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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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“On the other hand, alpha values tend to increase with both the number of items in a scale and with the average item intercorrelation (Cortina, 1993).”
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“Section 1: Self-Devaluation As anticipated, a scree plot in a principle components factor analysis (Cortina 1993) confirmed that items from the selfdevaluation section loaded on a single factor.”
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“of items in a scale as well as the average inter-item correlation (Cortina, 1993).”
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“Cronbach’s alpha was used to assess the internal consistency to determine how well a set of variables or items measured a single latent construct (Cortina, 1993).”
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“769, respectively, indicating that the scale had adequate internal consistency across both cultural groups (Cortina 1993; Nunnally and Bernstein 1994).”
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“is inappropriate for these indices ( Cortina, 1993”
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“These vary between 0 and 1, and generally a-values of 0.70 or above are considered acceptable (Andersen, Hansen, & Klemmensen, 2012; Cortina, 1992; Iacobucci, 2001; Spector, 1992).”
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“Cronbach’s alpha coefficients for each variable ranged from 0.695 (USE) to 0.950 (HM) (Table 2), which implies a sufficient (Cronbach’s alpha > 0.6) to good (Cronbach’s alpha > 0.8) reliability and construct reliability according to Cortina (1993).”
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“In fact, these correlations are comparable to what would be obtained from a scale of eight items with a Cronbach α of .80 (Cortina, 1993).”
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“The Cronbach’s alpha reliabilities for these three tests—interpretable as the mean of all possible Spearman–Brown corrected split-half reliabilities (Cortina, 1993)—are .90, .80, and .81 for CFMT, AAMT, and VPMT, respectively.”
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“Cortina (1993) points out that shorter scales often have lower alpha reliability estimates.”
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“The present study found acceptable indices (Cortina, 1993; Ntoumanis, 2005) for autonomous motivation (a1⁄4 0.”
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“70 are acceptable, Cortina (1983) has indicated that with scales possessing a reduced number of items (e.”
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“Thus, although providing an internal consistency index reflecting item homogeneity, coefficient alpha may not provide the best index of how well the scales measure what may be heterogeneous constructs (Cortina, 1993; Schmitt, 1996), particularly in the case of acquired capability, which is comprised of both experience…”
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“For example, in a recent review by Cortina (1993), he stated, “Cronbach’s alpha is a lower bound of reliability because essential tau equivalency is seldom if ever achieved” (p.”
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“It should also be noted that the computation of the alpha value is related to the number of items a scale contains, with a high number of items inflating this value (Cortina, 1993).”
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“measures having fewer items rather than a lack of internal consistency (Clark & Watson, 1995; Cortina, 1993 ).”
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“Moreover, a high MIC/alpha for the PID-5-BF scales might be undesirable because it could indicate an overrepresentation of one particular PID-5 trait of a domain rather than a representative sampling consistent with the goal of content validity.”
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“Cronbach’s alpha was computed to assess the internal reliability of each scale (Cortina, 1993).”
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“Cortina (1993) suggests although convention is to accept an a of > .70 as adequate, ‘‘the level of reliability that is adequate depends on the decision that is made with the scale.”
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“However, alpha coefficients have been criticized for being imperfect indicators of internal consistency due to their reliance on the number of test items in addition to intercorrelations among the items (see, e.g., Cortina, 1993).”
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“For example, coefficient α is a lower-bound estimate of reliability and approaches reliability as the items in an instrument become linearly related (Cortina, 1993).”
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“Thus, the low Cronbach's alpha could likely be a function of the low number of items (Cortina, 1993).”
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“7 are considered to indicate adequate reliability (Cortina, 1993).”
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“The r scales with less items [35, 36], a closer to 0.”
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“Following the method outlined by Cortina (1993) the inter-item and item-total correlations were examined for the two items making up this scale.”
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“Although Cronbach’s alpha may overestimate internal consistency for scales with large numbers of items (Cortina, 1993), the LSRPS has only 26 items.”
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“60 and above have been suggested to be acceptable in constructs containing fewer than six items (Cortina, 1993) and for exploratory research (Robinson, Shaver, & Wrightsman, 1991).”
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“Responses to the retained 41-items were subject to an exploratory factor analysis using principal components analysis without rotation, as suggested by Cortina (1993).”
