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When setting out experiments, I want to make sure treatment groups are as balanced as possible. Instead of using randomization, I've started to use the following process. I first collect some measurements from the potential experimental units I have at my disposal. Then, I generate all the different possible combinations of treatment groups using all these potential experimental units (yes - I know it's computationally intensive). Finally, I see which combination keeps means, variances, and possibly higher-order moments of the measurements I took as consistent as possible across groups.

I'm wondering if I need to take into account degrees of freedom somehow. I know the process I described above is something you do before an experiment even begins and isn't really related to the final statistical analysis, but I can't help thinking about degrees of freedom with all these parameters I'm calculating.

As an aside, I've decided that, when you're placing n experimental units into each treatment group, that it only makes sense to calculate up to the nth or the (n - 1)th moment, but this idea is still a work in progress.

Does anyone have any thoughts? Thank you in advance for your help - I'm very grateful.

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if you hava few and categorical covariates variable(pre-experiment measurements) , you can try block: This approach achieves almost perfect balance between covariates, and degrees of freedom don't matter

if you have many or continuous covariates variable, you can try Rerandomization: here the degrees of freedom still don't matter here

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  • $\begingroup$ Thanks - this answer wasn't quite what I was hoping for, but it was the first time I heard of rerandomization, so I really appreciate that $\endgroup$ Commented Jun 1, 2023 at 18:21

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