Statistics and Scientific Method: An Introduction for Students and Researchers

by Peter J. Diggle, Amanda G. Chetwynd

Most introductory statistics text-books are written either in a highly mathematical style for an intended readership of mathematics undergraduate students, or in a recipe-book style for an intended audience of non-mathematically inclined undergraduate or postgraduate students, typically in a single discipline; hence, "statistics for biologists", "statistics for psychologists", and so on.

An antidote to technique-oriented service courses, Statistics and Scientific Method is different. It studiously avoids the recipe-book style and keeps algebraic details of specific statistical methods to the minimum extent necessary to understand the underlying concepts. Instead, the text aims to give the reader a clear understanding of how core statistical ideas of experimental design, modelling and data analysis are integral to the scientific method.

Aimed primarily at beginning postgraduate students across a range of scientific disciplines (albeit with a bias towards the biological, environmental and health sciences), it therefore assumes some maturity of understanding of scientific method, but does not require any prior knowledge of statistics, or any mathematical knowledge beyond basic algebra and a willingness to come to terms with mathematical notation.

Any statistical analysis of a realistically sized data-set requires the use of specially written computer software. An Appendix introduces the reader to our open-source software of choice, R, whilst the book's web-page includes downloadable data and R code that enables the reader to reproduce all of the analyses in the book and, with easy modifications, to adapt the code to analyse their own data if they wish. However, the book is not intended to be a textbook on statistical computing, and all of the material in the book can be understood without using either R or any other computer software.

190 pages, Hardcover

First published September 30, 2011

Reviews

[Anna Hepworth · Rating 5 out of 5]

So, I picked this up to be nosy, and find out what Peter Diggle considered to be introductory stats (I've more than one higher level textbook with their name on it). I'm not familiar with the work of Amanda Chetwynd, but might go see what else they have written. As such. I was not entirely surprised by the writing style, which I found very accessible -- my guess is that the average got-a-degree-in-science person with little previous knowledge statistics would find it accessible to somewhat challenging, while someone without that scientific background might be missing some of the assumed knowledge.

I was very pleased with the variety of topics covered, in particular that both time series and spatial statistics got a look in. Statistics is, in some ways, more accessible than when I started studying it, not least because there are many more computing tools to use, and this book has made good use of this.

The thing that isn't in there that I always want in an introductory sampler of statistics is qualitative analysis. But i guess not everything will fit (although this is a smaller book than many introductory stats books i've encountered)

Overall, this was nice and relaxing to read; the odd details that I'm 'oh, yes, that is a thing I should be able to articulate' but mostly a bit of history and a bit of how the data gets presented that just remind me of things I kind of know, and give some more context - particularly in terms of agricultural trials.

[Diffusion Tensor · Rating 3 out of 5]

The book is based on a course for first year postgraduate students in science and technology with no prior knowledge of statistics, and a mathematical background of basic algebra. The authors have written their book largely in a software-independent manner, but provide data sets and R scripts on a supplemental website. (R is a free, open source statistical software system that has emerged as the lingua franca of research statisticians.) The authors cover study design, exploratory data analysis, statistical models, and inference. Three special topics round out the book: survival analysis, time series, and spatial statistics. On the other hand, there is little coverage of other important topics such as categorical data (briefly discussed in Sec. 7.10) and nonparametric methods. The authors advocate a principled approach to statistical inference, based on the likelihood principle, and they stick to it throughout the text.

There is a lot to like in this book. The authors eschew the typical styles of statistics texts, which either dwell on the mathematical theory of probability and statistical inference, or avoid doing so by presenting a “recipe book” of techniques and formulae. The authors instead “have tried to emphasize statistical concepts, to link statistical method to scientific method, and to show how statistical thinking can benefit every stage of scientific inquiry, from processing the resulting data, to interpreting the results of the data-processing in their proper scientific context” (p. viii). I emphatically agree with the authors that this is the goal of a good applied statistics book, and with them I lament the lack of books that live up to this goal. Another major emphasis of the book is the authors’ encouragement of estimation at the expense of hypothesis testing. An interval estimate conveys both the magnitude and precision of a putative effect, neither of which is conveyed by reporting the result of a hypothesis test. Point and interval estimation help evaluate both practical (clinical) significance as well as statistical significance, whereas hypothesis testing addresses only the latter. The authors’ perspective on this issue helps reinforce the attitude that statistical analysis should be driven by fitness for purpose, rather than simply pattern-matching methods to data structures. Once again, I applaud the authors for taking this attitude, so sorely lacking in other texts, which tend to give only lip service to this issue when it is addressed at all.

Unfortunately, there are two reasons I think the book falls short of all that it could be. First, many opportunities are lost to teach about the common pitfalls of data analysis: concepts like the correlation vs. causation fallacy, regression to the mean, Simpson’s paradox, the winner’s curse, the hazards of multiplicity, and so on. These are statistical issues that often trip up working scientists and can lead to the publication of non-reproducible research.

The second reason for disappointment relates to details of the nuts and bolts of statistical analysis. The authors introduce histograms, but fail to warn their readers of the ease with which histograms can, deliberately or otherwise, give misleading impressions of the data. The visual impression given by a histogram can be extremely sensitive to the bin size and bin location used to construct the histogram; readers need to know this. The authors also introduce both the mean and standard deviation (moment-based measures of location and dispersion) but also the 5-number summary and interquartile range. They suggest the value of the latter for evaluating distributional shape, as well as potential outliers, but a more thorough discussion of the strengths and weaknesses of these descriptive statistics is needed. We need an example showing how the mean and standard deviation can go haywire when even a single outlier is present, and how both the median and interquartile range resist this problem. In general, the authors demonstrate a lack of interest in resistant and robust statistical methods, perhaps due to their stance on the likelihood principle? The authors do discuss checking assumptions, particularly using residual plots for statistical models. However, in the chapter on statistical modeling (Ch. 7), the authors often report estimates with many more decimal places than would seem to be justified.

One of the pedagogical choices made by the authors, perhaps to keep the book short, is their re-use of data sets by asking the reader to pretend that they were produced by different study designs. For instance, they analyze data from a chronic asthma treatment trial “as if” the data had been produced three ways: from a paired design, a parallel group design, and a cross-over design. A similar maneuver is used earlier in the book with a gene expression microarray data set. While these maneuvers certainly make for a shorter book, I fear that they undermine the central point that fitness for purpose should drive a statistician’s decisions, as well as potentially introducing confusion among students.

[Grey Sane · Rating 3 out of 5]

Pros:
Practical discussion

Cons:
Too detailed?