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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
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“If, however, a factor has a reduced number of items (e.g., 6 or fewer), .60 and higher may be acceptable (Cortina 1993).”
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“If its basic assumptions are violated, alpha may either over or under estimate the population reliability (Cortina, 1993; Green & Hershberger, 2000; Green, Lissitz, & Mulaik, 1977; Novick & Lewis, 1967; Raykov, 2001a).”
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“Cronbach ’ s α is weak evidence of construct validity because it: (a) is strongly in fl uenced by the number of items/indicators in the measure, (b) is a lower bound estimate of reliability, (c) does not address convergent or discriminant validity between constructs, and (d) assumes that the combined items/indicators a…”
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“Because coefficient alpha is dependent on the number of items a measure contains (Cortina, 1993), we examined the possibility that the mean number of items found in noncontextualized personality measures differed from the number of items found in contextualized measures.”
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“This is largely independent of whether the questions represent one or more dimensions (Cortina, 1993).”
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“7 is considered to be the lower bounds for inclusion of a scale (Nunnally 1978 ; Cortina 1993 ), further testing following the method outlined by Cortina ( 1993 ) and examination of the inter-item and item-total correlations were carried out on the two items making up this scale.”
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“This approach was based on the assumption that test items within each strand or subscale were measuring the same construct; that is, they were unidimensional (see Cortina, 1993).”
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“The alpha coeffi cients for admiration and contempt are relatively low, according to Rosenthal and Rosnow (1991), but not exceptionally so, given that both variables are composed of only two items (Cortina, 1993).”
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Schwarzer, R., Łuszczyńska, A., Ziegelmann, J. P., Scholz, U., & Lippke, S. (2008) · Health Psychology · doi:10.1037/0278-6133.27.1(suppl.).s54 · Cited by 256
OKOYE, K. O., Hussein, H., Arrona‐Palacios, A., Milián, H. N. Q., Ortega, L. O. P., Sanchez, A. L., Ortiz, E. A., Escamilla, J., & Hosseini, S. (2022) · Education and Information Technologies · doi:10.1007/s10639-022-11214-1 · Cited by 414
“…and multiple-choice questions with varying scales of measurement, including also an open-ended question, the study applied a factorial analysis (Cortina, 1993; Green et al., 1977; Jasper, 2010; Tate, 2003; Tavakol & Dennick, 2011) for the purpose of comparison and validation of the dataset,…”
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Scale quality: alpha is an inadequate estimate and factor-analytic evidence is needed first of all
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“An extensive literature is available explaining the technical background for this argument (Cortina, 1993; Dunn, Baguley, & Brunsden, 2014; Graham, 2006; Revelle & Zinbarg, 2009; Sijtsma, 2009).”
BackgroundFischer, R. D., & Boer, D. (2011) · Journal of Personality and Social Psychology · doi:10.1037/a0023663 · Cited by 263
“Several authors (Cortina, 1993b; Ganzach, 1997) have recommended that with correlated predictor variables, interactions need to be tested with the quadratic terms controlled.”
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“Cronbach's alpha is one of the most commonmethods that researchers employ to demonstrate the coherence of scales; however, this statistic does not demonstrate unidimensionality (Cortina, 1993; Schmitt, 1996), so a high alpha is no assurance that a particular scale taps one and only one latent construct.”
BackgroundA short, valid, predictive measure of work–family conflict: Item selection and scale validation.
Matthews, R. A., Kath, L. M., & Barnes-Farrell, J. L. (2010) · Journal of Occupational Health Psychology · doi:10.1037/a0017443 · Cited by 255
Calcular la fiabilidad de un cuestionario o escala mediante el SPSS: el coeficiente alfa de Cronbach
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“El coeficiente alfa de Cronbach es una fórmula general para estimar la fiabilidad de un instrumento en el que la respuesta a los ítems es dicotómica o tiene más de dos valores (Aiken, 2003; Cortina, 1993), como por ejemplo en una escala de actitudes con respuesta de tipo Likert.”
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“7 for combining variables into a single construct (Cortina, 1993).”
