```Interesting question here:  “I wonder, do we need to run a Cronbach's alpha, after we did the EFA, to measure the reliability of the items that we have grouped? What happens if the Cronbach's alpha value is low (eg. 0.5) and "Cronbach's alpha if item deleted" suggests removing one of the item to get a higher value?”

This seems to be a use of EFA for scale construction.  In other words, the analyst is trying to find scales/subscales amongst a set of items.  The factor analysis has suggested a particular grouping of items (let’s say Items 4, 7, 9, 12, and 15 on a 20-item scale).  The question doesn’t tell me what kind of EFA (e.g., promax?) or what the loadings are, or whether the factor seems to account for – say – 70% of the variance of each item.  These are all important, because I can already begin to judge whether this is a “good” scale based on that information.  If an item has a loading of just 0.3, for example, it’s unlikely to be a strong contributor to scale reliability.

That said, following up with Cronbach’s alpha is not a bad idea.  (There are actually formulas where you can derive the alpha from the communality, but I don’t have that at my fingertips right now).

What you SHOULD see is a pattern that almost perfectly mirrors the factor loading pattern.  Items most likely nominated by alpha to be deleted should be items that ALSO had your lowest loadings.  The two methods should give perfectly complementary information.  That’s because the factors that contribute to low alpha (low item-total correlation, low item variance) also contribute to low loadings.

If you’re in the process of scale construction, using the factor analysis and the alpha analysis to identify items that should be dropped is perfectly legitimate.

There are two caveats:

-          If you refine a scale based on factor analysis/alpha analysis, you really need to collect data from a NEW sample to INDEPENDENTLY VERIFY the scale

-          In general, item factor analyses are usually a bad idea (because items often have restricted ranges). We’ll be discussing that a lot in the weeks to come.

Michael

==

Michael Marsiske, Ph.D.
Associate Professor
University of Florida
Department of Clinical and Health Psychology
PO Box 100165, 1225 Center Dr., Rm. 3170
Gainesville, FL 32610-0165