The Cambridge Dictionary of Statistics

I am glad to have this handy reference on my bookshelves. The fourth edition has been revised and expanded; in its present state the book is a reasonably complete collection of definitions with many illustrations, examples, formulas, and equations where necessary. Also included are short biographies of mathematicians and statisticians who made an impact on the development of theory of probability and statistics. The book also contains descriptions of pertinent software packages. Almost all entries have source references to follow up if so desired.

I emphasize: this is a good and useful book; I have no qualms recommending it to professionals and, more generally, to anyone interested in statistics. However, is the book perfect? No, it is not. It is always a subjective call whether to include a particular term in the book or not. I, therefore, would not make an issue of a few terms that have been omitted from the book. There are a few entries, though, that could stand a revision. I’ll give a couple of examples.

• Such an important term as Median is defined only for discrete distributions.
• The short entry Extrapolation is rather generic and sheds no light on the essence of the method; it ends with a puerile warning, Often a dangerous procedure.
• The entry for Image Restoration is pretty brief: Synonym for segmentation. This is obviously incorrect. Image restoration is a special discipline; segmentation is a method — one of many — that is used in image restoration.

To my best judgment, such misdefinitions are rare. If I had to pick an issue with the book it would concern the biographical entries. Most are too short and offer information, like school attended or positions held, for which I could not care less. I am more interested in the importance of their contribution to the field. I compared these with the corresponding entries in the competitor Oxford Dictionary of Statistics. It has the same problem. In both books the biographies are overly concise and rather shallow. May it be an industry standard? On the other hand, the entries have not been entirely reduced to chronological information, so many would disagree with may opinion. For example, a review of the book in the Journal of the American Statistical Association recommends the book to “…anyone interested in statistics. The short biographies alone make it worthwhile.”

By the way, each of the two Dictionaries has terms not included in the other, including among the biographies. I believe the Cambridge Dictionary might also benefit from inclusion of some statistical tables and a list of notations.

Alex Bogomolny is a freelance mathematician and educational web developer. He regularly works on his website Interactive Mathematics Miscellany and Puzzles and blogs at Cut The Knot Math.