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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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“In addition, if alpha-if item deleted values are higher than the Cronbach’s alpha for scores on the full scale, the questions (items) are deemed harmful to reliability (Cortina, 1993).”
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“However, as with any statistical rule of thumb, this figure is only one benchmark, and the evaluation of reliability should consider multiple factors in a more complete assessment of reliability, including the number of items in the scale and its intended use (Cortina, 1993; Peters, 2014).”
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“In fact, Cortina (1993) recommends not using this coefficient in multidimensional measurements, arguing that if the set of items in a test is explained by orthogonal (or poorly correlated) factors, the alpha coefficient of that set of items can provide values greater than 0.70 when the true…”
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“In addition to consuming brandrelated content (Cronbach’s alpha ¼ 0.764), all Cronbach’s alphas were greater than 0.80, which indicated a good level of internal consistency reliability (Cortina 1993).”
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“90 are considered acceptable for multidimensional scales and scores [15,16].”
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“Furthermore, Cortina (1993) demonstrated the dependence of Cronbach’s α on the number of items, and Nunnally (1978) and George and Mallery (2014) recommended Cronbach’s α values also below the threshold for exploratory analyses.”
BackgroundEffect Of Varying Sample Size In Estimation Of Coefficients Of Internal Consistency
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“The factors were estimated by means of averages of markers, number of markers, and Cronbach’s alpha (Cortina, 1993; Cronbach, 1951; Shelvin et al., 1999) values given below, and were interpreted as follows:”
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“90 respectively, showing acceptable internal consistency (Cortina, 1993).”
MethodInfluentialDebono, A. E., Ewoldt, K. B., Heimbauer, M., Mendelsohn, E., & Cohen, J. A. (2025) · Learning Disability Quarterly · doi:10.1177/07319487241301400 · Cited by 73
“The WESS’s internal consistency for the entire scale is quite good (Cronbach’s α = .92; Cortina, 1993).”
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“Intraclass correlation coefficient values were interpreted using the criteria of Cortina (17), where ICC $0.80 is highly reliable, although Weir (35) cautions the use of interpreting absolute categories for ICCs and suggests incorporating SEMs and SDD (or meaningful difference), as described below.”
MethodInfluentialThe effect of integrated product development on efficiency and innovation
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“In case of multi-dimensionality or heterogeneousness of a test, Cronbach’s alpha is underestimating reliability and, therefore, not suitable as a reliability coefficient (Cortina 1993).”
MethodFalk, C. F., & Savalei, V. (2011) · Journal of Personality Assessment · doi:10.1080/00223891.2011.594129 · Cited by 75
“For example, one frequently cited expository article on coefficient alpha incorrectly states that standardized alpha is always greater than or equal to unstandardized alpha (Cortina, 1993; cited 1,186 times according to Google Scholar, 2010).”
BackgroundInfluentialBeyond Cronbach's Alpha: Considering Confirmatory Factor Analysis and Segmentation
Shelby, L. B. (2011) · Human Dimensions of Wildlife · doi:10.1080/10871209.2011.537302 · Cited by 73
“Cronbach’s alpha tests the extent to which scale items are similar and interrelated, but it does not imply that a scale is measuring the same concept (i.e., is unidimensional or homogenous) (Cortina, 1993; Sijtsma, 2009).”
BackgroundZatzick, C. D., & Iverson, R. D. (2011) · The International Journal of Human Resource Management · doi:10.1080/09585192.2011.561016 · Cited by 74
“65, which is reasonable for measures with only two items (Cortina 1993 ).”
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“This idea has been conveyed indirectly in the past, in cautionary comments that overly high internal consistencies may denote a lack of heterogeneity in item content (Cortina, 1993; Schmitt, 1996).”
BackgroundSchwarz (1999) · doi:10.1097/acm.0000000000002002 · Cited by 67
Ambaw, F., Mayston, R., Hanlon, C., & Alem, A. (2017) · BMC Psychiatry · doi:10.1186/s12888-017-1231-4 · Cited by 72
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Sutherland, C. A. M., Rhodes, G., Burton, N. S., & Young, A. W. (2019) · British Journal of Psychology · doi:10.1111/bjop.12390 · Cited by 75
“conclusions at the group level, because alpha measures the extent to which the group of items (here, observers) will agree with other groups tested in future (Cortina, 1993), but it is inappropriate for measuring agreement at the individual level because alpha is inflated by the number of items (i.”
BackgroundΚοψιδάς, Α., Milioti, C. P., Kepaptsoglou, K. L., & Vlahogianni, E. I. (2021) · Transportation Letters · doi:10.1080/19427867.2021.1901029 · Cited by 72
“For evaluating the internal consistency of this set, the Cronbach-a value was used and demonstrated a minimally accepted consistency, reaching the value of 0.668 (Cortina 1993).”
