Statistical Rules of Thumb (Wiley Series in Probability and Statistics) [Paperback]

What a great idea. Rather than write a comprehensive text, Dr. VanBelle writes about a large number of statistical topics, focussing on areas that are confusing, or frequently misunderstood. Some of his "rules of thumbs" are approximate formulae for doing quick (but approximate) analyses. Most are more general advice, based on decades of consulting. Topics range from designing studies to making graphs, but most are about data analysis. Something for everyone in a well-written book.

Excellent reference for statisticians. Only two complaints:
1) In many instances, wording is not clear - you have to really pick sentences apart to figure out what the author meant.
2) Reasons for a particular rule sometimes leave you wanting. But at least you're introduced to the concept and can look elsewhere for assistance in understanding.

Also, the title might lead some non-statisticans to think that they can pick this book up and learn how to plug and chug in all sorts of situations. This is not the case.

Gerald van Belle is a biostatistician and professor at the University of Washington. He has coauthored an excellent text on biostatistics with Lloyd Fisher. In this delightful and clearly written text van Belle provides 99 rules of thumb based on his vast experience as a consultant and researcher in statistics and biostatistics. For a statistician or a student of statistics along with the term "rule of thumb" one thinks of the three sigma rule or the use of range divided by sample size as a quick estimate of standard error of the mean. But this text is much more than a compilation of such simple rules. Professor van Belle organizes the book into topical chapters on sample size determination, covariation, epidemiology, environmental studies, design, conduct and analysis of experiments, tables and graphics, and consulting. Each rule is put into proper context and is justified with mathemetical theorems or empirical evidence.
Some of the rules are more like guidance for proper approaches to problems. For example in reviewing the basics in chapter 1 van Belle discusses the linear model in terms of the key assumptions of independence, equal variance and normality. The rule of thumb in section 1.4 states that assumptions should be considered in the order (1) independence, (2) equal variance and (3) normality. Van Belle explains this order by showing that the inferences are far more sensitive to violations in the independence assumption than in either the assumption of equal variance or the assumption of normality. As a statistician, I am aware of the sensitivity to correlation and the fact that variances need to differ by a factor of nearly four before results are seriously affected. Also when the data do not fit the normal distribution we have the nonparametric alternatives based on ranks. Nevertheless,in practice it is easiest and routine to test normality first, variances second and correlation becomes an afterthought. In some situations this may be okay since we may have good reason to believe that the observations were generated independently. But the rule is a good practical guidance. If you question all three assumptions it makes sense to test them in the order van Belle is suggesting.

Other practical advice of this type include the following rules of thumb:
1. Start with the Poisson to model incidence or prevalence.
2. Begin with the exponential model for time to event data.
3. Begin with two exponentials to compare two survival distributions.
4. Begin with the lognormal distribution in environmental studies.

These rules are not meant to suggest that simple models always work or even that they work in the majority of case. It is just that it is best to start simple and let the analysis and diagnostics tell you when more complicated models are needed.

This book will be a great guide for statistical practitioners and a terrific reference for professional and consulting statisticians. The references suppoting the rules are as valuable as the rules themselves.