Chapter 1
What is statistics?

(from The Crimson Petal and the White, Michael Faber, p. 334)

In this introductory chapter, we give a general description of the topics of statistics and probability theory. Some examples illustrate the purpose and applications of both disciplines, as well as the differences between them. As statistics has more applications in science, industry, and economics than probability theory, statistics is typically given far more attention in degree subjects like business, industrial and bio-science engineering, applied economics, and natural or social sciences. Nevertheless, one should pay some attention to probability theory as well. In fact, both disciplines are strongly connected to each other: it is impossible to understand the working of statistical inference without a sound knowledge of probability theory. Therefore, in this book, we discuss both probability theory and statistics.

1.1 Why statistics?

For many years, statistics has been a subject, often a dreaded one, in several fields of study at universities and colleges. The reason is that quite a few people will, sooner or later, be confronted with problems of data analysis during their professional activities. A sound statistical background not only allows us to analyze the data and to make concrete decisions based on the analysis, but it also provides an advantage in the data collection process.

Nevertheless, statistics is not immediately perceived as useful by most students. This is mainly due to the fact that, during a statistics course, they are still unfamiliar with the sorts of practical decision problems managers, economists, engineers, andresearchers face on a daily basis. Many students will start realizing the usefulness of statistics when they start to work on their bachelor's or master's thesis. The many examples in this basic course are intended to advance this awareness by several years.

In an introductory statistics course, one often finds a whole series of quotes as an attempt to motivate students. A classic example is "Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write." from the British writer Herbert George Wells (1866-1946). More recent is the judgment by the US quality guru W. Edwards Deming, to whom a large part of the downright spectacular economic recovery in Japan after World War II is attributed. He claimed that "Statistics is too important to be left to statisticians. The goal is to have many statistically-skilled workers: engineers, scientists, managers..." Hal Varian, chief economist at Google says the following: "I keep saying that the most sexy job in the next 10 years will be statistician. And I'm not kidding." In Europe, Willy Buysse, former CEO at SN Brussels Airlines, states that too few decisions are made based on data. Only recently, his many years of diligence establishing a research department, where statistical and other quantitative methods are used to address all sorts of problems, has been rewarded.

Another justification for a thorough training in statistical methods can be found in the so-called Six Sigma improvement program. The purpose of this program is to solve concrete problems with a large financial impact both in service and industrial companies, and to reduce the number of faults and defects to 3.4 per million opportunities. The approach is based on statistical methods, as presented in Figure 1.1. The figure shows that the traditional method to solve a practical problem is to immediately search for practical solutions. This approach is typically based on guessing and trial-and-error, so that it will often take a long time to find a final solution to the problem. The Six Sigma improvement program promotes a more thoughtful, scientific approach to problems. First, data is collected in the so-called measurement phase. Then, using statistical methods, the data is carefully examined. This often leads to interesting insights and recommendations to improve existing products, services, or processes. The Six Sigma approach also relies on the use of statistical process control and statistically designed experiments. Hence, statistics helps to find the best possible solution for all kinds of practical problems.

Figure 1.1 Using statistical methods to solve problems.

To achieve a successful cooperation between practitioners, on one hand, and statisticians, on the other, some openness is required on both sides. Engineers, economists, or scientists need a solid knowledge of the basic principles and techniques of statistics. Statistics is thus an indispensable skill in the repertoire of an effective employee. This explains why statistics is taught not only in the first and second years of many bachelor's degrees in engineering, sciences, and economics, but also later, for example in master's programs.

Finally, a thorough training in statistics is also a prerequisite for students of political and social sciences. They will also be confronted with numerous data sets in their professional careers that are impossible to interpret without a statistical background. For them, statistics is a stepping stone to econometric research methods.

1.2 Definition of statistics

The word statistics may sound familiar to anyone. A statistic usually refers to numerical information, for example, information about

• the population of a country: birth and death rates, immigration and emigration,.(such statistics are called population statistics),
• the economy: employment and unemployment rates, investments, prices, gross national products (GNP),.(these statistics are called economic statistics), or
• a company or sector: sales figures, income statements, growth, acquisitions, layoffs,.(these figures are called business statistics).

More formally, statistics can be defined as the set of methodologies for collecting, representing, analyzing, and interpreting data. This shows that the statistical science is a very general auxiliary science, which plays an important role in almost any environment. Applications of statistics are countless in engineering, medicine, economics, natural sciences, and business management, but statistics is also used in literature, history, political science, criminology, and even musicology.

In our modern society, data is massively present:

• computer files in companies contain sales data, cost data, and customer data (such as addresses, ordered quantities, and order frequencies),
• the financial pages of newspapers contain stock prices, commodity prices, and exchange rates,
• federal and regional authorities regularly publish data on population, trade, and industry, and
• the Internet is a source of numerous data sets.

Companies collect data naturally and actively. Among other things, this takes place by carrying out experiments (e.g., to design new products), in the context of statistical process control, or by measuring all kinds of properties of products, services, and processes. By continuously analyzing data, quality departments of companies attempt to deliver products or services with as few defects as possible and with the highest reliability. In addition, business processes are organized in such a way that waste is minimized, inspections of finished products are reduced to the minimum, and customer requirements are satisfied with minimal costs.

Research agencies collect data via surveys by phone, by post, via the Internet or by street interviews. Such surveys are designed to gather information about the shopping behavior of consumers, about the voting behavior of the population, or public opinion on social issues.

Statistics allows us to turn data into usable information. The role that statistics plays herein may be best illustrated based on some examples.

1.3 Examples

Example 1.3.1

An airline conducted a study on the behavior of its passengers on intercontinental flights and recorded

• the number of passengers with reservations that do not show up (the so-called no-shows),
• the weight of the luggage of passengers (often there is a limit of 20 kilograms), and
• the time the passengers arrive before the official departure time of the flight (for intercontinental flights, the passengers are asked to be at the airport at least two hours prior to departure).

The company recorded this data over several months and then made a distinction between passengers in economy class and passengersin business class. The data is analyzed with the aim of instituting appropriate policies. An example may be to allow overbooking, that is, to take more reservations than there are seats on the plane, or to apply more stringent action against passengers carrying too much luggage.

Example 1.3.2

In the production of coffee, the humidity during production is of crucial importance for the quality of the final product. The humidity is kept under control by a system that does not work flawlessly. Therefore, several measurements of the humidity are taken daily to determine whether it remains within appropriate limits. This approach is referred to as statistical process control.

Example 1.3.3

A filling machine for bottles usually has several filling heads, so that many bottles can be...