I have difficulty in understanding Cronbach's Alpha's formula. I searched for google and StackExchange able to understand it. Even there are some topics trying to explain it intuitively, I could not get the idea yet.
I know, it is used to measure reliability and to determine presence of unidimensionality.
In extreme cases, the results are obvious:
- If there is no correlation between items(variables) Cronbach's Alpha is 0
- If there is perfect relationship, it's value is 1.
That is okey. But why don't we just use average of inter correlation's of items.
It seems to me more intuitive. That value will be 0 when all items are independent and will be 1 if there perfect linear relation.
So what information gives Cronbach's Alpha beside the average of inter item correlations.
I also wonder does Cronbach's Alpha used to determine multicollinerity.
I will be very glad for any help. I need and very clear explanation. Thanks a lot.
Best Answer
A couple of minor points to start with:
First, if alpha is based on correlations, then it's referred to as standardized alpha. Alpha is calculated based on variances.
Second, alpha is not used (or should not be used) to determine the presence of unidimensionality.
Onto the main point. Alpha is a measure of reliability, and reliability is the correlation between the true score and the measured score.
As you increase the length of a scale, you get better reliability and the correlation increases (via the Spearman Brown prediction formula - which has a Wikipedia entry). Just like when you increase the size of a sample, your estimates become more reliable. A short scale with a low average interitem correlation will have low reliability, a long scale with the same average interitem correlation will be more reliable.
(I'm not sure I understand the part of the question about multicollinearity).