
In the citing paper
“We chose these two tools, instead of traditional measures of internal consistency (i.e., Cronbach's Alpha [Cronbach, 1951] or KR-20 for dichotomous data [Kuder and Richardson, 1937]) because unlike traditional estimates which do not assess homogeneity (Cortina, 1993; Clark and Watson, 1995), omega and CFA, simultaneously provide estimates of both.”
From A psychometric analysis of the reading the mind in the eyes test: toward a brief form for research and applied settings (2015) · cites this paper as Cortina, 1993
In the citing paper
“Also, Cronbach's alpha is highly biased by long tests; Cortina (1993) recommended Cronbach's alpha not be used for tests with more than 40 items and the Eyes Test, at 36 items, is close to this limit.”
From A psychometric analysis of the reading the mind in the eyes test: toward a brief form for research and applied settings (2015) · cites this paper as Cortina, 1993
In the citing paper
“Reliability estimates are biased towards number of items, and on scales with small numbers of items the alpha is a poor indicator of measure fit (Cortina 1993).”
From Sleep Problems Across Development: A Pathway to Adolescent Risk Taking Through Working Memory (2015) · cites this paper as Cortina 1993
Citations
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“70 based on the Cortina’s criteria [12].”
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“Furthermore, if there is one common factor to a scale, alpha should be a measure of the strength of that factor (Cortina, 1993).”
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“The low alpha may have been in part due to the small number of items (i.e., three) in this scale (see Cortina, 1993).”
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“Given that the AR scale was an established scale (from Stern 2005), and Cortina (1993) and Gay (1991) have indicated that it is acceptable to retain scales with borderline reliability coefficients when working with scales in new contexts, we decided to retain the scale.”
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“each scale (Cortina, 1993).”
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“Internal consistency for all measures was found to be satisfactory and within acceptable boundaries (Cortina, 1993).”
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“Internal consistency was acceptable to good [52], with alpha reliability coefficients of 0.”
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“Taking into account that the scales are short, and that coefficient alpha is a lower-bound estimate of the reliability (Cortina, 1993), the reliabilities of the scales are sufficiently high for the purpose of comparing structural relationships.”
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“While the Cronbach’s alpha score is slightly less than the traditional 0.70 rule-of-thumb, alpha can be interpreted as a lower bound for estimating reliability and is biased downwards when there are few items included in the scale (Cortina 1993).”
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“The internal consistency of the positive and negative scales was then examined using Cronbach’s alpha, where values above 0.7 are commonly considered acceptable and above 0.8 are considered good (Cortina, 1993; Nunnaly, 1978).”
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“existence of internal consistency among the measurement scales (Cortina, 1993).”
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“Interpretative guidelines for internal consistency by Cortina [53]: 0.”
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“…control orientation is a theoretically important aspect of police culture.4 Because the scale is otherwise unidimensional, the low reliability may result in part from measurement error related to question wording or the relatively small number of items in the scale (Cortina, 1993; Schmitt, 1996).”
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Chen, X.-J., Hannibal, N., & Gold, C. (2016) · International Journal of Offender Therapy and Comparative Criminology · doi:10.1177/0306624x15572795 · Cited by 91
“Coefficient alpha is influenced by the number of items, item correlations, and dimensionality (Cortina, 1993).”
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“It is worth clarifying that these scale-level reliability and internal consistency coefficients assume that the original dimensionality of the SSP is correct and are therefore not interpretable if an alternate factor model is deemed more appropriate for the data (Cortina 1993; Crutzen and Peters 2017; Davenport et al.…”
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“For the entire scale we found a good reliability (cf., Cortina, 1993) of Cronbach’s α = 0.90 (emotional creepiness Cronbach’s α = 0.87; creepy ambiguity Cronbach’s α = 0.89).”
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“83 for the only fouritem scale, indicating a reasonable degree of inter-item reliability [8, 23, 67].”
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“Although low estimates of internal consistency might be expected given the number of items on the scale (Cortina, 1993), such low estimates are nonetheless likely to influence the magnitude of validity coefficients possible with the scale (Kaplan & Saccuzzo, 2009) and having such a small number of…”
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“The KR-20 of the pre- and post-test was 0.52 and 0.91, respectively, indicating an acceptable internal consistency (Cortina, 1993).”
