When we have a composite measure (i.e. an index) – often derived from factor analysis – it is possible to evaluate it by means of the Cronbach’s alpha. Formally speaking, the Cronbach’s alpha is a measure of internal consistency; how closely related a number of items are as a group. The coefficient ranges between 0 and 1. A high alpha value indicates that items measure an underlying factor. However, it is not a statistical test but a test of reliability/consistency.

One important thing to note is that the Cronbach’s alpha is affected by the number of variables: including a higher number of variables automatically increases the alpha value to some extent.

There are many rules of thumb with regard to what is considered a good or bad alpha value. Generally, an alpha value of at least 0.7 is considered acceptable.

Alpha values

Between 0.7 and 1.0	Acceptable
Below 0.7	Not acceptable

Function

Basic command

alpha varlist

Useful options

alpha varlist, item

Explanations
varlist	List which variables that you want to include in the analysis.
item	Display item-test and item-rest correlations. Useful to see what the effect would be if removing an item.

More information help alpha

Practical example

Dataset

StataData2.dta

Variable name	Variable label
imp_secure imp_help imp_behave imp_environ imp_trad	Important living in secure surroundings Important to help people Important to always behave properly Important looking after the environment Important with tradition

Variable name	Variable label
imp_ideas imp_rich imp_good imp_success imp_risk	Important to think up new ideas Important to be rich Important to have a good time Important to be successful Important with adventure and taking risk

alpha imp_secure imp_help imp_behave imp_environ imp_trad, item

alpha imp_ideas imp_rich imp_good imp_success imp_risk, item

The scores for Test scale show the actual alpha values. For the first example, it is 0.7165 and for the second 0.6723. This is largely acceptable (at least for the first one). We can also see from the column called alpha that deleting any of the items would actually decrease the alpha score.