I am working on a consult for a behavioral researcher's ongoing project. The current study uses three experimental conditions (A, B, & C), each with roughly-equal sample sizes (~n) at current. However, two of the conditions (A & B) are essentially variants of each other, and we found no significant difference in the outcome of these two groups.
Given this finding, the researcher wants to start making comparisons between A+B and C, rather than all three groups. She thus wants to adjust further recruitment to balance the number of participants in group A+B (2*n) compared to group C (n), such that for each participant randomized to A+B going forward, two are randomized to group C.
I was trying to explain that this might be problematic for a few reasons, but was having trouble giving sufficient statistical detail as to why. The two main concerns I had were as follows: -Altering condition allocation procedures midway through an experiment can have a detrimental impact on ensuring sufficiently random assignment to experimental conditions -Trying to maintain random allocation while essentially assigning twice as many participants to one condition compared to the other would be difficult
Can anyone provide any more concrete reasoning behind my concerns, or other concerns? Or ways, if possible, of adjusting the condition allocation procedure going forward that is not problematic? Google and Cross-Validated searches have not been successful so far. I have a reasonable background in stats (undergrad major and current PhD student in Quant Psych), so more technical responses are certainly appreciated!