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“Structure identification: structure identification is driven by exploratory factor analysis (EFA), which has long been recommended by researchers for initial scale development (Cortina 1993; Russell 2002) .”
MethodRequirements for Quality of Life Instruments in Clinical Research
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“This is because it is rare to have all items on a scale having equal loadings on a single factor (Reuterberg and Gustafsson 1992), and there is little chance for all items to contribute exactly the same amount of variance to a single factor (Cortina 1993).”
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“The Cronbach alpha test is used to assess the internal consistency among multiple raters (23).”
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“Using the often used rule of thumb of 0.7 as an acceptable alpha value, and given the unidimensionality of the scales (Cortina 1993; George and Mallery 2003; Nunnaly 1978), all scales are acceptable, despite the small number of items in some of the scales.”
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“Average interitem correlationsmay be affected by skew (Cortina, 1993).”
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“internal consistency of the scales through the use of an interitem correlation, item-total correlation, Cronbach’s a and the a value if an item was deleted.(29,30) The Kolmogorov–Smirnov test(8) did not assume a normal distribution of the QoLIP-10 outcome variable.”
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“items may appear to be less reliable based on alpha but that may be a function of the number of items, not the reliability of the items in the measure (Cortina, 1993; Streiner, 2003).”
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“99—with maximum possible value a = 1—showed that survey items measured reliably the constructs within and across participants (Cortina 1993).”
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“According to Cortina (1993) , coefficient alpha is a function of three variables: (a) the number of items, (b) their degree of interrelatedness (internal consistency), and (c) their unidimensionality (homogeneity); the lower they are, the less reliable the coefficient.”
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“Even though the alpha might have been influenced by the small number of items (see Cortina, 1993 ), the findings involving this scale should be interpreted with caution.”
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“A problem with Cronbach's alpha is that it may fail to identify a multi-dimensional structure (see Cortina, 1993 ).”
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“Cortina, J. M. (1993). What is coefficient alpha? An examination of theory and application. Journal of Applied Psychology, 78, 98–104. http://dx .doi.org/10.1037/0021-9010.78.1.98 Cortina, J. M. (2003). Apples and oranges (and pears, oh my!): The search for moderators in meta-analysis.”
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“Cronbach's α was considered adequate if it ranged from 0.70 to 0.95 (Cortina, 1993; Terwee et al., 2007).”
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“Second, post-study, all instruments were checked for consistency using Cronbach alpha (Cortina, 1993), which proved robust across all variables as detailed in Appendix A.”
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“All scales were found to have an acceptable internal consistency, as indicated by Cronbach’s alpha of greater than 0.7 (Cortina, 1993; see Table 1).”
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“The overall Cronbach's Alpha coefficient for all dimensions was 0.882 considered as appropriate value and it is > 0.7 ( Cortina, J. M. (1993) .”
InfluentialPechorro, P. S., Ray, J. V., Raine, A., Marôco, J. P., & Gonçalves, R. A. (2015) · Journal of Interpersonal Violence · doi:10.1177/0886260515590784 · Cited by 69
“70 (Cortina, 1993; Kaplan & Saccuzzo, 2009), somewhat higher than those reported in previous studies (e.”
ResultAsberg, K. K., & Renk, K. (2012) · Substance Use & Misuse · doi:10.3109/10826084.2012.669446 · Cited by 69
“For the present study, the Kuder-Richardson (i.e., a measure of internal consistency for scales with dichotomous items; Cortina, 1993) was .”
MethodPatterns and Correlates of Gun Ownership Among Nonmetropolitan and Rural Middle School Students
Cunningham, P. B., Henggeler, S. W., Limber, S. P., Melton, G. B., & Nation, M. A. (2000) · Journal of Clinical Child Psychology · doi:10.1207/s15374424jccp2903_14 · Cited by 69
“The failure to achieve acceptable internal consistency for the remaining five scales may reflect the limited number of items in these scales (Cortina, 1993).”
BackgroundCoping Strategies in Call Centres: Work Intensity and the Role of Co‐workers and Supervisors
Deery, S. J., Iverson, R. D., & Walsh, J. T. (2009) · British Journal of Industrial Relations · doi:10.1111/j.1467-8543.2009.00755.x · Cited by 69
Evaluating deterrents of illegal behaviour in conservation: Carnivore killing in rural Taiwan
John, F. A. V. S., Mai, C.-H., & Pei, K. J. (2014) · Biological Conservation · doi:10.1016/j.biocon.2014.08.019 · Cited by 72
“Before modelling, we used Cronbach’s alpha coefficient (Cortina, 1993) to check each set of four species-specific statements measuring the probability of being caught, probability of receiving a penalty, injunctive norm and self-imposed guilt for internal consistency.”
