Preface To the Student
Statistics is a mathematical science.
Although this is a very short sentence, perhaps a self-evident one, and certainly one of the shortest that you will find in this book, we want to draw your attention to several things about it:
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We use the singular "is" and not the plural "are." It is certainly grammatically correct and more common usage to say "statistics are...", but that use of the term refers to statistics as numerical values. In this sentence we mean statistics as a field of study, one that has its own concepts and techniques, and one that can be exciting to study and practice.
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We use "mathematical" as an adjective. Statistics certainly makes use of much mathematics, but it is a separate discipline and not a branch of mathematics. Many, perhaps most, of the concepts and methods in statistics are mathematical in nature, but there are also many that do not involve mathematics. You will see an example of this early in the book as you study the difference between observational studies and controlled experiments. You will find that even in cases where the mathematical aspects of two situations may be identical, the scope of one’s conclusions depends crucially on how the data were collected, a statistical rather than a mathematical consideration.
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We use the noun "science." Statistics is the science of gaining insight from data. Data are (notice the plural here) pieces of information (often but not always numerical) gathered on people or objects or processes. The science of statistics involves all aspects of inquiry about data. Well-designed studies begin with a research question or hypothesis, devise a plan for collecting data to address that issue, proceed to gather the data and analyze them, and then often make inferences about how the findings generalize beyond the particular group being studied. Statistics concerns itself with all phases of this process and therefore encompasses the scientific method.
In these materials, our goal is to introduce you to this practice of statistics, to help you think about the applications of statistics and to study the mathematical underpinnings of the statistical methods. Most of all, we hope you will find fun and engaging examples. Statistics is a vitally important subject, and also fun to study and practice, largely because it brings you into contact with all kinds of interesting questions. You will analyze data from medical studies, legal cases, psychology experiments, sociological studies, and many other contexts. To paraphrase the late statistician John Tukey, "the best thing about statistics is that it allows you to play in everyone’s backyard." You never know what you might learn in a statistics class!
One of the first features you will notice about these materials is that you will play the active role of investigator. You will read about an actual study and consider the research question, and then we will lead you to discover and apply the appropriate tools for carrying out the analysis. A primary reason for the investigative nature of these materials is that we strongly believe that you will better understand and retain the concepts if you build your own knowledge and are engaged in the context. Be sure to also pay attention to the Study Conclusions to see how to effectively convey statistical information and to the Practice Problems for testing your understanding. Key terms are also hyperlinked (though some pdf viewers change the # to %23, so you need to change back or just go to the main glossary link).
Though you will only scratch the surface of the statistical methods used in practice, you will learn fundamental concepts (such as variability, randomness, confidence, and significance) that are an integral part of many statistical analyses. A distinct emphasis will be the focus on how the data are collected and how this determines the scope of conclusions that you can draw from the data.
