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Nando Lewis, Circular Statistics in R, Journal of the Royal Statistical Society Series A: Statistics in Society, Volume 179, Issue 4, October 2016, Page 1132, https://doi.org/10.1111/rssa.12222
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Circular Statistics in R faces little competition among statistical texts as it is one of only seven books on circular statistics and the only one published in over a decade. Examples of circular data include directions, angles and time measurements. For data of this type linear analysis is not suitable. For example, in linear statistics the mean of two angles a1=1∘ and a2=359∘ would be 180∘: the opposite side of the circle. This example could lead an analyst who is interested in wind directions to interpret incorrectly two northerly winds as having a mean direction due south, which is nonsense.
Although each chapter builds on the last, the authors link equations and code back to previous sections so that readers can use any chapter individually. The first four chapters provide an introduction to graphics, summary statistics and modelling distributions of circular data. Chapters 5 and 6 focus on basic inference and model fitting but only for single samples of circular data. It is only the final two chapters that begin to cover methods for data sets that are used by most researchers. Chapter 7 offers methods to compare means, medians and concentrations of different circular data sets. Chapter 8 introduces Pearson and Spearman equivalents for circular correlations and different univariate regression models for circular and linear data. The final five lines of the book provide the reader with recommended readings related to multivariate regression.
As an introduction to circular statistics this book is successful. In choosing R as the companion software the authors allow a wider range of researchers to use this text. Unfortunately, the lines of code that are included within the book are often lengthy and messy. Although the authors helpfully provide the code on line it is slightly different from that in the book and sometimes in the wrong order. Although this could be a limitation (and perhaps is for those who are new to R or code-based software), I feel that it, perhaps begrudgingly, forces the reader to develop a better understanding of the code and methods behind circular statistics. This book is ideal for a novice circular statistician who is interested in gaining a general understanding of circular statistics. For readers using complex data sets or who are interested in analyses beyond univariate regression this book is not sufficient.