MethodThe Effect of Loading on Kinematic and Kinetic Variables During the Midthigh Clean Pull
Comfort, P., Udall, R., & Jones, P. A. (2012) · The Journal of Strength and Conditioning Research · doi:10.1519/jsc.0b013e3182510827n · Cited by 69
“Intraclass correlation coefficients (ICCs) were performed to determine the reliability of 1RM performances and to determine the repeatability of performances between repetitions for each dependent variable, using the criteria of Cortina (9), where r $ 0.”
MethodInfluentialJob insecurity in the younger Spanish workforce: Causes and consequences
Silla, J. M. P., Sora, B., & Caballer, A. (2011) · Journal of Vocational Behavior · doi:10.1016/j.jvb.2011.09.007 · Cited by 79
Kapoutsis, I., Papalexandris, A., Nikolopoulos, A. G., Hochwarter, W. A., & Ferris, G. R. (2010) · Journal of Vocational Behavior · doi:10.1016/j.jvb.2010.09.009 · Cited by 74
Development and Construct Validation of an Academic Emotions Scale
Govaerts, S. J., & Grégoire, J. C. (2008) · International Journal of Testing · doi:10.1080/15305050701808649 · Cited by 88
“Such indices are excellent, especially with rather small subscales comprised of three to six items (Cortina, 1993).”
BackgroundGreen, E. G. T., Sarrasin, O., Fasel, N., & Staerklé, C. (2011) · Swiss Political Science Review · doi:10.1111/j.1662-6370.2011.02030.x · Cited by 69
“70) partly due to the low number of items per score (Cortina 1993).”
BackgroundGroulx, M. W., Lemieux, C. J., Dawson, J., Stewart, E. J., & Yudina, O. (2016) · Journal of Sustainable Tourism · doi:10.1080/09669582.2015.1134556 · Cited by 69
“Levels of Chronbach’s alpha for the scales that measured visitor motivations (a D 0.87), NR (a D 0.81), place identity (a D 0.73) and concern for climate change (a D 0.75) all indicated acceptable internal reliability (Cortina, 1993).”
BackgroundInfluentialStandardized Usability Questionnaires
Sauro, J., & Lewis, J. R. (2012) · Elsevier eBooks · doi:10.1016/b978-0-12-384968-7.00008-4 · Cited by 80
User Acceptance of Usable Blockchain-Based Research Data Sharing System: An Extended TAM-Based Study
Shrestha, A. K., & Vassileva, J. (2019) · IEEE International Conference on Trust, Privacy and Security in Intelligent Systems and Applications (TPS-ISA) · doi:10.1109/tps-isa48467.2019.00033 · Cited by 80
“In practice, CR does not assume factor loadings to be the same for all items but take into consideration the varying factor loadings of the items, whereas Alpha assumes factor loadings to be the same for all items.”
BackgroundMethodInfluentialTrigg, R., & WOOD, V. A. (2000) · Clinical Rehabilitation · doi:10.1191/026921500678119607 · Cited by 69
Han, T., Nunes, V. X., Souza, L. F. D. F., Marques, A. G., Silva, I. C. L., Ferreira, M. A. A., Sun, J., & Filho, P. P. R. (2020) · IEEE Access · doi:10.1109/access.2020.2987932 · Cited by 69
“The value of the reliability coefficient (α) commonly adopted is 5%, and formore rigorous tests, a value of 3% [81].”
BackgroundMethodSoral, P., Pati, S., & Kakani, R. K. (2022) · Journal of business research · doi:10.1016/j.jbusres.2021.12.075 · Cited by 62
Kaba, B., & Osei-Bryson, K.-M. (2013) · International Journal of Information Management · doi:10.1016/j.ijinfomgt.2013.01.010 · Cited by 68
Dowrick, A. S., Wootten, A. C., Murphy, D. G., & Costello, A. J. (2015) · Urology · doi:10.1016/j.urology.2015.01.046 · Cited by 68
Computer-Assisted Therapies: Examination of Therapist-Level Barriers to Their Use
Becker, E. M., & Jensen-Doss, A. (2013) · Behavior Therapy · doi:10.1016/j.beth.2013.05.002 · Cited by 68
Gender-Blind Sexism and Rape Myth Acceptance’,
Stoll, L. C., Lilley, T. G., & Pinter, K. (2017) · Violence Against Women · doi:10.1177/1077801216636239 · Cited by 68
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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