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Tenko Raykov - One of the best experts on this subject based on the ideXlab platform.
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Strong Convergence of the Coefficient Alpha Estimator for Reliability of Multiple-Component Measuring Instruments
Structural Equation Modeling: A Multidisciplinary Journal, 2018Co-Authors: Tenko RaykovAbstract:It is shown that in general the popular Coefficient Alpha estimator for reliability of multi-component measuring instruments converges almost surely to a quantity that is not equal to the population reliability Coefficient. This convergence with probability 1 is a stronger statement than convergence in probability (consistency) and convergence in distribution for the Alpha estimator, which have been studied in the past. In the special case of congeneric measures with uncorrelated errors and equal loadings on the common true score, the Alpha estimator converges almost surely to the population reliability Coefficient that equals population Alpha, which implies also its consistency as a reliability estimator. When the loadings are unequal but sufficiently high and similar, the Alpha estimator converges almost surely to population Alpha that is essentially indistinguishable from the population reliability Coefficient, which implies Alpha’s approximate consistency then. For the general case, the results entail...
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Multiple-Component Measurement Instruments in Heterogeneous Populations: Is There a Single Coefficient Alpha?
Educational and psychological measurement, 2017Co-Authors: Tenko Raykov, George A. Marcoulides, Michael Harrison, Natalja MenoldAbstract:This note confronts the common use of a single Coefficient Alpha as an index informing about reliability of a multicomponent measurement instrument in a heterogeneous population. Two or more Alpha Coefficients could instead be meaningfully associated with a given instrument in finite mixture settings, and this may be increasingly more likely the case in empirical educational and psychological research. It is argued that in such situations explicit examination of class-invariance in the Alpha Coefficient must precede any statements about its possible value in the studied population. The approach permits also the evaluation of between-class Alpha differences as well as point and interval estimation of the within-class Alpha Coefficients. The method can similarly be used in situations with (a) known class membership when distinct (sub)populations are investigated while their number is known beforehand and membership in them is observed for studied persons, as well as (b) in settings where only the number of latent classes is known for a population under investigation. The outlined procedure is illustrated with numerical data.
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Thanks Coefficient Alpha, We Still Need You!.
Educational and psychological measurement, 2017Co-Authors: Tenko Raykov, George A. MarcoulidesAbstract:This note discusses the merits of Coefficient Alpha and their conditions in light of recent critical publications that miss out on significant research findings over the past several decades. That earlier research has demonstrated the empirical relevance and utility of Coefficient Alpha under certain empirical circumstances. The article highlights the fact that as an index aimed at informing about multiple-component measuring instrument reliability, Coefficient Alpha is dependable then as a reliability estimator. Therefore, Alpha should remain in service when these conditions are fulfilled and not be abandoned.
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a direct latent variable modeling based method for point and interval estimation of Coefficient Alpha
Educational and Psychological Measurement, 2015Co-Authors: Tenko Raykov, George A. MarcoulidesAbstract:A direct approach to point and interval estimation of Cronbach’s Coefficient Alpha for multiple component measuring instruments is outlined. The procedure is based on a latent variable modeling application with widely circulated software. As a by-product, using sample data the method permits ascertaining whether the population discrepancy between Alpha and the composite reliability Coefficient may be practically negligible for a given empirical setting. The outlined approach is illustrated with numerical data.
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Evaluation of Coefficient Alpha for Multiple-Component Measuring Instruments in Complex Sample Designs
Structural Equation Modeling: A Multidisciplinary Journal, 2014Co-Authors: Tenko Raykov, Brady T. West, Anne TraynorAbstract:A readily applicable procedure for point and interval estimation of Coefficient Alpha is outlined for complex sample designs, in cases where this Coefficient is close to composite reliability. As a by-product, point and interval estimation of the change in Alpha due to measuring instrument revision is also possible. This approach can be used as an aid for scale construction and development in empirical investigations involving analyses of complex sample survey data, in particular for secondary data analyses from large-scale studies. The procedure is illustrated with data from an educational survey.
