Block what you can, except when you shouldn't

Several branches of the potential outcome causal inference literature have discussed the merits of blocking versus complete randomization. Some have concluded it can never hurt the precision of estimates, and some have concluded it can hurt. In this paper, we reconcile these apparently conflicting views, give a more thorough discussion of what guarantees no harm, and discuss how other aspects of a blocked design can cost, all in terms of precision. We discuss how the different findings are due to different sampling models and assumptions of how the blocks were formed. We also connect these ideas to common misconceptions, for instance showing that analyzing a blocked experiment as if it were completely randomized, a seemingly conservative method, can actually backfire in some cases. Overall, we find that blocking can have a price, but that this price is usually small and the potential for gain can be large. It is hard to go too far wrong with blocking.
Comment: arXiv admin note: text overlap with arXiv:1710.10342