Step 1: Divide the test into equivalent halves.
Step 2: Compute a Pearson r between scores on the two halves of the test.
Step 3: Adjust the half-test reliability using the Spearman-Brown formula
Cronbach's Alpha (a)
If we compute one split-half reliability and then randomly divide the items into another set of split halves and recompute, we can keep doing this until we have computed all possible split half estimates of reliability. Cronbach's Alpha is the geek equivalent to the average of all possible split-half estimates (although that's not how we do it.)
In saying we compute all possible split-half estimates, it doesn't mean that each time we go and actually measure a new sample! Instead, we calculate all split-half estimates from the same sample. Because we measured all of our sample on each of the six items, all we have to do is have the computer analyze the random subsets of items and compute the resulting correlations.
The figure shows several of the split-half estimates for our six item example and lists them as SH with a subscript. Just keep in mind that although Cronbach's Alpha is equivalent to the average of all possible split half correlations we would never actually calculate it that way.
Rulon's Split-half Method