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Statistical analysis of circular data
Book Reviews ~Earth-Science Reviews 36 (1994) 243-276
planet, the evolution of the crust and mantle, and changing sea level and continental freeboard. Thereafter the author treats the subject in chronological order. Three chapters on the Archaean and Proterozoic are followed by two each on the Palaeozoic and Mesozoic-Cenozoic, the first on life and palaeoenvironments and the second on tectonics. The range of subjects dealt with, from Archaean greenstone belts to mass extinctions, is immense, and they are presented with the impressive clarity that indicates a thorough mastery of the material. Rogers's own research has been on Precambrian rocks, so it is not surprising that the chapters on the Archaean and Proterozoic are written with real authority. It is all the more impressive that he deals competently with very different subjects, such as the changing life of the Phanerozoic. The balance in the treatment of a great diversity of topics is in my view just about right and a large and up-to-date literature is cited. Thus if the reader wishes to know the current views on, for example, ice ages, displaced terranes or the evolution of the atmosphere, he or she will find a lucid and concise summary, with abundant references for further reading. No hobby horses are ridden and level headed and judicious interpretations prevail. Where controversy is acute or unsupported speculation prevalent this is clearly indicated, such that no one is likely to be misled as to the current state of knowledge on a given subject. The writing style is good and there is an abundance of excellent diagrams which have been specially drawn, but I was not impressed with many of the photographs, which are generally not much of an aid to understanding. The book is aimed primarily at advanced undergraduate and graduate students, but many professionals would find it invaluable. I know of no better global historical geology textbook at this level and, at a very reasonable price for a large format work, it deserves to sell well. A. Hallam, Birmingham
SSD1 0 0 1 2 - 8 2 5 2 ( 9 4 ) 0 0 0 0 3 - F
249
Statistics N.I. Fisher, 1993. Statistical Analysis of Circular Data. Cambridge University Press, Cambridge, U.K., 277 pp. Price: $35.00 hardcover. ISBN 0521-35018-2. This book is the latest word on circular statistics, which is to say, the side of statistics that deals with directions, angles, occurrences during daily or annual cycles and so forth. It deals strictly with two-dimensional problems, and is thus intended to be the companion volume to Statistical Analysis of Spherical Data (Fisher, Lewis and Embleton, 1987), which deals with problems of orientation in three dimensions. This subject was covered in 1981 by Batschelet, in a book that is a model of clarity and organization, and one which I have greatly enjoyed using, so this review must ask how the two books stack up against each other: does Fisher's book improve on Batschelet's or add to it sufficiently to warrant the purchase? To cut to the conclusion, the books are complementary, and both are necessary to someone working with circular data. Fisher's book is very nicely made: everything is well laid out, the paper is good, the diagrams (all line drawings) are well reproduced, and I didn't notice any typographical errors. The book consists of 11 pages of references, 17 pages of datasets taken from the literature and used as examples throughout the text, 19 pages of statistical tables and 219 pages of text. The chapters cover descriptive methods, probability distributions, analysis of single datasets, analysis of multiple datasets, correlation and regression, temporal and spatial data, and modern statistical techniques. Fisher's and Batschelet's reference lists are complementary. The basic references appear in both, but Fisher uses many newer case studies and drops the older ones. The difference (and the age of Batschelet's book) is made apparent by the fact that none of Fisher's articles are cited in Batschelet's book because they are younger, whereas the updating of references and case studies means that nothing of Batschelet's, except his book, is cited by Fisher.
250
Book Reviews~Earth-Science Rev&ws36 (1994) 243-276
The statistical tables also show surprisingly little overlap between the two books. Most of the relatively few duplicates are significantly different in coverage or organization. As a general comment, it would be very useful, now that calculation is no longer expensive and difficult, if authors of statistical tables would include, with their instructions on using the table, an algorithm for computing the probability of any score. Fisher covers a lot of material that Batschelet largely ignores. For example, he has a fascinating historical introduction (Florence Nightingale pioneered rose diagrams to show seasonality of causes of death!). He discusses data display and related problems of arbitrariness and artefacts, and he makes a plea for publishing plots of raw data. He offers an excellent discussion on various probability models and their assumptions and applications. The core of the book is the analysis of distributions in single-sample datasets, comparing the distributions of multiple datasets, and analyzing relationships between circular variables (correlation and regression), and it contains a significant but overall minor amount of post-Batschelet material. To broaden his book's appeal, Fisher has included many examples from the earth sciences, but he still draws heavily from biology. This is nice for a geologist, but it is not especially important. Near the end of the book, Fisher spends a little more time than Batschelet on analysis of spatial and temporal data, but this is far from everything that one needs to know in this field (the S T A T G R A P H I C S instruction manual is a slightly better starting place for time-series analyses, for example). Lastly, Fisher describes a variety of randomization and bootstrap techniques, new since Batschelet's book. Bootstrapping (repetitive recalculation of statistics using various subsamples of the main sample) gives an idea of the overall robustness and significance of the statistical parameters derived from the overall sample, and can provide a way of dealing with small samples. Randomization (e.g., of Y-axis scores relative to associated X-axis values) can help identify the source of a weak correlation and whether it indicates true randomness or not.
