A more powerful test is proposed for the treatment effect in two-level block randomized designs where random assignment takes place at the first level. When clustering at the second level is assumed to be known, the proposed test produces higher estimates of power than the typical test.
"Constructing a More Powerful Test in Two-Level Block Randomized Designs,"
Journal of Modern Applied Statistical Methods:
1, Article 8.
Available at: http://digitalcommons.wayne.edu/jmasm/vol12/iss1/8