Introduction

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Introduction

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The definition of what is meant by statistics and statistical analysis has changed considerably over the last few decades. Here are two contrasting definitions of what statistics is, from eminent professors in the field, some 60+ years apart:

"Statistics is the branch of scientific method which deals with the data obtained by counting or measuring the properties of populations of natural phenomena. In this definition 'natural phenomena' includes all the happenings of the external world, whether human or not." Professor Maurice Kendall, 1943, p2 [MK1]

"Statistics is: the fun of finding patterns in data; the pleasure of making discoveries; the import of deep philosophical questions; the power to shed light on important decisions, and the ability to guide decisions..... in business, science, government, medicine, industry..." Professor David Hand [DH1]

As these two definitions indicate, the discipline of statistics has moved from being grounded firmly in the world of measurement and scientific analysis into the world of exploration, comprehension and decision-making. At the same time its usage has grown enormously, expanding from a relatively small set of specific application areas (such as design of experiments and computation of life insurance premiums) to almost every walk of life. A particular feature of this change is the massive expansion in information (and misinformation) available to all sectors and age-groups in society. Understanding this information, and making well-informed decisions on the basis of such understanding, is the primary function of modern statistical methods.

Our objective in producing this Handbook is to be comprehensive in terms of concepts and techniques (but not necessarily exhaustive), representative and independent in terms of software tools, and above all practical in terms of application and implementation. However, we believe that it is no longer appropriate to think of a standard, discipline-specific textbook as capable of satisfying every kind of new user need. Accordingly, an innovative feature of our approach here is the range of formats and channels through which we disseminate the material - web, ebook and in due course, print. A major advantage of the electronic formats is that the text can be embedded with internal and external hyperlinks. In this Handbook we utilize both forms of link, with external links often referring to a small number of well-established sources, notably MacTutor for bibliographic information and a number of other web resources, such as Eric Weisstein's Mathworld and the statistics portal of Wikipedia, for providing additional material on selected topics.

The treatment of topics in this Handbook is relatively informal, in that we do not provide mathematical proofs for much of the material discussed. However, where it is felt particularly useful to clarify how an expression arises, we do provide simple derivations. More generally we adopt the approach of using descriptive explanations and worked examples in order to clarify the usage of different measures and procedures. Frequently convenient software tools are used for this purpose, notably SPSS/PASW, The R Project, MATLab and a number of more specialized software tools where appropriate.

Just as all datasets and software packages contain errors, known and unknown, so too do all books and websites, and we expect that there will be errors despite our best efforts to remove these! Some may be genuine errors or misprints, whilst others may reflect our use of specific versions of software packages and their documentation. Inevitably with respect to the latter, new versions of the packages that we have used to illustrate this Handbook will have appeared even before publication, so specific examples, illustrations and comments on scope or restrictions may have been superseded. In all cases the user should review the documentation provided with the software version they plan to use, check release notes for changes and known bugs, and look at any relevant online services (e.g. user/developer forums and blogs on the web) for additional materials and insights.

The interactive web version of this Handbook may be accessed via the associated Internet site: www.statsref.com. The contents and sample sections of the PDF version may also be accessed from this site. In both cases the information is regularly updated. The Internet is now well established as society’s principal mode of information exchange, and most aspiring users of statistical methods are accustomed to searching for material that can easily be customized to specific needs. Our objective for such users is to provide an independent, reliable and authoritative first port of call for conceptual, technical, software and applications material that addresses the panoply of new user requirements.

Readers wishing to obtain a more in-depth understanding of the background to many of the topics covered in this Handbook should review the Suggested Reading topic. Those seeking examples of software tools that might be used for statistical analysis should refer to the Software section.

References

[DH1] D Hand (2009) President of the Royal Statistical Society (RSS), RSS Conference Presentation, November 2009

[MK1] Kendall M G, Stuart A (1943) The Advanced Theory of Statistics: Volume 1, Distribution Theory. Charles Griffin & Company, London. First published in 1943, revised in 1958 with Stuart