To test a sunburn lotion we get a batch of subjects who will lie on the beach under the hot sun. Half of them will have sunburn lotion spread over their backs. Of course we decide by random means which subjects get lotion and which placebo. Since this is a fiction story, assume that upon looking at any two backs, we can tell which is burned worse. In 31 of the 36 comparisons, the placebo subject was worse burned.
Backs have a right and a left side.
Better to apply lotion to one side, placebo to the other side, and compare each subject only with him or herself.