The material in this book is an enlarged version of a highly successful, short course of lectures given to graduate students in the Nuclear Physics Laboratory, Oxford. The course was designed to interest both nuclear structure and elementary particle physicists.

I am an experimental high energy physicist, and although as an undergraduate I suffered a course in statistics, it was only later during my research work, when I had to deduce something from my own data, that I learned how to use statistics. I also discovered that there were many things that one learned by experience and which were not explicitly mentioned in text-books; I tried to incorporate these aspects of the subject in my lectures. The emphasis of my lectures was thus not on formal proofs or on a rigorous treatment of the subject, but rather on practical applications and on how to use statistics to obtain the best results from one's data and to know the limitations of the results. In short, this was a course given by a non-statistician to non-statisticians.

My course did not attempt to cover every single example of statistics problems that can arise in nuclear and particle physics. The aim was rather to explain as fully as possible the different techniques that are available for attacking data analysis problems, to explain their relative merits and drawbacks, and to try to give the students sufficient confidence in their own ability to tackle any new problems that they might encounter. The book has maintained this approach.

Why do we do experiments?

There are basically two different types of results of experiments that scientists perform in order to learn about the physical world. In one type, we set out to determine the numerical value of some physical quantity, while in the second we are testing whether a particular theory is consistent with our data. These two types are referred to as ‘parameter determination’ and ‘hypothesis testing’ respectively. (Of course, in real life situations there is a degree of overlap between the two: a parameter determination may well involve the assumption that a specific theory is correct, while a particular theory may predict the value of a parameter.) For example, a parameter determination experiment could consist of measuring the velocity of light, while a hypothesis testing experiment could check whether the velocity of light has suddenly increased by several percent since the beginning of this year.

In this chapter, we are mainly concerned with various aspects of calculating the accuracy of parameter determination type experiments. We will have more to say about hypothesis testing experiments in Chapter 2.

Why estimate errors?

When we performed parameter determination experiments at school, we considered that the job was over once we obtained a numerical value for the quantity we were trying to measure. At university, and even more so in every-day situations in the laboratory, we are concerned not only with the answer but also with its accuracy.

FINDING A CLOCK THAT WOULDN'T GET SEASICK

Navigation has provided one of the most persistent motives for measuring time accurately. All navigators depend on continuous time information to find out where they are and to chart their course. But until about two centuries ago, no one was able to make a clock that could keep time accurately at sea.

COOLING OFF

How do you make something colder? Making something hotter is easy. For example, if you need to warm yourself on a chilly night, you can build a fire with little or no technology. But to cool yourself on a hot day is quite another matter.

THE GENESIS OF AN IDEA

The year was 1665, the month was August, and Cambridge, England, was besieged by bubonic plague. Isaac Newton, then a 23-year-old university student, retired to the solitude of his family's farm in Lincolnshire until the plague subsided and the university reopened. Not taking kindly to inactivity, Newton composed 22 questions for himself to tackle, ranging from geometric constructions to Galileo's new mechanics to Kepler's planetary laws. During the next 18 months, he immersed himself in the search for answers and along the way discovered calculus, the laws of motion, and the universal law of gravity.

THE UNIVERSE AS A MACHINE

In the seventeenth century science assumed its modern form and the scientific spirit infected Europe. It was then that Aristotle's view of nature was rejected and Galileo's great book of the universe was adopted. The new science was nourished by an optimism that mankind could discover the laws of nature.

One of the most significant and influential figures in seventeenth-century natural philosophy was René Descartes. Early in his life, Descartes rebelled against the traditions in which he had been thoroughly educated. He sought new foundations for knowledge, foundations which could underpin confidence in our understanding of nature. Convinced of the indubitable logic of mathematics, Descartes chose to identify mathematics with physics.

Descartes is credited with having been the first person to state the law of inertia correctly.

FREEWAYS IN THE SKY

Not many years ago, the only conceivable use of the beautiful celestial mechanics developed over hundreds of years was to compute the positions of bodies in the heavens. Today that situation has changed radically.