You hear about split-half correlations often as a measure of reliability. But is there a reason that split-third correlations (or split-fourth, split-fifth, etc.) are never used? Shouldn't they provide a better sense of the internal reliability if the dataset is large enough?
The way I figure they would work is you would split the data up into thirds, and correlate each third to the other two and find the average of all three correlations. (Or of all six correlations if you split the data into fourths, and so on.)
Is this ever done/does this make sense/would this be an acceptable practice?