Samuel B Green - One of the best experts on this subject based on the ideXlab platform.
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Evaluation of Dimensionality in the Assessment of Internal Consistency Reliability: Coefficient Alpha and Omega Coefficients
Educational Measurement: Issues and Practice, 2015Co-Authors: Samuel B Green, Yanyun YangAbstract:In the lead article, Davenport, Davison, Liou, & Love demonstrate the relationship among homogeneity, internal consistency, and Coefficient Alpha, and also distinguish among them. These distinctions are important because too often Coefficient Alpha—a reliability Coefficient—is interpreted as an index of homogeneity or internal consistency. We argue that factor analysis should be conducted before calculating internal consistency estimates of reliability. If factor analysis indicates the assumptions underlying Coefficient Alpha are met, then it can be reported as a reliability Coefficient. However, to the extent that items are multidimensional, alternative internal consistency reliability Coefficients should be computed based on the parameter estimates of the factor model. Assuming a bifactor model evidenced good fit, and the measure was designed to assess a single construct, omega hierarchical—the proportion of variance of the total scores due to the general factor—should be presented. Omega—the proportion of variance of the total scores due to all factors—also should be reported in that it represents a more traditional view of reliability, although it is computed within a factor analytic framework. By presenting both these Coefficients and potentially other omega Coefficients, the reliability results are less likely to be misinterpreted.
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Coefficient Alpha: A reliability Coefficient for the 21st century?
Journal of Psychoeducational Assessment, 2011Co-Authors: Yanyun Yang, Samuel B GreenAbstract:Coefficient Alpha is almost universally applied to assess reliability of scales in psychology. We argue that researchers should consider alternatives to Coefficient Alpha. Our preference is for structural equation modeling (SEM) estimates of reliability because they are informative and allow for an empirical evaluation of the assumptions underlying them. An example is presented to illustrate the advantages of SEM estimates of reliability.
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Commentary on Coefficient Alpha: A cautionary tale
Psychometrika, 2009Co-Authors: Samuel B Green, Yanyun YangAbstract:The general use of Coefficient Alpha to assess reliability should be discouraged on a number of grounds. The assumptions underlying Coefficient Alpha are unlikely to hold in practice, and violation of these assumptions can result in nontrivial negative or positive bias. Structural equation modeling was discussed as an informative process both to assess the assumptions underlying Coefficient Alpha and to estimate reliability
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Reliability of Summed Item Scores Using Structural Equation Modeling: An Alternative to Coefficient Alpha
Psychometrika, 2008Co-Authors: Samuel B Green, Yanyun YangAbstract:A method is presented for estimating reliability using structural equation modeling (SEM) that allows for nonlinearity between factors and item scores. Assuming the focus is on consistency of summed item scores, this method for estimating reliability is preferred to those based on linear SEM models and to the most commonly reported estimate of reliability, Coefficient Alpha.
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A Coefficient Alpha for test-retest data
Psychological methods, 2003Co-Authors: Samuel B GreenAbstract:Transient errors are caused by variations in feelings, moods, and mental states over time. If these errors are present, Coefficient Alpha is an inflated estimate of reliability. A true-score model is presented that incorporates transient errors for test-retest data, and a reliability estimate is derived. This estimate, referred to as the test-retest Alpha, is less than Coefficient Alpha if transient error is present and is less susceptible to effects due to item recall than a test-retest correlation. An assumption underlying the test-retest Alpha is essential tau equivalency of items. A test-retest split-half Coefficient is presented as an alternative to the test-retest Alpha when this assumption is violated. The test-retest Alpha is the mean of all possible test-retest split-half Coefficients.
Robert A. Peterson - One of the best experts on this subject based on the ideXlab platform.
