In my example, did I use the comma correctly?

The IV cannot be randomized in this case, but randomization allows for balance between two groups, one on each side of the threshold.

Maybe the sentence I just wrote below is better?

The IV cannot be randomized in this case. Randomization allows for balance between two groups, one on each side of the threshold. I believe both groups are very similar except for drinking and death rate. Thus, I believe assumption 1 is met.

Solution 1:

Yes, this usage is correct. Your second example does a better job of showing why:

Randomization allows for balance between two groups, one on each side of the threshold.

If you removed the comma:

Randomization allows for balance between two groups one on each side of the threshold.

The two clauses merge and the sentence becomes meaningless.