What is the point of reporting split-half reliability together with Cronbach's alpha? In several journal articles I read, autors report split-half reliability (Guttman formula obtained if questionnaire is splited into two parts: odd items and even items, usually) together with Cronbach's alpha.
Correct me, please, if I'm wrong: if we calculate split-half reliability for every possible split and take arithmetic mean, we get Cronbach's alpha. So reporting split-half reliability for one single split is pointless, since we report mean for every possible split.
 A: Indeed, Cronbach alpha is equivalent to the average of all possible split-half estimates, hence it's not really necessary to report both indices, unless odd items and even items (or any other item splits) play a specific role. For instance, sometimes we assess the same item content but using two different wording, or a reverse scoring scheme, to check that subjects are not answering at random, or the polarity of the response options (e.g., 1 = strongly disagree ... 5 = strongly agree versus 1 = strongly agree ... 5 = strongly disagree) does not affect the average responses. Such scenario are really parallel form of the same questionnaire, for which split-half reliability makes sense.
A: It is true that the Cronbach's alpha is often a preferable statistic to an odd-even split since it can be interpreted as a central tendency of the item consistency across all of the possible ways to split the items, whereas the odd-even split represents only one possible way to split the items.
However, there are some cases in which the two metrics may have qualitatively different interpretations. For example, in my own research I investigate the internal consistency of learning assessments - scores are expected to change over the course of the assessment (hopefully improving). Imagine looking at a dataset with two patterns: 1) test takers reliably vary in their baseline skill on the test and 2) some test-takers improve throughout the test, some don't, and some even get worse over time. Judged by an odd-even split, that test might look pretty internally consistent - a person's performance on the odd-numbered items could be used to predict their performance on the even-numbered items. But, judged by a first half vs last half split, the test items could look pretty inconsistent. The Cronbach's alpha mashes those two splits together, along with every single other possible split.
