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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.

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1 Answer 1

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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).

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    $\begingroup$ Thanks a lot @Jeremy Miles. The minor points that you emphasized and the explanation was very helpful. Now the formula is much more clear for me. $\endgroup$
    – oercim
    Apr 28, 2016 at 16:44
  • $\begingroup$ Nice explanation. I get now how alpha improves on average correlation with increasing number of items. But at some point, that virtue becomes a drawback, right? For example, a 1000-item scale with an average inter-item correlation of .01 gives an alpha of 0.91 (an extreme example, from Kline's book). $\endgroup$
    – ba_ul
    Oct 2, 2016 at 23:09
  • $\begingroup$ Kline is talking about the practical use of a scale, in psychology, and he is talking about scales of reasonable lengths. If you have an alpha of 0.91, you could have had a shorter scale. If you already have a short scale, your alpha is very, very high. $\endgroup$ Oct 3, 2016 at 18:42
  • $\begingroup$ Correlations of 0.01 mean that your measurement is very poor. But you can make it good by having lots of measures. If you are measuring the size of something, and measurement is cheap, you might as well measure it 1000 times to get the most accurate measure. (Think about things like CERN physicists looking for Higgs Bosons.) $\endgroup$ Oct 3, 2016 at 18:45

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