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“All scales used in this study meet the Mokken criteria, their unidimensionality was good (Loevinger’ s H of at least .40), and their internal consistency was good too (Cronbach’s a of at least .75; cf. Cortina, 1993).”
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“2 MIIC ‡ 0Æ25 was considered as being a sufficient level of internal consistency or reliability.”
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“Cronbach (1951) and more recently Cortina (1993) and Schmitt (1996) argued that the appropriate interpretation of an estimate of internal consistency depends on the assumptions met.”
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“An acceptable range of Cronbach’s alpha is normally considered >0.70 (Cortina, 1993).”
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“In addition, a reliability coefficient will generally increase as the number of items increase and as the variance of the scores across subjects increase (Cortina 1983; Crocker and Algina 1986; Peter 1979), with low reliability coefficients shown to result from low score variance (e.”
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“However, alpha is a function of the number of items in a scale (Cortina, 1993).”
BackgroundEffect of Variability on Cronbach Alpha Reliability in Research Practice
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“Cortina reported that in a review of the Social Sciences Citations Index (SCCI) for the literature from 1966 to 1990, Cronbach’s 1951 article had been cited nearly 60 times every year in a total of 278 different journals that wrap a variety of research fields including not only psychology but also education, sociology…”
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“with Cronbach’s alpha (Cronbach 1951; Cortina 1993) using the pilot study participants and meeting a target alpha of 0.”
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“However, it is now generally accepted that it is only indicative of the extent to which the constituent items are inter-related [13].”
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“An ⍺ of over .70 was considered acceptable (Cortina 1993).”
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“In other words, in contrast to the previous semesters when the items were stated in negative terms, eliminating the two items in their direct positive form would hurt the internal consistency reliability of the scale (not to be confused with ‘unidimensionality’; see Cortina 1993 ).”
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“The Cronbach alpha reliability coeffi cient for these questions is 0.74, which well exceeds the recommended minimum of 0.6 for combining them into one measure ( Cortina, 1993 ).”
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“First, it is important to note that Cronbach’s coefficient alpha is a conservative estimate of reliability and is greatly influenced by the number of items used (Cortina, 1993).”
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“Although some scales had alpha values lower than the recommended 0.70 criterion, it should be noted that alpha coefficients are highly dependent upon the number of items (Cortina, 1993; Schmitt, 1996).”
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“7) suggested the possible existence of additional subscales within that scale [57].”
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“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.”
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“Given that each factor scale has only three items, these Cronbach's alphas appear reasonable as the number of items has been shown to heavily affect a (Cortina 1993).”
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“” This scale’s modest alpha level may be a function of its small number of items (Bernardi, 1994; Cortina, 1993).”
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“When measuring this construct, the use of multiple items may result in question redundancy ( Cortina, 1993”
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“The items also demonstrated strong internal consistency (α = .87; see, e.g., Cortina, 1993) and, as such, were summed into an index.”
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“Even weakly correlated ratings of targets will have high alphas provided enough perceivers are included (Cortina, 1993).”
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“Loadings are generally above the accepted threshold of 0.7 (Cortina, 1993; Cronbach, 1951), both for indicators and first-order factors related to reflective higher-order constructs.”
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Within-Person Variability in Job Performance
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“However, coefficient alpha assesses only item-specific errors (i.e., errors on account of the use of different items for a focal unidimensional measure; Cortina, 1993).”
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“Although at first glance this a may appear to be low, it must be remembered that holding average item intercorrelation constant, increasing the number of items increases a (Cortina 1993; Streiner 2003).”
Reliability and validity of a short form of the Marijuana Craving Questionnaire
Heishman, S. J., Evans, R. J., Singleton, E. G., Levin, K. H., Copersino, M. L., & Gorelick, D. A. (2009) · Drug and Alcohol Dependence · doi:10.1016/j.drugalcdep.2008.12.010 · Cited by 212
“Although there is no commonly agreed minimum alpha level (Cortina, 1993; Schmitt, 1996), 0.70 has become convention (Nunnally, 1978).”
