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Unfortunately, just examining how you feel after taking aspirin a single time won’t be adequate, since the aspirin may be more helpful some times and less helpful others. For example, it could be the case that it works on moderate headaches but not on severe ones, so if your next headache happened to be really severe, it would look like aspirin was useless. To solve this problem, and give yourself more data, you might resolve to make these records of how you’re feeling for each of the next 20 headaches you get.

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Your analyses would be a lot simpler if you scored how unpleasant each headache was on a simple scale from 1 to 5 (1 meaning slight unpleasantness, 3, moderate unpleasantness, and 5, extreme unpleasantness). That way, you can simply look at all the scores you got just before taking aspirin and average them together. You can then compare this to the average of the scores 30 minutes after taking the aspirin and 60 minutes after taking it. That way, you can see if the amount of unpleasantness you feel really does drop substantially after taking aspirin.

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Fortunately, these problems are easily remedied. Instead of giving half the group nothing, you instead give them pills in an aspirin bottle that look just like aspirin, but which have no effect on headaches. Sugar pills are a reasonable choice, because a small amount of sugar is unlikely to effect a person’s headaches.

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But, if the results fluctuate randomly, that implies that sometimes, just by luck alone, the aspirin might seem to be effective even if it isn’t. Likewise, it might, through bad luck, seem to be ineffective, even though it does work. So whatever your experiment shows, how can you be sure you’re getting the right answer?

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