By Professor J. H. GADDUM, Sc.D., F.R.S., M.R.C.S., L.R.C.P.
Professor of Pharmacology in the University of Edinburgh
When the truth is not plain to see the way is open for the expression of opinions, but opinions often differ and must be weighed against one another. The weight of an opinion may be increased by the quotation of authorities, but in these sceptical days even the highest possible authority carries less weight than it did. In some circles it is enough to assert that a new fact has been proved scientifically, and no further questions will be asked, but this gambit is not effective among the scientists themselves, and the need has been felt for some more emphatic formula of assertion.
The evidence that may be advanced in support of medical opinions is generally too complicated to be examined in detail by everyone concerned, and many things must be accepted by most doctors on the authority of experts, but the final answer to sceptics commonly depends on statistical evidence. In recognition of this fact, it has become the custom in recent years to support conclusions reached in the medical press by the statement that the results have been examined by a statistician and found to be significant. However, even this form of words is not enough to silence the really determined sceptic, who wishes to know how the statistician has examined the results and what he means when he says that they are significant. A large number of books have been written to explain these matters; the techniques used by statisticians have been described again and again, but generally with little reference to their logical basis and in terms which repel those who react against mathematical jargon.
It is generally agreed that some form of instruction in the elements of statistics is a desirable ingredient in the medical curriculum, but those who have tried to give this instruction have sought in vain for the ideal textbook to recommend to their students. Dr. L. Bernstein and Dr. M. Weatherall have had this experience and have decided to write the textbook themselves. They have explained the simpler statistical techniques in simple terms and have given an indication of their logical basis. It is hoped that their book will fulfil a real need.
This book has developed from a short course of lectures and practical classes given by us to medical students in their first year of preclinical studies. The experimental material quoted is mainly medical, but specialized medical knowledge is not necessary to understand the subject-matter, and the book is intended to be intelligible to students of other biological sciences and to any intelligent layman. Our aim has been not only to describe but also to explain the logical and mathematical bases of those statistical procedures which are commonly used in medical and biological research. The only mathematical knowledge assumed is arithmetic and elementary algebra, and some mathematical demonstrations have been omitted deliberately and explicitly where they would have required difficult or lengthy mathematical argument. As it has been our experience that most of our students come to us with a considerable amount of factual knowledge of a technical character but with little or no knowledge of the philosophy or logic of scientific method, we have considered this subject also in a very simple way.
We have included no recipes for practical work, but we believe it to be desirable that the student should test for himself that what is said in Chapters II to IV about the results of tossing coins or dice is confirmed in practice, and that he should collect data concerning many kinds of variables and analyse their frequency distributions. In our experience students do not usually grasp the subject-matter unless they have done the appropriate sums often enough to be familiar with them, but we feel that it is more valuable for them to solve problems of their own creation than to work through printed exercises; and most courses in experimental biochemistry, pharmacology and physiology will provide opportunities for applying the various procedures described, especially if the results obtained by a whole class are combined so as to provide a sufficient number of observations. All the calculations likely to be useful in this context are exemplified in the text. For their performance a slide rule is convenient but not essential; tables of squares, square roots and logarithms, which are more essential, are given at the end of the book.
The material in Chapters X to XIII is more difficult than the rest of the book, and should be read only if the earlier chapters have presented no great difficulty. These chapters may in any case be omitted at a first reading. The last three chapters should present difficulty to no one, and are in many ways the most important in the book.