There are a vast number of books on statistics — Amazon alone lists 10,000+ "professional and technical" works with statistics in their title. There is no single book or website on statistics that meets the need of all levels and requirements of readers, so the answer for many people starting out will be to acquire the main 'set books' recommended by their course tutors and then to supplement these with works that are specific to their application area. Every topic and subtopic in this Handbook almost certainly has at least one entire book devoted to it, so of necessity the material we cover can only provide the essential details and a starting point for deeper understanding of each topic. As far as possible we provide links to articles, web sites, books and software resources to enable the reader to pursue such questions as and when they wish.
Most statistics texts do not make for easy or enjoyable reading! In general they address difficult technical and philosophical issues, and many are demanding in terms of their mathematics. Others are much more approachable — these books include 'classic' undergraduate text books such as Feller (1950, [FEL1]), Mood and Graybill (1950, [MOO1]), Hoel (1947, [HOE1]), Adler and Roessler (1960, [ADL1]), Brunk (1960, [BRU1]), Snedecor and Cochrane (1937, [SNE1]) and Yule and Kendall (1950, [YUL1]) — the dates cited in each case are when the books were originally published; in most cases these works then ran into many subsequent editions and though most are now out-of-print some are still available. A more recent work, available from the American Mathematical Society and also as a free PDF, is Grinstead and Snell's (1997) An Introduction to Probability [GRI1]. Still in print, and of continuing relevance today, is Huff (1954, [HUF1]) "How to Lie with Statistics" which must be the top selling statistics book of all time. A more recent book, with a similar focus, is Blastland and Dilnot's "The Tiger that Isn't" [BLA1], which is full of examples of modern-day use and misuse of statistics. Another delightful, lighter weight book that remains very popular, is Gonik and Smith's "Cartoon Guide to Statistics" (one of a series of such cartoon guides by Gonik and co-authors, [GON1]). A very useful quick guide is the foldable free PDF format leaflet "Probability & Statistics, Facts and Formulae" published by the UK Maths, Stats and OR Network [UKM1]. The free Statistics Guide for Lawyers (PDF) available on the RSS website is a highly recommended resource (RSS and ICCA) for both lawyers and non-lawyers alike.
Essential reading for anyone planning to use the free and remarkable "R Project" statistical resource is Crawley's "The R Book" (2007, 2015 [CRA1]) and associated data files; and for students undertaking an initial course in statistics using SPSS, Andy Field's "Discovering Statistics Using SPSS" provides a gentle introduction with many worked examples and illustrations [FIE1]. Both Field and Crawley's books are large — around 900 pages in each case. Data obtained in the social and behavioral sciences do not generally conform to the strict requirements of traditional (parametric) inferential statistics and often require the use of methods that relax these requirements. These so-called nonparametric methods are described in detail in Siegel and Castellan's widely used text "Nonparametric Statistics for the Behavioral Sciences" (1998, [SIE1]) and Conover's "Practical Nonparametric Statistics" (1999, [CON1]).
A key aspect of any statistical investigation is the use of graphics and visualization tools, and although technology is changing this field Tufte's "The Visual Display of Quantitative Information" [TUF1] should be considered as essential reading, despite its origins in the 1980s and the dramatic changes to visualization possibilities since its publication.
With a more practical, applications focus, readers might wish to look at classics such as Box et al. (1978, 2005, [BOX1]) "Statistics for Experimenters" (highly recommended, particularly for those involved in industrial processes), Sokal and Rohlf (1995, [SOK1]) on Biometrics, and the now rather dated book on Industrial Production edited by Davies (1961, [DAV1]) and partly written by the extraordinary George Box whilst a postgraduate student at University College London. Box went on to a highly distinguished career in statistics, particular in industrial applications, and is the originator of many statistical techniques and author of several groundbreaking books. He not only met and worked with R A Fisher but later married one of Fisher's daughters! Crow et al. (1960, reprinted in 2003, [CRO1]) published a concise but exceptionally clear "Statistics Manual" designed for use by the US Navy, with most of its examples relating to ordnance — it provides a very useful and compact guide for non-statisticians working in a broad range of scientific and engineering fields.
