xvi What Is Statistics? Information the goal The goal of doing statistics is to gain some information or to make a decision. Statistics is useful because it helps us answer questions like the following: Which of two treatment plans leads to the best clinical outcomes? How strong is an I-beam constructed according to a particular design? Is my cereal company complying with regulations about the amount of cereal in its cereal boxes? In this sense, statistics is a science a method for obtaining new knowledge. Uncertainty the context The tricky thing about statistics is the uncertainty involved. If we measure one box of cereal, how do we know that all the others are similarly filled? If every box of cereal were identical and every measurement perfectly exact, then one measurement would suffice. But the boxes may differ from one another, and even if we measure the same box multiple times, we may get different answers to the question How much cereal is in the box? So we need to answer questions like How many boxes should we measure? and How many times should we measure each box? Even so, there is no answer to these questions that will give us absolute certainty. So we need to answer questions like How sure do we need to be? Probability the tool In order to answer a question like How sure do we need to be?, we need some way of measuring our level of certainty. This is where mathematics enters into statistics. Probability is the area of mathematics that deals with reasoning about uncertainty. So before we can answer the statistical questions we just listed, we must first develop some skill in probability. Chapter 2 provides the foundation that we need. Once we have developed the necessary tools to deal with uncertainty, we will be able to give good answers to our statistical questions. But before we do that, let’s take a bird’s eye view of the processes involved in a statistical study. We’ll come back and fill in the details later. A First Example: The Lady Tasting Tea There is a famous story about a lady who claimed that tea with milk tasted different depending on whether the milk was added to the tea or the tea added to the milk. The story is famous because of the setting in which she made this claim. She was attending a party in Cambridge, England, in the 1920s. Also in attendance were a number of university dons and their wives. The scientists in attendance scoffed at the woman and her claim. What, after all, could be the difference? All the scientists but one, that is. Rather than simply dismiss the woman’s claim, he proposed that they decide how one should test the claim. The tenor of
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