Sample Chapter

Chapter 4 - Introducing the Logic of Inference Using Confidence Intervals

“Inference” refers to a reasoning process that begins with some information and leads to some conclusion. If you have ever taken a logic course or thought about logical reasoning, you have probably heard things like, “All mammals are warm-blooded animals; this animal is a mammal; therefore this animal is warm-blooded.” That particular sentence is known as a “syllogism” and it represents a kind of inference called “deduction.” Another kind of inference, induction, reasons from specific cases to the more general. If I observe a cat jumping from a tree and landing on its feet, and then I observe another cat, and another, and another doing the same thing, I might infer that cats generally land on their feet when jumping out of trees. Statistical inference takes this same kind of logical thinking a step further by dealing systematically with situations where we have uncertain or incomplete information. Unlike the syllogism about warm-blooded animals presented above, conclusions that we draw inductively from samples of data are never fixed or firm. We may be able to characterize our uncertainty in various ways, but we can never be 100% sure of anything when we are using statistical inference. This leads to an important idea that you should always keep in mind when reasoning from samples of data:

You cannot prove anything from samples or by using statistical inference.

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