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“Yet this approach is outdated (cf. Cortina, 1993; Jarvis et al., 2003) and has long been replaced by modern construct validation methods, such as confirmatory factor analysis (Bollen, 1989; Brown, 2006; Gerbing & Anderson, 1988).”
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“Cronbach’s alpha can be compared across scales, but it is often considered a crude measure of reliability as it can be unduly influenced by factors such as number of items in a scale and blatantly redundant items (8,11).”
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“Step 1 Determine of GLS enablers set for prioritization (1)p2 × q (cov)∕sum (var∕cov) (Cortina 1993); The first step of BWM deals with the determination of GLS enablers set for prioritization.”
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“has only three items, that could affect its values [45, 51].”
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“875, which indicated an excellent internal consistency of the scale [42].”
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“62, respectively, indicating acceptable internal consistency for the two tests (Cortina, 1993).”
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“In survey development, best practice demands that the dimensions or subscales of the measure be identified empirically, through factor analysis or similar multivariate procedures (Cortina, 1993; Gardner, 1995).”
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“With respect to latent construct reliability, the reliability of latent constructs exceeded the recommended level of .70 (.73, .88, .93, and .92, respectively; Cortina, 1993).”
BackgroundInfluentialMeta‐Analysis of Coefficient Alpha: A Reliability Generalization Study
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“Although alpha is influenced by more than just inter-item correlations (Cortina, 1993), it is the most common reliability coefficient reported in the organisational sciences (Cho, 2016).”
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“Some of the scales had a rather low internal consistency, which typically weakens relationships with other constructs; although it should be noted that scales with few items naturally often results in relatively low alpha values [62].”
BackgroundKrink, S., Mühlhan, C., Luyten, P., Romer, G., & Ramsauer, B. S. (2018) · Journal of Child and Family Studies · doi:10.1007/s10826-017-1000-5 · Cited by 87
“11 Another restriction concerning internal validity is in the low reliabilities of the PRF subscales pre-12 mentalizing modes and interest and curiosity in mental states, whereby the small number of items must be 13 considered (Cortina 1993).”
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“To confirm that these measures are reliable or internally consistent, they were analyzed using Cronbach ’ s α , which showed acceptable values (see Cortina, 1993): perceived relevance (Cronbach ’ s α 5 0.92), institutional barriers (Cronbach ’ s α 5 0.79), incentives (Cronbach ’ s α 5 0.71) and…”
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Πέλλας, Ν. (2023) · Smart Learning Environments · doi:10.1186/s40561-023-00276-4 · Cited by 120
“In terms of reliability, Cronbach’s alpha coefficient was determined to be 0.844, which is considered acceptable according to the standards set by Cortina (1993).”
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Gignac, G. E. (2013) · European Journal of Psychological Assessment · doi:10.1027/1015-5759/a000181 · Cited by 86
Africentrism: Psychometric Analyses of a Self-Report Measure
Grills, C. T., & Longshore, D. L. (1996) · Journal of Black Psychology · doi:10.1177/00957984960221007 · Cited by 87
Yazici, H. J. (2014) · International Journal of Information Management · doi:10.1016/j.ijinfomgt.2014.04.010 · Cited by 86
Magana, A. J., Falk, M. L., Vieira, C., & Reese, M. (2016) · Computers in Human Behavior · doi:10.1016/j.chb.2016.03.025 · Cited by 88
“Cronbach's alpha was used to measure the reliability of the self-belief measures (Cortina, 1993).”
Influence of the Reactive Strength Index Modified on Force– and Power–Time Curves
McMahon, J. J., Jones, P. A., Suchomel, T. J., Lake, J. P., & Comfort, P. (2017) · International Journal of Sports Physiology and Performance · doi:10.1123/ijspp.2017-0056 · Cited by 86
Wongwatkit, C., Panjaburee, P., Srisawasdi, N., & Seprum, P. (2020) · Journal of Computers in Education · doi:10.1007/s40692-020-00154-9 · Cited by 81
“Cronbach’s α was assessed for internal consistency and reliability for each individual item in the construct with a lowest accepted value of 0.70 (Cortina 1993; Goffee and Jones 1996).”
MethodInfluentialKurzrok, J., McBride, E. R., & Grossman, R. B. (2021) · Autism · doi:10.1177/1362361321990931 · Cited by 93
“Cronbach’s alpha for the scale was 0.91, indicating a high level of internal consistency across scale items (Cortina, 1993).”
