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A gardener gives fertiliser A to 3 plants and fertiliser B to 3 others, chosen at random…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A gardener gives fertiliser A to plants and fertiliser B to others, chosen at random. After a month the A plants have grown cm, cm and cm, and the B plants cm, cm and cm. These are made-up results. Find the observed difference in mean growth, A minus B, to two decimal places. How many ways are there to split the growths into two groups of ? In how many splits is the difference at least as large as the observed one? Find the exact p-value.
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. Observed. cm.
Step 2. Splits. .
Step 3. Large splits. The total of all six growths is cm, so a larger A total means a larger difference. The observed A total is cm. Only with cm beats it, and the real split equals it. So splits.
Step 4. The p-value. .
Answer: cm, splits, splits and a p-value of .
What it means. With only six plants, even a clear-looking difference is not significant at the level. Small experiments have little power.
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