[7] GRBD designs for models without interaction terms offer more degrees of freedom for testing treatment-effects than do RCBs with more blocks: An experimenter wanting to increase power may use a GRBD rather than RCB with additional blocks, when extra blocks-effects would lack genuine interest.
For vector responses, multivariate analysis considers similar two-way models with main effects and with interactions or errors.
Tukey's test is valid when Mandel's multiplicative model holds and when the errors independently follow a normal distribution.
Tukey's F-statistic for testing interaction has a distribution based on the randomized assignment of treatments to experimental units.
Other methods and heuristics for block-treatment interaction in unreplicated studies are surveyed in the monograph Milliken & Johnson (1989).