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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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“…considered to indicate acceptable, if not desirable, internalconsistencygiven thateachsubscaleconsistedof only five items and that this study reflected only the very early stages of research on CFD as a psychological construct (Cortina, 1993; DeVellis, 1991; Nunnally, 1967, 1978; Streiner, 2003).”
BackgroundCoefficient Alpha: A Reliability Coefficient for the 21st Century?
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“We adopt the distinction made by Cortina (1993), Green, Lissitz, and Mulaik (1977), and Schmitt (1996) in discussing coefficient alpha that internal consistency is the interrelatedness among items (i.e., the average interitem correlation), whereas homogeneity is the degree that items are…”
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“However, alpha is also affected by the length of the scale, so that instruments that have more than 15 items may show high values even if the items reflect different underlying constructs (Cortina 1993).”
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“Cortina (1993) warned that the number of items used to build a scale must be taken into consideration when interpreting alpha, noting that a 10-item scale with an alpha of .80 will have a lower mean inter-item correlation (.28) when compared to a 3-item scale with the same alpha level (mean…”
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“However, the a coefficient is only an estimate of the reliability of a total score and does not inform us about the dimensionality of the item set, for which factor analysis is needed (Cortina, 1993; Schmitt, 1996).”
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“Cortina (1993) descreve outras interpretações para o índice de Cronbach, referindo que o α é uma medida estável de fiabilidade pois não está sujeito à variabilidade resultante da forma como o instrumento ou teste é dividido para calcular a fiabilidade split-half.”
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“Differences in internal consistencies between the two forms are unsurprising given that alpha increases with the number of items in a measure (Cortina, 1993).”
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“These workflow integration measures are formative scales, hence Cronbach’s alpha is not a relevant measure (Cortina, 1993; Diamantopoulos & Siguaw, 2006).”
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“Checklist score reliability was estimated in 2 ways: (a) interrater reliability was calculated using the k coefficient(37) adjusted using the formula of Brennan and Prediger,(38) while (b) internal consistency reliability was derived using Cronbach’s a coefficient.(39) Within-group differences from pretest (baseline)…”
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“Because high internal consistency reliability, as commonly measured by coefficient α, does not necessarily guarantee high test-retest reliability (Cortina, 1993; Crocker & Algina, 1986), the impact of scale design on test-retest reliability warrants direct investigation.”
BackgroundMethodResultInfluentialMeasures of Cognitive Functioning in the AHEAD Study
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“The coefficient alpha (Cortina, 1993) provides an indication of the reliability of a multi-item index.”
BackgroundDevelopment and Validation of a Rasch-Derived CES-D Short Form.
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“This trade-off can be mitigated by increasing the number of items used to construct the composite scores, but that strategy can result in an instrument so long that respondents find it burdensome to complete (Cortina, 1993; Ghiselli, 1964). We sought to sample the domain of each construct widely but also to keep the T…”
BackgroundMethodTesting the Difference Between Reliability Coefficients Alpha and Omega
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“…of reliability of the total score have been developed, including coefficient alpha (also referred to as Cronbach’s alpha; Cronbach, 1951; see also Cortina, 1993; Raykov, 1997; Raykov& Marcoulides, 2011, 2015), coefficient omega (McDonald, 1999), the greatest lower bound reliability (Bentler,…”
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“…consistencies (i.e., Cronbach's coefficient alpha; Cronbach, 1951) will necessarily be found for any task that makes use of a large number of trials ( " items " ) that do not systematically differ in their difficulty or content (Cortina, 1993), the other criteria are important to demonstrate.”
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“6 is a moderate level of reliability for scales with reduced number of items (Cortina, 1993; Hatcher, 1994; Nunnally, 1978).”
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“The most commonly reported estimate of reliability, coefficient alpha, refers to internal consistency reliability, the degree that items of a given scale are measuring the same construct (Cortina, 1993).”
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“Many users perform the reverse; they calculate reliability to identify unidimensionality, misconceiving that a high value of a unidimensional reliability coefficient indicates unidimensionality (Cortina, 1993; Green, Lissitz, & Mulaik, 1977; Hattie, 1985; Schmitt, 1996).”
