I have been brushing up on some stats and figure I'd have a look at Cronbach's alpha. As I understand it, a higher alpha coefficient means a greater interrelation between all the items.
If items are all measuring the same construct of interest, then it follows that the score on one item will predict the score on the others.
However, I came across this reference:
Multifaceted Assessment for Early Childhood Education
It states "the optimum value of an alpha coefficient is 1.00". I believe that this statement is wrong — while a higher reliability is certainly desirable, and ideally >0.90, the only thing that could be worse than alpha = 1.0 is when alpha = 0.00.
My reasoning: suppose I had a 30 item questionnaire with an alpha coefficient of 1.00, then it means that there are 29 items that offer no predictive value, because having one item would do just as well. When alpha = 0.00, then of course, there is no point in even administering the questionnaire.
Am I missing something?
I also came across the following statement somewhere:
Cronbach's alpha will not tell you whether your scale is
uni-dimensional (i.e., whether all your items measure the same
construct)
I get what they're saying: a high alpha is necessary but insufficient evidence that there is one underlying construct. However, let's suppose that alpha = 0.99 — can someone give me an example where we can meaningfully speak of two constructs? The only way I can interpret such a correlation would be to say that what we think are different constructs are actually the same construct that have been given different names.
Best Answer
What for many people was the canonical account of the issues here was published by Green and colleagues in an article entitled "Limitations of Coefficient Alpha as an Index of Test Unidimensionality" available here. They give an example of a test with five separate underlying latent variables with $\alpha = 0.811$ which is not as extreme as your request but getting close.
They state:
Their article is well worth reading in full.