BackgroundInfluentialBrandstätter, V., Heimbeck, D., Malzacher, J., & Fresé, M. (2003) · European Journal of Work and Organizational Psychology · doi:10.1080/13594320344000011 · Cited by 88
Reliability and Validity of Scores on Scales to Measure Managerlal Aspirations
Tharenou, P., & Terry, D. J. (1998) · Educational and Psychological Measurement · doi:10.1177/0013164498058003008 · Cited by 86
Trinkner, R. J., Cohn, E. S., Rebellon, C. J., & Gundy, K. T. V. (2011) · Journal of Adolescence · doi:10.1016/j.adolescence.2011.05.003 · Cited by 96
Wilcox, B. R., & Lewandowski, H. J. (2016) · Physical Review Physics Education Research · doi:10.1103/physrevphyseducres.12.010123 · Cited by 86
“For a unidimensional test, Cronbach’s alpha is a measure of this type of internal consistency [32].”
BackgroundMethodPrimary School Children’s Self-Efficacy for Music Learning
Ritchie, L., & Williamon, A. (2011) · Journal of Research in Music Education · doi:10.1177/0022429411405214 · Cited by 98
“The results confirmed the scale’s reliability, with a robust Cronbach alpha of 0.87 (Cortina, 1993; Kline, 1999), and factor analysis indicated a single underlying factor within the questionnaire.”
InfluentialReligion and Substance Use among Youths of Mexican Heritage: A Social Capital Perspective
Hodge, D., Marsiglia, F., & Nieri, T. (2011) · Social work research (Print) · doi:10.1093/swr/35.3.137 · Cited by 55
“Holding interitem correlation constant, the fewer the items in the scale, the lower the alpha (Cortina, 1993).”
BackgroundSports clubs’ use of social media to increase spectator interest
Nisar, T. M., Prabhakar, G. P., & Patil, P. P. (2018) · International Journal of Information Management · doi:10.1016/j.ijinfomgt.2018.08.003 · Cited by 102
Ahmed, S., Hossain, M. M., & Haq, I. (2020) · International Journal of Building Pathology and Adaptation · doi:10.1108/ijbpa-04-2019-0037 · Cited by 85
RetractedTransformational and passive avoidant leadership as determinants of absenteeism
Frooman, J., Mendelson, M. B., & Murphy, J. K. (2012) · Leadership & Organization Development Journal · doi:10.1108/01437731211241247 · Cited by 85
“First, for exploratory work, such as this, lower as are considered acceptable (Nunnally, 1978); and second, for scales with fewer items, such as this one, there is greater reliability than the reliability coefficient can indicate, because the coefficient is a function of the number of items in a scale (Cortina, 1993).”
BackgroundAn Initial Evaluation of the Comprehensive Quality of Life Scale‐‐Intellectual Disability
Cummins, R. A., McCabe, M. P., Romeo, Y., Reid, S. B., & Waters, L. E. (1997) · International Journal of Disability Development and Education · doi:10.1080/0156655970440102 · Cited by 85
Liu, J. H.-F., & Sibley, C. G. (2004) · Journal of Environmental Psychology · doi:10.1016/j.jenvp.2003.12.003 · Cited by 84
Metadata
- Authors
- Cortina, J. M.
- Venue
- Journal of Applied Psychology
- Published
- 1993-02
- Volume
- 78
- Issue
- 1
- Pages
- 98-104
- ISSN
- 0021-9010 (ISSN-L)
- 1939-1854
- OpenAlex
- W2117012826
- Cited by
- 8,810
- References
- 26
- Citations by year
- 2026: 523 · 2025: 499 · 2024: 518 · 2023: 606 · 2022: 639 · 2021: 685 · 2020: 589 · 2019: 474 · 2018: 407 · 2017: 411 · 2016: 418 · 2015: 428 · 2014: 437 · 2013: 372 · 2012: 309
- FWCI
- 29.15
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Applied Psychology (publishedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Reliability and Agreement in Measurement
- Social Sciences › Psychology › Applied Psychology › Psychological Testing and Assessment
- Keywords
- Cronbach's alpha, internal consistency, reliability theory, scale development, test length, dimensionality
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