Overall, the strength of this book lies in its up-to-date overview, and in its broad thoughtfulness on what to do and why. However, I find that the review of basic circular statistics is a little more concise and less clear than it might be. In contrast, Batschelet spells out in the clearest possible fashion when and how to apply each test, what its assumptions and requirements are, and what its quirks and complications are. Fisher has a tendency to refer the readers back to the original articles for some of the information that I think a beginner would like to know. I therefore conclude that readers more expert than I in circular statistics will probably find Fisher's book to be a complete, concise, selfsufficient and up-to-date review, but for myself I anticipate starting any new statistical problem by reading Batschelet and then checking with Fisher before I actually begin. In short, if you need Batschelet's book, then you need this one too.
References Batschelet, E., 1981, Circular Statistics in Biology.Academic Press, London, 371 pp. Statistical Graphics Corporation, 1988, STATGRAPHICSR User's Guide, STSC, Inc. N.A. Wells, Kent, O H
SSDIOO12-8252(94)OOOO4-G
Crystal Field Theory Roger G. Burns, 1993. Mineralogical Applications of Crystal FieM Theory. Cambridge University Press. Hardcover, XXIII + 551 pp. Price: £50.00. ISBN 0-521-43077-1 This book is the revised and greatly enlarged version of an introduction to mineralogical applications of crystal field theory which first appeared in 1970. At that time, only relatively few Earth scientists were familiar with the concepts of crystal field theory, and therefore, the first edition of this book stimulated extensive research
planet, the evolution of the crust and mantle, and changing sea level and continental freeboard. Thereafter the author treats the subject in chronological order. Three chapters on the Archaean and Proterozoic are followed by two each on the Palaeozoic and Mesozoic-Cenozoic, the first on life and palaeoenvironments and the second on tectonics. The range of subjects dealt with, from Archaean greenstone belts to mass extinctions, is immense, and they are presented with the impressive clarity that indicates a thorough mastery of the material. Rogers's own research has been on Precambrian rocks, so it is not surprising that the chapters on the Archaean and Proterozoic are written with real authority. It is all the more impressive that he deals competently with very different subjects, such as the changing life of the Phanerozoic. The balance in the treatment of a great diversity of topics is in my view just about right and a large and up-to-date literature is cited. Thus if the reader wishes to know the current views on, for example, ice ages, displaced terranes or the evolution of the atmosphere, he or she will find a lucid and concise summary, with abundant references for further reading. No hobby horses are ridden and level headed and judicious interpretations prevail. Where controversy is acute or unsupported speculation prevalent this is clearly indicated, such that no one is likely to be misled as to the current state of knowledge on a given subject. The writing style is good and there is an abundance of excellent diagrams which have been specially drawn, but I was not impressed with many of the photographs, which are generally not much of an aid to understanding. The book is aimed primarily at advanced undergraduate and graduate students, but many professionals would find it invaluable. I know of no better global historical geology textbook at this level and, at a very reasonable price for a large format work, it deserves to sell well. A. Hallam, Birmingham
SSD1 0 0 1 2 - 8 2 5 2 ( 9 4 ) 0 0 0 0 3 - F
249
Statistics N.I. Fisher, 1993. Statistical Analysis of Circular Data. Cambridge University Press, Cambridge, U.K., 277 pp. Price: $35.00 hardcover. ISBN 0521-35018-2. This book is the latest word on circular statistics, which is to say, the side of statistics that deals with directions, angles, occurrences during daily or annual cycles and so forth. It deals strictly with two-dimensional problems, and is thus intended to be the companion volume to Statistical Analysis of Spherical Data (Fisher, Lewis and Embleton, 1987), which deals with problems of orientation in three dimensions. This subject was covered in 1981 by Batschelet, in a book that is a model of clarity and organization, and one which I have greatly enjoyed using, so this review must ask how the two books stack up against each other: does Fisher's book improve on Batschelet's or add to it sufficiently to warrant the purchase? To cut to the conclusion, the books are complementary, and both are necessary to someone working with circular data. Fisher's book is very nicely made: everything is well laid out, the paper is good, the diagrams (all line drawings) are well reproduced, and I didn't notice any typographical errors. The book consists of 11 pages of references, 17 pages of datasets taken from the literature and used as examples throughout the text, 19 pages of statistical tables and 219 pages of text. The chapters cover descriptive methods, probability distributions, analysis of single datasets, analysis of multiple datasets, correlation and regression, temporal and spatial data, and modern statistical techniques. Fisher's and Batschelet's reference lists are complementary. The basic references appear in both, but Fisher uses many newer case studies and drops the older ones. The difference (and the age of Batschelet's book) is made apparent by the fact that none of Fisher's articles are cited in Batschelet's book because they are younger, whereas the updating of references and case studies means that nothing of Batschelet's, except his book, is cited by Fisher.
