# Monte-Carlo Simulation of Cronbach’s Alpha under Violated Assumptions / Rebernjak, Blaž ; Urch, Dražen.

##### By: Rebernjak, Blaž.

##### Contributor(s): Urch, Dražen [aut].

Material type: ArticleDescription: 43-43.Other title: Monte-Carlo Simulation of Cronbach’s Alpha under Violated Assumptions [Naslov na engleskom:].Subject(s): 5.06 | Cronbach's alpha, violated assumptions, monte carlo simulation hrv | Monte-Carlo Simulation of Cronbach’s Alpha under Violated Assumptions engOnline resources: Elektronička verzija sažetka In: 20. Dani Ramira i Zorana Bujasa (7-9.4.2011 ; Zagreb, Hrvatska) 20. Dani Ramira i Zorana Bujasa, sažetci priopćenja str. 43-43Čorkalo Biruški, Dinka ; Vukasović, TenaSummary: Cronbach's alpha is unequivocally the most widely used estimate of scale reliability in scientific research and psychological practice. Alpha can be defined as the mean of all split-half reliabilities and is generally considered to be the lower bound of true scale reliability. The calculation of alpha, as is true for all statistical tests or methods, is based on a number of assumptions, most of which are routinely not evaluated before the calculation of the coefficient. The most important of these assumptions are essential tau-equivalence of the measurement model and independence of item errors. If the test is shown not to conform to the criteria of essential tau-equivalence, but is congeneric in nature, alpha will underestimate the reliability. If, on the other hand, covariation exists between errors of items that comprise a test, alpha can overestimate the reliability by overestimating the average intercorrelation between items. In this study we explored in detail how Cronbach’s alpha behaves in the case of violated assumptions, with regard to number of items, number of observations, item characteristics (mean and variance) and degree of assumption violation. A Monte-Carlo simulation was preformed with the aforementioned factors varying. Cronbach’s alpha was calculated and compared to the reliability estimated using confirmatory factor analysis approach. Results are discussed in the framework of classical test theory and several recommendations are made with regard to reliability estimation under various circumstances.Cronbach's alpha is unequivocally the most widely used estimate of scale reliability in scientific research and psychological practice. Alpha can be defined as the mean of all split-half reliabilities and is generally considered to be the lower bound of true scale reliability. The calculation of alpha, as is true for all statistical tests or methods, is based on a number of assumptions, most of which are routinely not evaluated before the calculation of the coefficient. The most important of these assumptions are essential tau-equivalence of the measurement model and independence of item errors. If the test is shown not to conform to the criteria of essential tau-equivalence, but is congeneric in nature, alpha will underestimate the reliability. If, on the other hand, covariation exists between errors of items that comprise a test, alpha can overestimate the reliability by overestimating the average intercorrelation between items. In this study we explored in detail how Cronbach’s alpha behaves in the case of violated assumptions, with regard to number of items, number of observations, item characteristics (mean and variance) and degree of assumption violation. A Monte-Carlo simulation was preformed with the aforementioned factors varying. Cronbach’s alpha was calculated and compared to the reliability estimated using confirmatory factor analysis approach. Results are discussed in the framework of classical test theory and several recommendations are made with regard to reliability estimation under various circumstances.

Projekt MZOS 130-1301683-1402

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