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On the relationship between Coefficient Alpha and composite reliability
Journal of Applied Psychology, 2013Co-Authors: Robert A. Peterson, Yeolib KimAbstract:Cronbach's Coefficient Alpha is the most widely used estimator of the reliability of tests and scales. However, it has been criticized as being a lower bound and hence underestimating true reliability. A popular alternative to Coefficient Alpha is composite reliability, which is usually calculated in conjunction with structural equation modeling. A quantitative analysis of 2,524 pairs of Coefficient Alpha and composite reliability values derived from empirical investigations revealed that although the average composite reliability value (.86) exceeded the average corresponding Coefficient Alpha value (.84), the difference was relatively inconsequential for practical applications such as meta-analysis.
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Une méta-analyse du Coefficient Alpha de Cronbach
Recherche et Applications en Marketing (French Edition), 1995Co-Authors: Robert A. PetersonAbstract:Malgré quelques limites, le Coefficient Alpha de Cronbach reste l'indicateur de fidélité d'échelle le plus utilisé. Le but de cet article est de passer en revue l'ampleur des Coefficients Alpha obtenus dans les recherches comportementales empiriques, de confronter ces valeurs obtenues aux règles et aux recommandations préconisées par des chercheurs tels que Nunnally (1967, 1978), et d'apporter des éclairages sur les caractéristiques de plan de recherche susceptibles d'influencer la taille du Coefficient Alpha. Les moyennes des Coefficients Alpha rapportés dans la littérature vont de 0,70 pour les valeurs et les croyances, à 0,82 pour la satisfaction au travail. Hormis quelques exceptions, il n'existe aucune relation substantielle entre l'ampleur du Coefficient Alpha et les caractéristiques des plans de recherche examinés.
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Une méta-analyse du Coefficient Alpha de Cronbach:
Recherche et Applications en Marketing (French Edition), 1995Co-Authors: Robert A. PetersonAbstract:Malgre quelques limites, le Coefficient Alpha de Cronbach reste l'indicateur de fidelite d'echelle le plus utilise. Le but de cet article est de passer en revue l'ampleur des Coefficients Alpha obtenus dans les recherches comportementales empiriques, de confronter ces valeurs obtenues aux regles et aux recommandations preconisees par des chercheurs tels que Nunnally (1967, 1978), et d'apporter des eclairages sur les caracteristiques de plan de recherche susceptibles d'influencer la taille du Coefficient Alpha. Les moyennes des Coefficients Alpha rapportes dans la litterature vont de 0,70 pour les valeurs et les croyances, a 0,82 pour la satisfaction au travail. Hormis quelques exceptions, il n'existe aucune relation substantielle entre l'ampleur du Coefficient Alpha et les caracteristiques des plans de recherche examines.
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A Meta-Analysis of Cronbach's Coefficient Alpha
Journal of Consumer Research, 1994Co-Authors: Robert A. PetersonAbstract:Despite some limitations, Cronbach's Coefficient Alpha remains the most widely used measure of scale reliability. The purpose of this article was to empirically document the magnitudes of Alpha Coefficients obtained in behavioral research, compare these obtained values with guidelines and recommendations set forth by individuals such as Nunnally (1967, 1978), and provide insights into research design characteristics that may influence the size of Coefficient Alpha. Average reported Alpha Coefficients ranged from .70 for values and beliefs to .82 for job satisfaction. With few exceptions, there were no substantive relationships between the magnitude of Coefficient Alpha and the research design characteristics investigated.
Seonghoon Kim - One of the best experts on this subject based on the ideXlab platform.
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cronbach s Coefficient Alpha well known but poorly understood
Organizational Research Methods, 2015Co-Authors: Eunseong Cho, Seonghoon KimAbstract:This study disproves the following six common misconceptions about Coefficient Alpha: (a) Alpha was first developed by Cronbach. (b) Alpha equals reliability. (c) A high value of Alpha is an indica...
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Cronbach’s Coefficient Alpha Well Known but Poorly Understood
Organizational Research Methods, 2014Co-Authors: Eunseong Cho, Seonghoon KimAbstract:This study disproves the following six common misconceptions about Coefficient Alpha: (a) Alpha was first developed by Cronbach. (b) Alpha equals reliability. (c) A high value of Alpha is an indica...
Yanyun Yang - One of the best experts on this subject based on the ideXlab platform.