250
Book Reviews~Earth-Science Rev&ws36 (1994) 243-276
The statistical tables also show surprisingly little overlap between the two books. Most of the relatively few duplicates are significantly different in coverage or organization. As a general comment, it would be very useful, now that calculation is no longer expensive and difficult, if authors of statistical tables would include, with their instructions on using the table, an algorithm for computing the probability of any score. Fisher covers a lot of material that Batschelet largely ignores. For example, he has a fascinating historical introduction (Florence Nightingale pioneered rose diagrams to show seasonality of causes of death!). He discusses data display and related problems of arbitrariness and artefacts, and he makes a plea for publishing plots of raw data. He offers an excellent discussion on various probability models and their assumptions and applications. The core of the book is the analysis of distributions in single-sample datasets, comparing the distributions of multiple datasets, and analyzing relationships between circular variables (correlation and regression), and it contains a significant but overall minor amount of post-Batschelet material. To broaden his book's appeal, Fisher has included many examples from the earth sciences, but he still draws heavily from biology. This is nice for a geologist, but it is not especially important. Near the end of the book, Fisher spends a little more time than Batschelet on analysis of spatial and temporal data, but this is far from everything that one needs to know in this field (the S T A T G R A P H I C S instruction manual is a slightly better starting place for time-series analyses, for example). Lastly, Fisher describes a variety of randomization and bootstrap techniques, new since Batschelet's book. Bootstrapping (repetitive recalculation of statistics using various subsamples of the main sample) gives an idea of the overall robustness and significance of the statistical parameters derived from the overall sample, and can provide a way of dealing with small samples. Randomization (e.g., of Y-axis scores relative to associated X-axis values) can help identify the source of a weak correlation and whether it indicates true randomness or not.
Overall, the strength of this book lies in its up-to-date overview, and in its broad thoughtfulness on what to do and why. However, I find that the review of basic circular statistics is a little more concise and less clear than it might be. In contrast, Batschelet spells out in the clearest possible fashion when and how to apply each test, what its assumptions and requirements are, and what its quirks and complications are. Fisher has a tendency to refer the readers back to the original articles for some of the information that I think a beginner would like to know. I therefore conclude that readers more expert than I in circular statistics will probably find Fisher's book to be a complete, concise, selfsufficient and up-to-date review, but for myself I anticipate starting any new statistical problem by reading Batschelet and then checking with Fisher before I actually begin. In short, if you need Batschelet's book, then you need this one too.
References Batschelet, E., 1981, Circular Statistics in Biology.Academic Press, London, 371 pp. Statistical Graphics Corporation, 1988, STATGRAPHICSR User's Guide, STSC, Inc. N.A. Wells, Kent, O H
SSDIOO12-8252(94)OOOO4-G
Crystal Field Theory Roger G. Burns, 1993. Mineralogical Applications of Crystal FieM Theory. Cambridge University Press. Hardcover, XXIII + 551 pp. Price: £50.00. ISBN 0-521-43077-1 This book is the revised and greatly enlarged version of an introduction to mineralogical applications of crystal field theory which first appeared in 1970. At that time, only relatively few Earth scientists were familiar with the concepts of crystal field theory, and therefore, the first edition of this book stimulated extensive research