BackgroundMethodInfluentialThe Asian American Values Scale--Multidimensional: Development, reliability, and validity.
Kim, B. K., Li, L. C., & Ng, G. F. (2005) · Cultural Diversity & Ethnic Minority Psychology · doi:10.1037/1099-9809.11.3.187 · Cited by 212
“However, it should be noted that the coefficient alpha, which is strongly influenced by test length, especially if there are 40 items or more, could be irrelevant for the AAVS–M total (Cortina, 1993).”
BackgroundMulticultural Employees: A Framework for Understanding How They Contribute to Organizations
Fitzsimmons, S. (2013) · Academy of Management Review · doi:10.5465/amr.2011.0234 · Cited by 209
Self-Reported Morisky Score for Identifying Nonadherence with Cardiovascular Medications
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JONGE, J. D., Mulder, M. J. G. P., & Nijhuis, F. J. N. (1999) · Social Science & Medicine · doi:10.1016/s0277-9536(98)00429-8 · Cited by 224
Tett, R. P., Fox, K. E., & Wang, A. (2005) · Personality and Social Psychology Bulletin · doi:10.1177/0146167204272860 · Cited by 221
“Considered as a multidimensional construct, trait-EI might be expected to yield weaker alphas when all items are included in the calculation (Cortina, 1993).”
BackgroundReliability reconsidered: Cronbach's alpha and paediatric assessment in occupational therapy
Spiliotopoulou, G. (2009) · Australian Occupational Therapy Journal · doi:10.1111/j.1440-1630.2009.00785.x · Cited by 211
Stebbings, J., Taylor, I. M., Spray, C. M., & Ntoumanis, N. (2012) · Journal of Sport and Exercise Psychology · doi:10.1123/jsep.34.4.481 · Cited by 237
“This may be attributable to the low number of items to measure the constructs (three items in each subscale; Cortina, 1993); therefore, we retained these subscales because all the observed items loaded strongly onto their corresponding latent factors (i.”
BackgroundKaswan, M. S., & Rathi, R. (2019) · Journal of Cleaner Production · doi:10.1016/j.jclepro.2019.05.253 · Cited by 210
Volunteering, subjective well-being and public policy
Binder, M., & Freytag, A. (2012) · Journal of Economic Psychology · doi:10.1016/j.joep.2012.11.008 · Cited by 233
Love & Loans The Effect of Race, Beauty and Personal Characteristics in Credit Markets 1Preprint
Ravina, E. (2008) · SSRN Electronic Journal · doi:10.2139/ssrn.1107307 · Cited by 209
“See Cortina (1993) for more details on reliability analysis.”
Bartels, A. L., Peterson, S. J., & Reina, C. S. (2019) · PLoS ONE · doi:10.1371/journal.pone.0215957 · Cited by 286
“Altogether, the improvement of model fit for a two-factor model when compared to a one-factor model and the strong interrelationships among the two dimensions support the two-dimensional structure [75]; therefore, Hypothesis 1 is supported.”
ResultAn approach to the implementation of sustainability practices in Spanish universities
Larrán Jorge, M., Herrera Madueño, J., Calzado Cejas, M. Y., & Andrades Peña, F. J. (2015) · Journal of Cleaner Production · doi:10.1016/j.jclepro.2014.07.035 · Cited by 207
Congruence and Functions of Personal and Cultural Values: Do My Values Reflect My Culture’s Values?
Fischer, R. D. (2006) · Personality and Social Psychology Bulletin · doi:10.1177/0146167206291425 · Cited by 218
“The reliabilities were .64 and .49, which is comparable to reliabilities reported by Bardi and Schwartz (2003) and which is reasonable given the number of items (Cortina, 1993).”
