Great questions. I can't say for sure, but I believe you might be right on 1). When there's low variability within each group, a smaller sample size will yield

Great questions. I can't say for sure, but I believe you might be right on 1). When there's low variability within each group, a smaller sample size will yield higher statistical power. That's why pairing is so popular in clinical studies. However the trick to solving 2) is that you pair and then randomly assign the groups within each pair. I found this great article [1] on the subject. It has an interesting discussion of the history. John Stuart Mill's approach was to stamp out heterogeneity however possible (e.g. breeding the differences out of mice). However, Fisher showed that no matter how much you tried to stamp out hetero, it was an uncountable and infinite enumerable list. It says that Fisher made a list of all the possible differences in the tea cups used in his famous Lady Tasting Tea experiment [1, 2]. Fisher's contribution was noticing that random assignment could balance out hetero. This article [1] puts it succinctly: "If treatments are randomly assigned, so treatment effects may be estimated without bias, increasing the sample size and decreasing the heterogeneity of experimental units have similar consequences: they reduce the sampling variability of unbiased estimates." [1] http://www-stat.wharton.upenn.edu/~rosenbap/heteroReprint.pdf http://www-stat.wharton.upenn.edu/~rosenbap/heteroReprint.pd... [2] https://en.wikipedia.org/wiki/Lady_tasting_tea https://en.wikipedia.org/wiki/Lady_tasting_tea