How many unit are necessary in randomized experiment?

Let's say we want to conduct an experiment with binary treatment.

How do I decide how many units do I need to assing the treatment to, to get internally valid results? I understand that you need to reach a certain number of units for detecting statistically significant effect. But in this case I am concern about finding the (average) causal effect of my treatment free of possible confounders. (In this case I don't care about external validity and generalization of my results to the broader population). I just want to be sure that I have enough units to control the confounders with randomization.

Edit: I am basically trying to measure SATE and I am not sure what role does the statistical significance test play in this context. Can it tell me anything about the internal validity of the experiment, or is it strictily directed toward external validity and generalization to the broader population?

• Doing proper sample size calculation is only possible with detailed information on study design, endpoints, hypotheses etc., along with significance level, power, intended analyses and ways to deal with multiple testing. You have not provided any of these and so I'd refer to the following little piece of art: youtube.com/watch?v=PbODigCZqL8 Jul 17, 2020 at 21:13
• Oh, I see. I am not a scientist nor a student. I'm asking just out of my own curiosity. But do I understand correctly that the significance level is relevant even for internal validity? Jul 18, 2020 at 6:26
• Not necessarily a significance level, but something similar. In your case it could be the desired precision of the estimated validity measure, but this is (admittedly) pure speculation. Jul 18, 2020 at 7:28
• I've edited the main post: I am basically trying to measure SATE and I am not sure what role does the statistical significance test play in this context. Can it tell me anything about the internal validity of the experiment, or is it strictily directed toward external validity and generalization to the broader population? Jul 18, 2020 at 7:31