BackgroundTeacher self-efficacy: a classroom-organization conceptualization
Friedman, I. A., & Kass, E. (2002) · Teaching and Teacher Education · doi:10.1016/s0742-051x(02)00027-6 · Cited by 380
“The coefficient alpha is the function of the extent to which items in a test have commonalties and is the lower limit of the reliability of a set of test scores (Cortina, 1993).”
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“…opportunities for meaningful participation construct is slightly below the commonly accepted cutoff for good reliability attributed to Nunnally (1978), although this construct was also made up of the fewest items, and a small number of items in a scale strongly reduces alpha values (Cortina 1993).”
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“It is also important to note that alpha scores are sensitive to the number of items (Cortina 1993; Engs and Hanson 1994); therefore, although Cronbach’s alpha for the time sub-construct was low, it was deemed acceptable based on the conceptual consistency of items and the small number of items.”
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“The only exception was for the imaginal processes facet scale from the community sample; however, as indicated by Cortina [”
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“…intenion (α = .63) but still indicates reasonable internal consistency. unnally (1978) suggested that α = .70 represents strong inner onsistency, but Cortina (1993) urges researchers to consider he number of items used—a moderate alpha with small number f items (as here) may well represent…”
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“When a factor only includes a few items (Cortina, 1993; Nunnally & Bernstein, 1994), however, values between .”
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“Cortina (1993) discusses alpha in considerable depth, noting that the same mean inter-item correlation will yield higher alpha coefficients for longer scales than shorter scales, and advises cautious interpretation.”
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“However, intercomponent correlations that cluster into subgroups indicate heterogeneity (Cortina, 1993).”
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“As shown in Table 1, the values of Cronbach’s alpha and CR in all constructs were higher than the acceptable level of .7 (Bagozzi & Yi, 1988; Cortina, 1993).”
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“The value of α is determined through number of quality measurement items in a construct, their inter relatedness and homogeneity (Cortina 1993).”
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“However, the items were not excluded because coefficient alpha value tends to be low when the number of items is low (Cortina, 1993).”
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“It is well known, however, that coefficient alpha is a conservative estimate of reliability and is influenced by the number of items (Cortina, 1993).”
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“Time and again, the positive impact of test length on reliability has been invoked to demonstrate this; see, for instance, Cortina (1993) and Schmitt (1996).”
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“Although the reliability of the job satisfaction variable was high given the limited number of items (Cortina, 1993), some degree of measurement error remains.”
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“68) maintained acceptable internal consistency (Cortina, 1983).”
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“, Cronbach’s alpha [18]) and validity (i.”
A meta-analysis of interrater and internal consistency reliability of selection interviews.
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“To determine whether to retain or eliminate the factor, the inter-item correlations of the three novelty items were examined using Principal Components Analysis (PCA) (Cortina, 1993).”
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Commentary on Coefficient Alpha: A Cautionary Tale
Green, S. B., & Yang, Y. (2008) · Psychometrika · doi:10.1007/s11336-008-9098-4 · Cited by 316
“The argument against alpha to assess internal consistency is relatively transparent and has been made multiple times in the literature (e.g., Cortina, 1993, Green, Lissitz, & Mulaik, 1977); nevertheless, this interpretation persists.”
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“Cronbach’s Alphas ranged from .60 to .88 (Table 3) for all scales, which is satisfactory for this stage of research (DeVellis, 1991) and considering the low number of items per scale (Cortina, 1993).”
Gielnik, M. M., Frese, M., Kahara-Kawuki, A., Wasswa Katono, I., Kyejjusa, S., Ngoma, M., Munene, J., Namatovu-Dawa, R., Nansubuga, F., Orobia, L., et al. (2015) · Academy of Management Learning & Education · doi:10.5465/amle.2012.0107 · Cited by 305
“70) was satisfactory for such a short scale (Cortina, 1993).”
BackgroundVerheul, R., Andrea, H., Berghout, C. C., Dolan, C. V., Busschbach, J. J. V., van der Kroft, P. J. A., BATEMAN, A. W., & Fonagy, P. (2008) · Psychological Assessment · doi:10.1037/1040-3590.20.1.23 · Cited by 318
“Given the relatively small number of items per facet (i.e., seven or eight), an alpha of at least .70 was considered acceptable (Cortina, 1993; Kline, 1999).”
