Let's have four different running shoes, I want to test which ones are the fastest in terms of the average speed of the runner. I "hire" four different groups of runners (each getting one version of the shoes) of the same size, sampled randomly from the population for an experiment where I let them run and measure their speed.
Question 1: What is the appropriate testing strategy?
(i) Pairwise difference in means of speed between groups with one of the available p-value corrections such as Bonferroni (6 pairs)
(ii) Taking one shoe as the baseline and check whether the others are faster or slower, also applying a p-value correction (3 pairs)
Question 2: How do I tell the winner in case I choose strategy (ii)?
Question 3: How do I determine the neccessary sample size for my experiment?
R-examples are also welcome.