#### cronbach's alpha

arnold on Oct 05, 2008

**Lets Start With Some Definitions:**

**Cronbach’s Alpha** is mathematically equivalent to the average of all possible split-half estimates, although that’s not how we compute it (socialresearchmethods.net).

**Cronbach’s alpha** will generally increase when the correlations between the items increase. For this reason the coefficient is also called the internal consistency or the internal consistency reliability of the test. (Wikipedia)

**Cronbach’s alpha** allows us to estimate the reliability of a composite when we know the composite score variance and the covariances among all its components (Crocker and Algina, 1986, p. 117).

**Alpha** is an unbiased estimator of reliability if and only if the components are essentially τ-equivalent. Under this condition the components can have different means and different variances, but their covariances should all be equal – which implies that they have 1 common factor in a factor analysis (Wikipedia).

The major use of **reliability coefficients** is to communicate the repeatability of results (Nunnally and Bernstein, 1994).

**That’s all good and fun but what is Cronbach’s Alpha in simpler terms?**

Let’s use an example to clarify this. Assume that I have four items on a test. If I run a reliability test I could find that my coefficient alpha is .9. This tells me that my items are interrelated. However, it does not tell me that my items are unidimensional. I would have to do a factor analysis to figure out the dimensionality. If I did a factor analysis and found that two of my items do not measure the same latent construct as my other two items (ie. the items are loading on two different factors), then I would have to do another reliability test on each of those two items separately. There could be a situation where the original coefficient alpha was a low .35. If I then found two latent constructs I might go back and do the reliability test again and find out that the two constructs have a very high coefficient alpha.**This example helps to demonstrate what exactly it is that Cronbach’s Alpha measures:**

It is a function of the extent to which items in a test have high commonalities and thus low uniqueness. It is also a function of interrelatedness, although one must remember that this does not imply unidimensionality or homogeneity. (Schmittt, 1996)

**That is a lot of big words. Lets tone this bad boy down a bit.**

**Internal consistency:** refers to the degree of interrelatedness among the items**Homegeneity:** refers to the unidimensionality.

And, as a fan of beating dead horses I will also say:

Alpha is a function of internal consistency, but a set of items can be interrelated and multidimensional (Cortina, 1993). Alpha **is not** a measure of unidimensionality or homogeneity. Alpha **is** a function of the interrelatedness of items in a test and the test length.

**More good stuff to know!**

Cronbach views reliability as the proportion of test variance that was attributable to group and general factors. Specific item variance, or uniqueness was considered error. Reliability means precision. Measurement error is indexed by reliability. Reliability is the ratio of true variability to total variability (Ree and Carett, 2006).

**Factors that affect Cronbach’s Alpha from Cortina (1993):****# of item:** More Items, Alpha goes up**Item intercorrelation:** Higher intercorrelation, Alpha goes up**Dimensionality:** More dimensions, alpha goes down. But with more items and high intercorrelation, you can get an acceptable alpha which will tell you nothing about the unidimensionality.

The **estimate of precision** will tell will tell you about the departure from unidimensionality.