BackgroundUse of exploratory factor analysis in maritime research
Maskey, R., Fei, J., & Nguyen, H.-O. (2018) · The Asian Journal of Shipping and Logistics · doi:10.1016/j.ajsl.2018.06.006 · Cited by 327
“…2018 The Korean Association of Shipping and Logistics, Inc. Production and hosting by Elsevier B.V. Peer review under responsibility of the Korean Association of Shipping and Logistics, Inc. variables) (Cortina, 1993, Henson and Roberts, 2006, Tabachnick and Fidell, 2007).”
BackgroundDevelopment and Content Validation of a "Hyperdimensional" Taxonomy of Managerial Competence
Tett, R. P., Guterman, H. A., Bleier, A., & Murphy, P. J. (2000) · Human Performance · doi:10.1207/s15327043hup1303_1 · Cited by 297
“It is also a function of how strongly the test items are intercorrelated, that is, the degree to which the items are internally consistent (Cortina,1993).”
Reassessing the Foundations of Customer Delight
Finn, A. H. R. (2005) · Journal of Service Research · doi:10.1177/1094670505279340 · Cited by 301
Diefendorff, J. M., Hall, R. J., Lord, R. G., & Strean, M. L. (2000) · Journal of Applied Psychology · doi:10.1037/0021-9010.85.2.250 · Cited by 294
“…consistency estimates based on alpha are likely underestimates given that the items are dichotomous and do not meet tau-equivalence conditions (Cortina, 1993, p. 101), and (b) the slight drop in internal consistency that may have occurred is offset by improved definition of the three latent…”
BackgroundGird, A., & Bagraim, J. J. (2008) · South African Journal of Psychology · doi:10.1177/008124630803800410 · Cited by 295
“Cronbach alpha coefficients are therefore inappropriate as more than one factor is responsible for the correlations amongst the items in the attitudes towards entrepreneurship measure (Cortina, 1993).”
BackgroundKuenzi, M., Mayer, D. M., & Greenbaum, R. L. (2020) · Personnel Psychology · doi:10.1111/peps.12356 · Cited by 300
“We also assessed the reliability of the six-item EOC using Cronbach’s alpha (Cortina, 1993).”
MethodCarretero‐Dios, H., & Pérez, C. (2007) · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · Cited by 279
Hönekopp, J. (2006) · Journal of Experimental Psychology Human Perception & Performance · doi:10.1037/0096-1523.32.2.199 · Cited by 294
“…is the sum of all elements in the variance–covariance matrix (this computation being based on the assumption that all judges’ variances are equal; Cortina, 1993). rated: Such hypotheses have had a beneficial effect on facialattractiveness research by providing theoretical guidelines (e.g.,…”
BackgroundInfluentialPodsakoff, P. M., & MacKenzie, S. B. (1994) · Journal of Applied Psychology · doi:10.1037/0021-9010.79.5.702 · Cited by 306
More than money: Developing an integrative multi-factorial measure of entrepreneurial success
Wach, D., Stephan, U., & Gorgievski, M. J. (2015) · International Small Business Journal Researching Entrepreneurship · doi:10.1177/0266242615608469 · Cited by 318
“New scales often suffer from this problem, especially when the number of items is low (Cortina, 1993).”
BackgroundWhat makes a video go viral? An analysis of emotional contagion and Internet memes
Guadagno, R. E., Rempala, D. M., Murphy, S., & Okdie, B. M. (2013) · Computers in Human Behavior · doi:10.1016/j.chb.2013.04.016 · Cited by 280
“For the current sample, the Joy (a = .77), Interest (a = .51), and Activation (a = .70) subscales showed lower reliability than the Afraid and Upset subscales, but this is predictable, given the few items in the reliability analysis (Cortina, 1993).”