ResultStatistical power as a function of Cronbach alpha of instrument questionnaire items
Heo, M., Kim, N., & Faith, M. S. (2015) · BMC Medical Research Methodology · doi:10.1186/s12874-015-0070-6 · Cited by 207
The roles of firms' motives in affecting the outcomes of ISO 9000 adoption
Prajogo, D. I. (2011) · International Journal of Operations & Production Management · doi:10.1108/01443571111098753 · Cited by 206
Graziotin, D., Wang, X., & Abrahamsson, P. (2014) · PeerJ · doi:10.7717/peerj.289 · Cited by 206
Individualism-collectivism as Descriptive Norms
Fischer, R. D., Ferreira, M. C., Assmar, E. M. L., Redford, P., Harb, C., Glazer, S., Cheng, B., Jiang, D., Wong, C. C., Kumar, N., et al. (2009) · Journal of Cross-Cultural Psychology · doi:10.1177/0022022109332738 · Cited by 206
Creating inclusive classrooms by engaging STEM faculty in culturally responsive teaching workshops
O’Leary, E. S., Shapiro, C. A., Toma, S., Sayson, H. W., Levis‐Fitzgerald, M., Johnson, T., & Sork, V. L. (2020) · International Journal of STEM Education · doi:10.1186/s40594-020-00230-7 · Cited by 241
“, relevant survey items), their factor loading values, and the Cronbach’s alpha measuring reliability for both constructs (Cortina, 1993; Cronbach, 1951; Thompson, 2004).”
BackgroundBifactor Modeling and the Estimation of Model-Based Reliability in the WAIS-IV
Gignac, G. E., & Watkins, M. W. (2013) · Multivariate Behavioral Research · doi:10.1080/00273171.2013.804398 · Cited by 200
“As per Cortina (1993), coefficient ’ may be formulated as ’ D k2 COV P S2; COV (1) where k D number of indicators associated with the scale, COV D mean interindicator covariance, and P S2 COV D the sum of the square variance/covariance matrix (i.e., composite score variance).”
BackgroundThe Impact of Negative Publicity on Police Self-legitimacy
Nix, J., & Wolfe, S. E. (2015) · Justice Quarterly · doi:10.1080/07418825.2015.1102954 · Cited by 205
Classical and Modern Methods of Psychological Scale Construction
Simms, L. J. (2007) · Social and Personality Psychology Compass · doi:10.1111/j.1751-9004.2007.00044.x · Cited by 206
Play It Again, Sam! An Analysis of Constructive Replication in the Organizational Sciences
Köhler, T., & Cortina, J. M. (2019) · Journal of Management · doi:10.1177/0149206319843985 · Cited by 212
“The number of studies that contain such substantive moderators has been growing steadily for decades (Aguinis, Edwards, & Bradley, 2017; Cortina, 1993).”
BackgroundSelf-citationLuoma, J. B., O’Hair, A., Kohlenberg, B. S., Hayes, S. C., & Fletcher, L. B. (2009) · Substance Use & Misuse · doi:10.3109/10826080902864712 · Cited by 212
“Responses to the remaining eight items were subject to an exploratory factor analysis using principal components analysis without rotation, as suggested by Cortina (1993).”
MethodThe role of message framing in promoting MMR vaccination: Evidence of a loss-frame advantage
Abhyankar, P., O'Connor, D. B., & Lawton, R. (2007) · Psychology Health & Medicine · doi:10.1080/13548500701235732 · Cited by 210
“We acknowledge that the Cronbach’s alpha for PBC is below the satisfactory threshold (5.70, Cortina, 1993), although, it was retained in the analysis, for completeness, as exclusion did not alter the results.”
ResultInfluentialFactors influencing willingness-to-pay for the ENERGY STAR ® label
Ward, D., Clark, C. D., Jensen, K. L., Yen, S. T., & Russell, C. S. (2011) · Energy Policy · doi:10.1016/j.enpol.2010.12.017 · Cited by 211
Investigating the relationship between product involvement and consumer decision‐making styles
Bauer, H. H., Sauer, N. E., & Becker, C. (2006) · Journal of Consumer Behaviour · doi:10.1002/cb.185 · Cited by 199
Chang, S., Hsu, T., & Jong, M. S. (2019) · Computers & Education · doi:10.1016/j.compedu.2019.103758 · Cited by 212
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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