Taking a further step towards more demanding texts, appropriate for mathematics and statistics graduates and post-graduates, we would recommend Kendall's Library of Statistics [KEN1], a multi-volume authoritative series each volume of which goes into great detail on the area of statistics it focuses upon. For information on statistical distributions we have drawn on a variety of sources, notably the excellent series of books by Johnson and Kotz [JON1], [JON2] originally published in 1969/70. The latter authors are also responsible for the comprehensive but extremely expensive nine volume "Encyclopedia of Statistical Sciences" (1998, 2006, [KOT1]). A much more compact book of this type, with very brief but clear descriptions of around 500 topics, is the "Concise Encyclopedia of Statistics" by Dodge (2002, [DOD1]).
With the rise of the Internet, web resources on statistical matters abound. However, it was the lack of a single, coherent and comprehensive Internet resource that was a major stimulus to the current project. The present author's book/ebook/website www.spatialanalysisonline.com has been extremely successful in providing information on Geospatial Analysis to a global audience, but its focus on 2- and 3-dimensional spatial problems limits its coverage of statistical topics. However, a significant percentage of Internet search requests that lead users to this site involve queries about statistical concepts and techniques, suggesting a broader need for such information in a suitable range of formats, which is what this Handbook attempts to provide.
A number of notable web-based resources providing information on statistical methods and formulas should be mentioned. The first is Eric Weisstein's excellent Mathworld site, which has a large technical section on probability and statistics. Secondly there is Wikipedia (Statistics section) — this is a fantastic resource, but is almost by definition not always consistent or entirely independent. This is particularly noticeable for topics whose principal or original authorship reflects the individual's area of specialism: social science, physics, biological sciences, mathematics, economics etc, and in some instances their commercial background (e.g. for specific software packages). Both Mathworld and Wikipedia provide a topic-by-topic structure, with little or no overall guide or flow to direct users through the maze of topics, techniques and tools, although Wikipedia's core structure is very well defined. This contrasts with the last two of our recommended websites: the NIST/SEMATECH online Engineering Statistics e-Handbook, and the UCLA Statistics Online Computational Resource (SOCR). These latter resources are much closer to our Handbook concept, providing information and guidance on a broad range of topics in a lucid, structured and discursive manner. These sites have a further commonality with our project — their use of particular software tools to illustrate many of the techniques and visualizations discussed. In the case of NIST/SEMATECH e-Handbook a single software tool is used, Dataplot, which is a fairly basic, free, cross-platform tool developed and maintained by the NIST. The UCLA Statistics Online Computational Resource project makes extensive use of interactive Java applets to deliver web-enabled statistical tools. The present Handbook references a wider range of software tools to illustrate its materials, including Dataplot, R, SPSS, Excel and XLStat, MATLab, Minitab, SAS/STAT and many others. This enables us to provide a broader ranging commentary on the toolsets available, and to compare the facilities and algorithms applied by the different implementations. Throughout this Handbook we make extensive reference to functions and examples available in R, MATLab and SPSS in particular.
[BOX1] Box G E P, Hunter J S, Hunter W G (1978) Statistics for Experimenters: An Introduction to Design, Data Analysis and Model Building. J Wiley & Sons, New York. The second, extended edition was published in 2005
[JON1] Johnson N L, Kotz S (1969) Discrete distributions. J Wiley & Sons, New York. Note that a 3rd edition of this work, with revisions and extensions, is published by J Wiley & Sons (2005) with the additional authorship of Adrienne Kemp of the University of St Andrews.
[KOT1] Kotz S, Johnson L (eds.) (1988) Encyclopedia of Statistical Sciences. Vols 1-9, J Wiley & Sons, New York. A 2nd edition with almost 10,000 pages was published with Kotz as the Editor-in-Chief, in 2006
[MAK1] Mackay R J, Oldford R W (2002) Scientific method, Statistical method and the Speed of Light, Working Paper 2002-02, Dept of Statistics and Actuarial Science, University of Waterloo, Canada. An excellent paper that provides an insight into Michelson’s 1879 experiment and explanation of the role and method of statistics in the larger context of science
[UKM1] UK Maths, Stats & OR Network. Guides to Statistical Information: Probability and statistics Facts and Formulae. http://icse.xyz/mathstore/index.html
NIST/SEMATECH e-Handbook of Statistical Methods: http://www.itl.nist.gov/div898/handbook/