We designed a RCB experiment and assigned the factor levels to the experimental units randomly inside each block. Let's pretend we changed our mind and we would like to go for a Completely Randomized design. A new completely randomized assignment of factor levels to experimental units is not possible since the experiment has already begun. We have to stay with the RCB assigment (thus having 1 replicate in each former block).
The question is: how much bias would we introduce in the analysis of variance if we analysed the RCB configuration pretending it to be a CR configuration? I know that the RCB configuration can be considered as one of the $n$ equally probable random configurations, but is there a way to account for this bias in the further analysis?
The reason we would like to move from RCB to CR is that, from modelling studies, our block has no significant effect on the response varible, and, as gung pointed out, it would decrease the power of the test we will perform. Since Blocks do not significantly affect the response variable of the experimental units, in case we moved to a CR design, can the replicates (previously randomized within non-significant blocks) be considered as randomized within the whole population?
This question is relevant also for post-hoc analysis, if a RCB ANOVA results in blocks not being significant, is a CR ANOVA appropriate on a configuration that was not completely randomized?