BOOK REVIEWS

SMALL BUT PERFECTLY FORMED

New Cambridge Statistical Tables (2nd Edition) DV Lindley and WF Scott (Cambridge University Press, Cambridge. 1995, 96pp, ISBN 0 521 48485; £3.50, US$12.95)

This is an excellent book being the second edition of these tables, the first being published in 1984. The only change from the first edition is the inclusion of tables of Bayesian confidence intervals for the binomial and Poisson distributions and for the square of a multiple correlation coefficient.

The book is composed of 31 tables, covering standard procedures. These include binomial, Poisson, Normal, chi- squared, t, Behrens' and F distributions and non-parametric procedures (Spearman's S, Kendall's K, Kolmogorov -Smirnov, Wilcoxon signed-rank, Mann-Whitney). There are also tables of percentage points for the correlation coefficient (exact for a correlation coefficient of 0, and approximate for non-zero values). There are hypergeometric probabilities (useful for the procedures described in Bates and Lambert, 1991), random number tables and random normal deviates. Then there are the Bayesian confidence intervals. The table for Bayesian confidence intervals for the binomial distribution may be of use when a scientist is asked to comment on the relative frequency of a characteristic when, in his own experience, he has not observed such a characteristic, a situation described in Aitken (1991). It may be wondered what priors are used to construct these intervals. As always, all eventualities are considered. The tabulated values are given for reference priors and instructions are given for the incorporation of informative priors (beta for the binomial and gamma for the Poisson). The last table gives Bayesian confidence limits for the square of a multiple correlation coefficient. When considering the normal distribution of (k+l) quantities, this is the proportion of the first variable that is accounted for by the remaining k.

Interpolation may be necessary in certain situations. The tables explain which type of interpolation is necessary (linear, quadratic or harmonic) and at the back of the book there are explanations of how to do each. Thus, even if one does not need the tables for a particular piece of work but does need to know how to do a certain type of interpolation, this book will provide the answer.

This is an excellent book offered at an unusually low price of £3.50. Any forensic scientist who analyses data will be well advised to ensure that a copy is always close to hand.

References

Aitken CGG. Populations and samples. In: The use of statistics in forensic science. Aitken CGG and Stoney DA, eds. Ellis Horwood 199 1: 77-79.

Bates JW and Lambert JA. Use of the hypergeometric distribution for sampling in forensic glass comparison. Journal of the Forensic Science Society 199 1; 3 1: 449-455.

C Aitken

PROVED BY STATISTICS THAT SOME CAUSE WAS JUST

Statistics and the Evaluation of Evidence for Forensic Scientists CGG Aitken (John Wiley & Sons Ltd, Chichester; 1995, 260pp, index, 0 471 95532 9; £34.95)

The topic of statistics is one which many scientists react to adversely but if they have had the opportunity to read this book they may well change their views on statistics as an aid to the interpretation of scientific evidence. It contains eight well written chapters covering the topics of Uncertainty in Forensic Science, the Evaluation of Evidence, Variation, Historical Review, Transfer Evidence, Discreet Data, Continuous Data and DNA Profiling. Each chapter is well presented and draws the reader into the world of statistics in a sound and logical manner. It is a

There is more to this book than just sets of tables, however. book which is better read in large sections rather than, as many scientists do, dipped into. However, this does not

Each table has a useful introduction. It explains how to use mean that the reader will be unable to quickly find relevant

the table, which is only to be expected. However, it also parts of the statistical arguments presented. Rather the

gives the expressions for the underlying distributions. For contrary, but it is important that the reader spends some

example, for the t and chi-squared tables the formulae for time in reaching an understanding of the fundamentals set

the t and chi-squared distributions are given. These may not out in chapters 1, 2 and 3.

be essential for most forensic scientists but are certainly useful for students of mathematics and statistics. Also, the introductions give approximations to enable the determination of results when the parameter values exceed the range of the tables. Thus, approximations based on the Normal distribution are given for many familiar situations which could take some considerable time to find if one was left to search through text books.

Chapter 1 is mainly concerned with introducing the reader to the problems of probability. The author then moves on to discuss probability in terms of odds and Bayes theorem in chapter 2. Those familiar with the forensic science literature will be appreciative of the effort the author has made to introduce, define and describe Bayes theorem in terms which are readily recognisable to the forensic scientist. In

Science & Justice 1996; 36(1): 64-68