American Journal of Epidemiology Vol. 152, No. 3 : 295-296
Copyright © 2000 by The Johns Hopkins University School of Hygiene and Public Health
BOOK REVIEWS |
Probability without Equations: Concepts for Clinicians By Bart K. Holland
Department of Public Health Sciences Guy's, King's and St Thomas' School of Medicine King's College London London SE1 3QD, United Kingdom
This book has been written to meet the needs of health professionals who would otherwise be overwhelmed by the equations found in most introductory books on medical statistics. The author aims to explain the basic concepts of probability and statistics in plain English. There is a pressing need for an effective book of this type, and the author should be commended for tackling what is not an easy task.
The author begins with an introduction in which he describes explained and unexplained variability. The concept of random variation follows, and the value of statistical analysis becomes apparent.
Chapter 1 discusses statistical tests of significance. Null and alternative hypotheses are explained, and the p value is defined. Although the description is clear, there is a traditional emphasis on the testing of a hypothesis and on the need to obtain statistical significance for its rejection. The author appears to justify the retention of the well known p value thresholds (0.05, 0.01, and 0.001) on the rather unsatisfactory grounds that journal editors would look askance at other cutoff levels (p. 11). At this stage, the reader is not encouraged to quote exact p values, which is now acknowledged as good practice by most medical journals (this is remedied further on in the book).
Chapter 2 is by far the largest in the book. It gives an overview of the main concepts and tests used in statistical analysis and includes the t test, analysis of variance, nonparametric methods, the 
2 test and related tests, regression, correlation, and survival analysis! The description of methods based on the assumption of normality is satisfactory, if necessarily brief, but I found the discussion of nonparametric techniques very superficial. No mention is made of nonparametric tests for paired data. In addition, the remark on page 33 that for nonparametric methods, differences must often be substantial in order to be statistically significant is debatable for all but the smallest samples. This can be demonstrated by applying a nonparametric test and the equivalent normal assumption test to the same data. In my experience, the p values for the two tests are generally similar. The author should note that not all nonparametric methods are based on ranks–for example, the Pitman test, which uses the actual scores (1
).
Certain aspects of the 2 test are explained very well. On page 38, I found the argument for the number of degrees of freedom in a 2 x 2 table both simple and convincing. Imagine that the marginal totals are known. The number of degrees of freedom is the number of cells required in the table before the remaining cells can be calculated by subtraction. However, it is disappointing to see that the explanation for the calculation of proportions in a 2 x 2 table virtually amounts to the use of formulae. Fisher's exact test can be applied to larger tables than just the 2 x 2 case (p. 37). The descriptions of correlation, regression, and survival analysis which follow cover the main concepts and benefit considerably from several clear diagrams. I was relieved to see that chapter 2 concludes with a discussion of confidence intervals, including an exhortation to authors to quote them in writing up their research so that readers can make their own assessment of the strength of the evidence against the null hypothesis. The use of exact p values is also belatedly encouraged.
Chapter 3 concerns diagnostic testing. The definitions of sensitivity, specificity, and predictive values on page 68 are given in simple English. I was therefore surprised to see these measures also referred to by notation, such as P(D+|T+), which could perplex some readers. As a consequence, the numerical example on diagnostic testing is not particularly user-friendly.
Chapter 4 covers epidemiologic study design. At this stage in the book, it comes as a breath of fresh air, being written in language which can be readily understood. Cross-sectional and case-control studies are described, including an explanation of confounding variables, matching, and stratification, along with recall bias and selection bias.
The final chapter, which is about clinical trials, covers controls (particularly placebos), randomization stopping rules, and blind assessment of outcomes. This chapter concludes with a focus on consent and ethics, giving the reader a clear introduction to this important aspect of medical research. However, this could have been improved by explicit reference to the basic principles of ethics (autonomy, beneficence, nonmaleficence, and justice) (for example, see Gillon (2)).
Throughout the book, key concepts are described in separate sections which are clearly marked. These generally include simple diagrams, along with very understandable explanations. For instance, the figures for power against sample size (p. 18) give the clear message that small samples are ineffective. The busy clinician may well gain some benefit by scanning through these sections on key concepts. As a rare exception, the diagram on page 12 should have appropriate p values between 0 and 1 indicated along the horizontal axis. In addition, this diagram as it stands gives the misleading impression that the null hypothesis is true at the maximum possible p value (that is, when p = 1), even though the definition of a p value is clearly given in the text.
I found the remainder of the text somewhat disappointing. Readers who are dismayed by the use of symbols as well as equations will find chapter 2 off-putting. In addition, it should have been possible to avoid reference to certain technical terms such as "alpha error" and "beta error".
There are occasional mistakes in some of the numerical illustrations. The p value given on page 17 is a case in point, as the possibility of no successes with the three patients is overlooked. Also, in the example illustrating Wilcoxon's rank sum test (p. 32), the author claims that a 25:30 split in rank totals for the two groups demonstrates no difference between the two groups. In fact, an even closer split of 27:28 is possible (consider 1, 4, 6, 7, 9 and 2, 3, 5, 8, 10 as the ranks in the respective groups).
Given the target audience, a lighter tone should have been adopted, and possibly the use of cartoons, as in the recent introductory texy by Bowers (3). However, this book is a step in the right direction. It should be found useful by some of the clinicians who turn to me for statistical advice.
NOTES
ISBN 0-8018-5760-0, Johns Hopkins University Press, Baltimore, Maryland (Telephone: 800-537-5487, Fax: 410-516-6998), 1997, 128 pp., Hardcover $45.00, Paperback $16.95
REFERENCES
- Sprent P. Applied nonparametric statistical methods. 2nd ed. London, United Kingdom: Chapman and Hall Ltd, 1993.
- Gillon R. Philosophical medical ethics. Chichester, United Kingdom: John Wiley and Sons, 1986.
- Bowers D. Statistics from scratch: an introduction for health care professionals. Chichester, United Kingdom: John Wiley and Sons, 1996.
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