I'm designing an experiment, in which 40 participants answer 10 questions, 5 in condition $A$ and 5 in condition $B$, and I'm interested in the difference between the two conditions.
It's not clear to me what's the best way to allocate questions to each condition. A simple solution is to counterbalance - generate two lists: \begin{align} {\rm List}\ 1\ &=\ Q1A,\ Q2B,\ Q3A,\ Q4B,\ Q5A,\ Q6B,\ Q7A,\ Q8B,\ Q9A,\ Q10B \\ {\rm List}\ 2\ &=\ Q1B,\ Q2A,\ Q3B,\ Q4A,\ Q5B,\ Q6A,\ Q7B,\ Q8A,\ Q9B,\ Q10A \end{align} and randomly assign participants to one or other.
Alternatively, I could randomly assign 5 questions to each condition for each participant, fully randomizing the stimuli.
I plan on analysing the result using a mixed effects model, as I'm expecting some missing cases:
lmer(dv ~ condition + (condition|question) + (condition|subject))
My question is this: Is it more statistically appropriate to counterbalance, or to randomize in such a situation?