You are conducting research using rhesus macaques (monkeys). For ethical reasons as well as limited resources, you decide to use only 9 animals, 3 animals in each of 3 treatment groups. To increase the power of your statistical testing, you take 10 samples from each animal. What statistical test might you use in this instance?

Your graduate student objects, saying that taking multiple samples from each animal cannot increase statistical power. How should you respond?