Martin Bland's Text Book:
An Introduction to Medical Statistics
Contents of this page
An Introduction to Medical Statistics, now in its third edition,
is a book for medical students, doctors, medical researchers, and all who
want an introduction to statistics in a medical or health context. The
book has 410 pages with 118 figures.
The approach is firmly embedded in medical research, all the methods
described being illustrated with the use of real data, either from my own
research or from the medical literature. Equations and formulae are given
where appropriate and manual calculation is described, but the use of computers
for calculations is emphasised, together with the graphical methods which
computers make easy. For those who do not like to take things on trust,
mathematical appendices are included which explain the derivation of the
various statistical formulae, and graphical simulations are used to illustrate
some of the more surprising statistical principles.
The book begins with the design of clinical and epidemiological studies,
then describes methods for summarising and presenting the data collected.
Next probability is introduced, and the ways in which it can be used to
interpret data. The most commonly used statistical methods are described,
their assumptions and how these can be checked, their interpretation, and
how to choose the appropriate method for the analysis of different types
of data in various circumstances. Methods of particular relevance to medical
studies are discussed, such as the estimation of reference ranges, the
analysis of survival data, and the study of mortality. The book finishes
with chapters on multifactorial analyses and the choice of sample size.
Two types of exercises are included: 100 multiple choice questions of
the five branch True/False type, and long exercises involving calculations.
Full solutions are given.
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The third edition was published in August 2000. Due to cunning typesetting,
the length of the third edition is similar to that of the second edition,
but several new topics have been added and others extended.
New topics in the third edition include:

Consent in clinical trials

Ecological studies

Conditional probability

Confidence interval for a proportion when numbers are small

Correct confidence interval for group comparisons

Random effects in analysis of variance

Units of analysis and clusterrandomized trials

Intraclass correlation

Number needed to treat
Topics which have been considerably revised and/or extended include:

Experimental units

Histograms and other frequency graphs

Variables which follow a Normal distribution

The Normal plot

The use of transformations

The MannWhitney U test

Odds and odds ratios

Repeatability and measurement error

Sensitivity and specificity

Interaction in multiple regression

Logistic regression
A general change throughout the book is that sections containing material
usually found only in postgraduate courses have been starred *,
so that undergraduates can omit them at first reading.
The third edition was published together with a book by Martin Bland
and Janet Peacock: Statistical
Questions in Evidencebased Medicine, published by Oxford University
Press in September, 2000.
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Extracts from reviews of the first edition
The first edition was well reviewed, e.g.:
At last I have a book on medical statistics that I can safely
recommend to my students.  Journal of the Royal Statistical Society.
It is a book which I think anyone teaching an introductory
course in medical statistics should seriously consider as the main text.
 Statistics in Medicine.
If you want understand some of the statistical ideas important
to medicine but fear being overwhelmed by mathematics you will welcome
"An Introduction to Medical Statistics" by M. Bland.  British Medical
Journal.
Reviews of the second edition
Reviews received to date:
European Journal of Orthodontics
Martin Bland's textbook is one of those most commonly recommended
by academic medical statisticians in the UK for students and professionals
in healthrelated disciplines. According to the British Medical Journal
reviewer of the first edition, `If you want to understand some of the statistical
ideas important to medicine but fear being overwhelmed by mathematics you
will welcome this book'. And it is certainly sufficiently explicit and
prescriptive for those at the research stage of their careers. The second
edition is rather longer than the first, in particular sections on multifactorial
methods and determination of sample size have been greatly expanded to
form additional chapters. Each chapter includes several traditional multiple
choice questions, and a longer question: a section at the back of the book
gives full solutions to both. As in most other biostatistics texts, the
clinical and epidemiological examples used are medical rather than dental,
but do not presuppose specialized medical knowledge: the issues in dental
specialties are fundamentally similar, and a dental reader should find
the medical orientation no obstacle. The second edition is still good value
at 14.95 pounds.
R. G. Newcombe. (1996) European Journal of Orthodontics 18(3)
, 308.
N.B. The price is now higher, but still good value!  MB.
Academic Orthopaedic
Society Book Reviews
Title: An Introduction to Medical Statistics
Author: Martin Bland
Publisher: Oxford Medical Publications
Price: $27.95.
Comment: This paperback makes aspects of statistics and design
of experiments, sampling and observational studies, data presentation,
probability and other painful aspects of statistics relatively painless
although it does have a lot of math.
Reviews of the third edition
The third edition was reviewed by Les Huson (The Statistician,
50, 548). The review ends:
The coverage may not be very different from that of other introductory
texts, but in my view the style and content are, and they alone make this
text one of the best of its kind. The approach is very data driven, and
the use of real data makes this even more appealing. The concern throughout
is with statistical practice  i.e. with extracting meaningful information
from real data  and not statistical theory, although the necessary theoretical
ideas are explained in a nonmathematical way. The writing style  first
person throughout  is also attractive and makes the text easy to read
and digest, although it should also be said that this book contains a large
amount of material and to work through it thoroughly takes time! Using
the companion volume also [Statistical
Questions in Evidencebased Medicine], and working through the
exercises, would mean a very thorough course of study indeed.
All in all, this is an excellent book  it has been on my bookshelf
since the first edition, and in my view it should be the first choice for
any student wanting a serious introduction to the practice of medical statistics.
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An Introduction to Medical Statistics (ISBN 0 19 262428 8) is published
worldwide by Oxford University Press in
two versions: the standard soft cover edition (UK price 18.95 pounds) and
the subsidised English Language Book Service for developing countries.
In the USA it is published by Oxford
University Press Inc., New York. The ISBN is 0 19 263269 8.
There is an Arabic edition,
published by the Arab Center for Arabization, Translation, Authorship and
Publication (ACATAP),
Damascus.
There is an Italian edition,
published by Apogeo, Milan.
First edition: 16,000 copies (1987 to 1995).
Second edition: 13,495 copies (May 1995 to March 2001).
Second edition (ELBS): 1,551 copies (February 1997 to March 2001).
Third edition: 15,275 copies (August 2000 to March 2005).
Total sales to September 2004: 46,000 copies.
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Corrections
Corrections to the second edition
Despite the combined proofreading efforts of Doug Altman, Janet Peacock,
and myself, a few errors remain. An up to
date list of corrections to the second edition
is maintained on this site.
Corrections to the third edition
An up to date list of corrections to the third
edition is maintained on this site.
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Most of the datasets from An Introduction to Medical Statistics can
be found for downloading on my
download page.
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Contents of An Introduction to Medical Statistics
Highlighted sections can be read on the Web. Section in bold are new in
the third edition. Sections marked * contain material usually found only
in postgraduate courses.

