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A coach splits 8 runners at random into two groups of 4…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A coach splits runners at random into two groups of . Group A trains on hills and group B on flat roads. After a month, each runner's improvement in a km race is measured in seconds. Group A improves by s, s, s and s. Group B improves by s, s, s and s. These are made-up results. Find the mean improvement of each group and the difference, A minus B.
Need a reminder? The key ideaShow
If a treatment makes no difference, the group labels carry no information. Every split of the pooled values is then equally likely, and the p-value is the share of splits with a difference at least as large as the real one.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Group A: s.
Step 2. Group B: s.
Step 3. s.
Answer: s, s and s. A shuffling test would now ask how often a random split of the eight values gives a difference of s or more.
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