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“70 was used in assessing the scales as suggested by Nunnally (1978) and Cortina (1993). All three scales provided alphas above the threshold level as shown in Table 3 (Knowledge Stock=.”
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“The internal consistency is usually calculated using an alpha coefficient, which measures the interrelationship between items in the questionnaire (Cortina, 1993).”
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“Finally, following standard survey research practices, confirmatory factor analysis described scale dimensionality and Cronbach’s a defined the internal consistency and reliability of multi-item measures (Cortina 1993; Table 1).”
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“90 on day 2 (Cronbach’s a is an estimator of a scale’s internal consistency [31,32], with values .”
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The Meaning of Work for Post-retirement Employment Decisions
Fasbender, U., Wang, M., Voltmer, J.-B., & Deller, J. (2015) · Work Aging and Retirement · doi:10.1093/workar/wav015 · Cited by 130
“Although scale reliabilities were partly unsatisfactory (likely due to the small number of items that were used of each scale; Cortina, 1993), confirmatory factor analysis supported the three factor structure for the social, personal, and generative meaning of work [χ2 (24) = 158.91, p < .001;…”
MethodInfluentialParental COVID-19 Vaccine Hesitancy in the United States
Ruiz, J. B., & Bell, R. A. (2022) · Public Health Reports · doi:10.1177/00333549221114346 · Cited by 129
Time management training and perceived control of time at work
Häfner, A., & Stock, A. (2010) · The Journal of Psychology · doi:10.1080/00223980.2010.496647 · Cited by 131
“79 (Cortina, 1993).”
Maternal scaffolding behavior: Links with parenting style and maternal education.
Carr, A., & Pike, A. (2011) · Developmental Psychology · doi:10.1037/a0025888 · Cited by 129
“Internal reliabilities for both the positive discipline ( .53 at T1, .74 at T2) and the negative discipline ( .53 at T1, .67 at T2) scales were reasonable, taking into account the small number of items and the effect that this has on alpha values (Cortina, 1993; Field, 2004).”
BackgroundDo UK universities communicate their brands effectively through their websites?
Chapleo, C., Durán, M. V. C., & Díaz, A. C. (2011) · Journal of Marketing for HIGHER EDUCATION · doi:10.1080/08841241.2011.569589 · Cited by 129
“In order to demonstrate that the main variables in the fuzzy logic approach were reliable, Cronbach's Alpha was utilised, as a common measure of variables reliability that reinforces applicability (Cortina, 1993 ; Cronbach, 1951 ; Field, 2005 ).”
MethodPutting the Family Into Family Business Research
Dyer, W. G., & Dyer, W. J. (2009) · Family Business Review · doi:10.1177/0894486509333042 · Cited by 129
“Most salient to this discussion is that alpha is biased unless the items are tau equivalent (i.e., covariance between each of the items must be the same; Cortina, 1993).”
BackgroundMeta-Heuristics in Short Scale Construction: Ant Colony Optimization and Genetic Algorithm
Schroeders, U., Wilhelm, O., & Olaru, G. (2016) · PLoS ONE · doi:10.1371/journal.pone.0167110 · Cited by 138
“It is easily demonstrated that high values of internal consistency (i.e., Cronbach’s α ) allow no conclusion about the underlying structure of the measure [19,21].”
BackgroundMethodLabor-Management Cooperation: Antecedents and Impact on Organizational Performance
Deery, S. J., & Iverson, R. D. (2005) · Industrial and Labor Relations Review · doi:10.1177/001979390505800404 · Cited by 129
Psychometric Issues in the ELL Assessment and Special Education Eligibility
Abedi, J. (2006) · Teachers College Record The Voice of Scholarship in Education · doi:10.1111/j.1467-9620.2006.00782.x · Cited by 130
Martinussen, L. M., Hakamies-Blomqvist, L., Møller, M., Özkan, T., & Lajunen, T. J. (2013) · Accident Analysis & Prevention · doi:10.1016/j.aap.2012.12.036 · Cited by 128
Scale validation in applied health research: tutorial for a 6-step R-based psychometrics protocol
Dima, A. L. (2018) · Health Psychology and Behavioral Medicine · doi:10.1080/21642850.2018.1472602 · Cited by 147
“…by a consistent body of methodological works criticizing the undiscriminating use of Cronbach’s α as indicator of reliability (term used often interchangeably with internal consistency) in applied research (Cortina, 1993; Dunn et al., 2014; Graham, 2006; Revelle & Zinbarg, 2009; Sijtsma, 2009).”
