Halil YURDAGÜL

Minimum Sample Size for Cronbach's Coefficient Alpha: A Monte-Carlo Study

Eğitimsel ve psikolojik çalışmalarda birleşik ölçmelerin güvenirliğinin hesaplamasında yaygın olarak Cronbach (1951) tarafından geliştirilen alfa katsayısı kullanılmaktadır. Ancak bu tür çalışmalarda veri toplamanın zorluğu nedeniyle alfa katsayısı için gerekli olan minimum örneklem genişliği tartışma konusudur. Evren alfa katsayısının sağlam kestirimi için gerekli olan minimum örneklem genişliği için farklı öneriler vardır. Bu çalışmanın sonuçlarına göre; yansız ve tutarlı bir alfa kestirimi örneklem genişliğinin büyüklüğü kadar aynı zamanda ölçmelerin birinci özdeğerinin büyüklüğüne bağlıdır. Buna göre, birinci özdeğer büyüdükçe, düşük örneklem genişliklerinde alfa katsayısının yansız bir kestirimi olanaklıdır. Bu çalışmada kullanılan simulasyonlar bootstrap tekniği ile birlikte Monte-Carlo yöntemi üzerine kurulmuştur.

Cronbach Alfa Katsayısı İçin Minimum Örneklem Genişliği: Monte-Carlo Çalışması

The coefficient alpha is the most widely used measure of internal consistency for composite scores in the educational and psychological studies. However, due to the difficulties of data gathering in psychometric studies, the minimum sample size for the sample coefficient alpha has been frequently debated. There are various suggested minimum sample sizes for the robust estimate of the population coefficient alpha. This research indicates that the performance of an estimator of the coefficient alpha depends not only on the sample size but also on the largest eigenvalue of the sample data set. Thus, when the largest eigenvalue increases, unbiased estimation of the population coefficient alpha is possible, even though the sample size is small. The simulations in this study were based on Monte-Carlo method with bootstrap technique.

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