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To infer is to draw a conclusion from evidence. Statistical inference draws a conclusion about a population from evidence provided by a sample. Drawing conclusions in mathematics is a matter of starting from a hypothesis and using logical argument to prove without doubt that the conclusion follows. Statistics isn’t like that. Statistical conclusions are uncertain because the sample isn’t the entire population. So statistical inference has to not only state conclusions but also say how uncertain they are. We use the language of probability to express uncertainty.

Because inference must both give conclusions and say how uncertain they are, it is the most technical part of statistics. Texts and courses intended to train people to do statistics spend most of their time on inference. Our aim in this book is to help you understand statistics, which takes less technique but, often, more thought. We will look only at a few basic techniques of inference. The techniques are simple, but the ideas are subtle, so prepare to think. To start, think about what you already know and don’t be too impressed by elaborate statistical techniques: even the fanciest inference cannot remedy basic flaws such as voluntary response samples or uncontrolled experiments.