MethodFamily Firm Values Explaining Family Firm Heterogeneity
Rau, S. B., Schneider-Siebke, V., & Günther, C. (2019) · Family Business Review · doi:10.1177/0894486519846670 · Cited by 128
“Cronbach’s alpha for Factor 4 is below .50; however, how high the alpha should be for a data set with a particular amount of items is still a point of discussion (Cortina, 1993).”
BackgroundWatson, D., & Wu, K. D. (2005) · Assessment · doi:10.1177/1073191104271483 · Cited by 131
“Coefficient alphas are a function of both (a) scale length and (b) the average interitem correlation (see Clark & Watson, 1995; Cortina, 1993; Schmitt, 1996).”
BackgroundCIRCADIAN TYPOLOGY AND TEMPERAMENT AND CHARACTER PERSONALITY DIMENSIONS
Adán, A., Lachica, J., Caci, H. M., & Natale, V. (2010) · Chronobiology International · doi:10.3109/07420520903398559 · Cited by 128
“The internal consistency of the scales was estimated using Cronbach’s α coefficient, 0.70 being the minimum acceptable criterion (Cortina, 1993).”
MethodInfluentialValidity: Meaning and Relevancy in Assessment for Engineering Education Research
Douglas, K. A., & Purzer, Ş. (2015) · Journal of Engineering Education · doi:10.1002/jee.20070 · Cited by 132
“Educational measurement experts have extensively discussed the appropriate use of the coefficient alpha as a gauge for internal consistency and ways to increase consistency (Cortina, 1993; Schmitt, 1996; Weng, 2004).”
BackgroundAlpha Inflation? The Impact of Eliminating Scale Items on Cronbach's Alpha
Kopalle, P. K., & Lehmann, D. R. (1997) · Organizational Behavior and Human Decision Processes · doi:10.1006/obhd.1997.2702 · Cited by 127
Service Brand Relationship Quality
Nyffenegger, B., Krohmer, H., Hoyer, W. D., & Malär, L. (2014) · Journal of Service Research · doi:10.1177/1094670514547580 · Cited by 141
Assessing Causality and Persistence in Associations Between Family Dinners and Adolescent Well‐Being
Musick, K., & Meier, A. (2012) · Journal of Marriage and the Family · doi:10.1111/j.1741-3737.2012.00973.x · Cited by 127
“Kuder-Richardson coefficients for assessing the reliability of dichotomous items [Cortina, 1993]).”
MethodMeasuring the development of inhibitory control: The challenge of heterotypic continuity
Petersen, I. T., Hoyniak, C. P., McQuillan, M. E., Bates, J. E., & Staples, A. D. (2016) · Developmental Review · doi:10.1016/j.dr.2016.02.001 · Cited by 140
“Fifth, the measures should have high internal consistency (communality or equivalence) as measured by Cronbach’s alpha (Cortina, 1993) or McDonald’s total omega (Revelle & Zinbarg, 2009).”
MethodExploring teachers’ and students’ gender role bias and students’ confidence in STEM fields
Hand, S. B., Rice, L., & Greenlee, E. T. (2017) · Social Psychology of Education · doi:10.1007/s11218-017-9408-8 · Cited by 155
Holmes, A. F., & Douglass, A. (2021) · Journal of Emerging Technologies in Accounting · doi:10.2308/jeta-2020-054 · Cited by 153
An exploration of residents’ low-carbon awareness and behavior in Tianjin, China
Bai, Y., & Liu, Y. (2013) · Energy Policy · doi:10.1016/j.enpol.2013.06.014 · Cited by 123
Martinussen, L. M., Møller, M., & Prato, C. G. (2014) · Transportation Research Part F Traffic Psychology and Behaviour · doi:10.1016/j.trf.2014.06.008 · Cited by 126
“Acceptable high Cronbach’s alpha is 0.70 and above (Cortina, 1993), which is also in line with the original DBQ study and other previous DBQ studies (see Lajunen, Parker, & Summala, 2004; Özkan, Lajunen, Chliaoutakis, Parker, & Summala, 2006a; Reason et al., 1990).”
ResultInfluential
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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