8

Statistics for Experiments

It is possible, and indeed it is all too frequent, for an experiment to be so conducted that no valid estimate of error is available. In such a case the experiment cannot be said, strictly, to be capable of proving anything. Perhaps it should not, in this case, be called an experiment at all, but be added merely to the body of experience on which, for lack of anything better, we may have to base our opinions.

—Ronald A. Fisher

In this chapter we will look at statistical techniques that are common in many types of experiments. Many readers have probably heard about them but they are treated here because it is important for experimenters to understand how they work. An obvious reason is that it is difficult to interpret statistical results if you do not understand these techniques. Another reason is that it often helps to plan experiments so that they can be analyzed using statistical techniques. The foundations of the techniques were given in Chapter 7 and different aspects of planning experiments will be treated in subsequent chapters.

Keep in mind that you cannot learn any technique by reading about it in a book. Knowledge cannot be transferred – it comes about through an inner, intellectual process. Turning information into practical knowledge requires an active effort on your part. Although you may later use statistical software to analyze your data, you should complete the exercises in this chapter to make sure that you have not misunderstood details of the techniques. Many exercises can be solved manually and, in other cases, common software is sufficient to complete the tasks. The best way to learn statistics is to apply it. For this reason you are encouraged to actively think about ways to apply the techniques in this chapter to your own research.

It is important to point out that this chapter, and indeed this book, is too short to provide a comprehensive treatment of statistical techniques. I have simply chosen a few of the most common techniques in experimental science and tried to present them with less mathematics than many textbooks on statistics do. Further reading is suggested at the end of the chapter for those who want a deeper theoretical treatment of the subject. A good, general recommendation is to always keep a real statistics book within reach on the bookshelf.