Dear All,
I am following up on the question about standardized Cronbach's alpha raised by Francois and Christine earlier today. There are two issues here:
1) Cronbach's alpha employs the covariances among the items, whereas the alpha based on standardized items employs the correlations among items. The latter alpha is based on the assumption that all of the items have equal variances, which is often false in practice. The standardized Cronbach’s alpha could be utilized if we knew that all of the items had equal variance.
2) Standardized Cronbach’s alpha coefficient of internal consistency (when all scale items have been standardized) is used only when the individual scale items are not scaled the same.
For Q6b in hw#7, the scales of the items are quite different and the variances of the items are quite different, so we should probably use the ‘standardized’ Cronbach’s alpha as the more conservative (smaller) of the two.
Thanks,
Lydia