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Evaluation of Dimensionality in the Assessment of Internal Consistency Reliability: Coefficient Alpha and Omega Coefficients
Educational Measurement: Issues and Practice, 2015Co-Authors: Samuel B Green, Yanyun YangAbstract:In the lead article, Davenport, Davison, Liou, & Love demonstrate the relationship among homogeneity, internal consistency, and Coefficient Alpha, and also distinguish among them. These distinctions are important because too often Coefficient Alpha—a reliability Coefficient—is interpreted as an index of homogeneity or internal consistency. We argue that factor analysis should be conducted before calculating internal consistency estimates of reliability. If factor analysis indicates the assumptions underlying Coefficient Alpha are met, then it can be reported as a reliability Coefficient. However, to the extent that items are multidimensional, alternative internal consistency reliability Coefficients should be computed based on the parameter estimates of the factor model. Assuming a bifactor model evidenced good fit, and the measure was designed to assess a single construct, omega hierarchical—the proportion of variance of the total scores due to the general factor—should be presented. Omega—the proportion of variance of the total scores due to all factors—also should be reported in that it represents a more traditional view of reliability, although it is computed within a factor analytic framework. By presenting both these Coefficients and potentially other omega Coefficients, the reliability results are less likely to be misinterpreted.
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Comparing Fit and Reliability Estimates of a Psychological Instrument using Second-Order CFA, Bifactor, and Essentially Tau-Equivalent (Coefficient Alpha) Models via AMOS 22
Journal of Psychoeducational Assessment, 2014Co-Authors: Ryan A. Black, Yanyun Yang, Danette Beitra, Stacey A. MccaffreyAbstract:Estimation of composite reliability within a hierarchical modeling framework has recently become of particular interest given the growing recognition that the underlying assumptions of Coefficient Alpha are often untenable. Unfortunately, Coefficient Alpha remains the prominent estimate of reliability when estimating total scores from a scale with a hierarchical structure, in part because there are few published articles that provide a step-by-step demonstration of how to estimate reliability within the context of structural equation modeling. Using AMOS 22 to analyze simulated and Wechsler Adult Intelligence Scale–Fourth Edition (WAIS-IV) summary data, the authors demonstrate how to compare the fit and reliability estimates of a (a) second-order confirmatory factor analytic (CFA) model, (b) bifactor model, and (c) essentially tau-equivalent model, which conforms to the stringent assumptions underlying Coefficient Alpha. The variance–covariance matrices generated from the simulated data as well as the WAI...
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Coefficient Alpha: A reliability Coefficient for the 21st century?
Journal of Psychoeducational Assessment, 2011Co-Authors: Yanyun Yang, Samuel B GreenAbstract:Coefficient Alpha is almost universally applied to assess reliability of scales in psychology. We argue that researchers should consider alternatives to Coefficient Alpha. Our preference is for structural equation modeling (SEM) estimates of reliability because they are informative and allow for an empirical evaluation of the assumptions underlying them. An example is presented to illustrate the advantages of SEM estimates of reliability.
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Commentary on Coefficient Alpha: A cautionary tale
Psychometrika, 2009Co-Authors: Samuel B Green, Yanyun YangAbstract:The general use of Coefficient Alpha to assess reliability should be discouraged on a number of grounds. The assumptions underlying Coefficient Alpha are unlikely to hold in practice, and violation of these assumptions can result in nontrivial negative or positive bias. Structural equation modeling was discussed as an informative process both to assess the assumptions underlying Coefficient Alpha and to estimate reliability
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Reliability of Summed Item Scores Using Structural Equation Modeling: An Alternative to Coefficient Alpha
Psychometrika, 2008Co-Authors: Samuel B Green, Yanyun YangAbstract:A method is presented for estimating reliability using structural equation modeling (SEM) that allows for nonlinearity between factors and item scores. Assuming the focus is on consistency of summed item scores, this method for estimating reliability is preferred to those based on linear SEM models and to the most commonly reported estimate of reliability, Coefficient Alpha.