Leadership effects on organizational climate and financial performance
Koene, B. A. S., Vogelaar, A. L. W., & Soeters, J. L. (2002) · The Leadership Quarterly · doi:10.1016/s1048-9843(02)00103-0 · Cited by 299
Jang, J., Ko, Y., Shin, W. S., & Han, I. (2021) · IEEE Access · doi:10.1109/access.2020.3048708 · Cited by 334
Bruneel, J., Yli‐Renko, H., & Clarysse, B. (2010) · Strategic Entrepreneurship Journal · doi:10.1002/sej.89 · Cited by 288
Household Context and Subjective Well-Being Among the Oldest Old in China
Chen, F., & Short, S. E. (2008) · Journal of Family Issues · doi:10.1177/0192513x07313602 · Cited by 285
“Because alpha is known to be positively correlated to number of items used ( Cortina, 1993 ), our indices are indeed reasonable, given that we use three items to construct each.”
MethodCoefficient Alpha: Interpret With Caution
Panayiotis Panayides, A. (2013) · Europe’s Journal of Psychology · doi:10.5964/ejop.v9i4.653 · Cited by 277
“Cortina (1993) cited a series of definitions and descriptions of alpha and then proceeded to incorporate these in the following description of alpha: It is a function of the extent to which items in a test have high communalities and thus low uniquenesses.”
InfluentialTreating Cronbach’s Alpha Reliability Coefficients as Data in Counseling Research
Helms, J. E., Henze, K. T., Sass, T. L., & Mifsud, V. A. (2006) · The Counseling Psychologist · doi:10.1177/0011000006288308 · Cited by 276
“Our discussion focuses on Cronbach’s (1951) coefficient alpha (hereafter alpha) because, reportedly, it is the most frequently used procedure for estimating reliability in applied psychology (e.g., Cortina, 1993; Peterson, 1994).”
BackgroundMethodInfluentialAltruism, Helping, and Volunteering
Kahana, E. F., Bhatta, T. R., Lovegreen, L. D., Kahana, B., & Midlarsky, E. (2013) · Journal of Aging and Health · doi:10.1177/0898264312469665 · Cited by 322
“The number of items is a major determinant of Cronbach’s α estimate, because an increase in number of items can, independent of other factors, improve Cronbach’s α estimate (Cortina, 1993).”
BackgroundAdaptation of the Functional Independence Measure for use in Turkey
Küçükdeveci, A. A., Yavuzer, G., Elhan, A. H., Sonel, B., & Tennant, A. (2001) · Clinical Rehabilitation · doi:10.1191/026921501676877265 · Cited by 276
Qualitative Attributes and Measurement Properties of Physical Activity Questionnaires: A Checklist
Terwee, C. B., Mokkink, L. B., van Poppel, M. N. M., Chinapaw, M. J. M., van Mechelen, W., & de Vet, H. C. W. (2010) · Sports Medicine · doi:10.2165/11531370-000000000-00000 · Cited by 269
“Internal consistency is the degree of the inter-relatedness among the items of a questionnaire, generally assessed by Cronbach’s alpha.([45]) It is an important measurement property for uni-dimensional scales, consisting of homogeneous items that all reflect the construct to be measured.”
MethodSport involvement: A conceptual and empirical analysis
Beaton, A. A., Funk, D. C., Ridinger, L. L., & Jordan, J. S. (2010) · Sport Management Review · doi:10.1016/j.smr.2010.07.002 · Cited by 275
Trust in the Police: The Influence of Procedural Justice and Perceived Collective Efficacy
Nix, J., Wolfe, S. E., Rojek, J., & Kaminski, R. J. (2015) · Crime & Delinquency · doi:10.1177/0011128714530548 · Cited by 274
“The items also demonstrated strong internal consistency (α = .94; see, for example, Cortina, 1993) and, therefore, were summed to form an additive procedural justice scale with higher scores indicating more favorable evaluations of police fairness.”
MethodKyle, G. T., Graefe, A. R., Manning, R. E., & Bacon, J. (2004) · Journal of Leisure Research · doi:10.1080/00222216.2004.11950020 · Cited by 272
“70 are acceptable, Cortina (1983) has indicated that in scales with a reduced number of items (e.”
BackgroundReevaluating the Identity Status Paradigm: Still Useful after 35 Years
Berzonsky, M. D., & Adams, G. R. (1999) · Developmental Review · doi:10.1006/drev.1999.0495 · Cited by 271
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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