Introduction

Statistics and medicine

Statistics and mathematics

Statistics and computing

The scope of this book

The design of experiments

Comparing treatments

Random allocation

* Methods of allocation without random numbers

Volunteer bias

Intention to treat

Crossover designs

Selection of subjects for clinical trials

Response bias and placebos

Assessment bias and double blind studies

* Laboratory experiments

* Experimental units

* Consent in clinical trials

Multiple Choice Questions 1 to 6

Exercise: The `Know Your Midwife' trial

Sampling and observational studies

Observational Studies

Censuses

Sampling

Random sampling

Sampling in clinical and epidemiological studies

Crosssectional studies

Cohort studies

Casecontrol studies

* Questionnaire bias in observational studies

* Ecological studies

Multiple Choice Questions 7 to 13

Exercise: Campylobacter jejuni infection

Summarizing data

Types of data

Frequency distributions

Histograms and other frequency graphs

Shapes of frequency distribution

Medians and quantiles

The mean

Variance, range and interquartile range

Standard deviation

Appendix: The divisor for the variance

Appendix: Formulae for the sum of squares

Multiple Choice Questions 14 to 19

Exercise: Mean and standard deviation

Presenting data

Rates and proportions

Significant figures

Presenting tables

Pie charts

Bar charts

Scatter diagrams

Line graphs and time series

Misleading graphs

Logarithmic scales

Appendix: Logarithms

Multiple choice questions 20 to 24

Exercise: Creating graphs

Probability

Probability

Properties of probability

Probability distributions and random variables

The Binomial Distribution

Mean and variance

Properties of means and variances

* The Poisson Distribution

* Conditional probability

Appendix: Permutations and combinations

Appendix: Expected value of a sum of squares

Multiple choice questions 25 to 31

Exercise: Probability and the life table

The Normal distribution

Probability distributions for continuous variables

The Normal distribution

Properties of the Normal distribution

Variables which follow a Normal distribution

The Normal plot

Appendix: The Chisquared, t, and F distributions

Multiple choice questions 32 to 37

Exercise: A Normal plot

Estimation

Sampling distributions

Standard error of a sample mean

Confidence intervals

Standard error of and confidence interval for a proportion

The difference between two means

Comparison of two proportions

* Standard error of a sample standard deviation

* Confidence interval for a proportion when numbers are small

* Confidence interval for a median and other quantiles

What is the correct confidence interval?

Multiple choice questions 38 to 43

Exercise: Means of large samples

Significance tests

Testing a hypothesis

An example: the sign test

Principles of significance tests

Significance levels and types of error

One and two sided tests of significance

Significant, real and important

Comparing the means of large samples

Comparison of two proportions

* The power of a test

* Multiple significance tests

* Repeated significance tests and sequential analysis

Multiple Choice Questions 44 to 49

Exercise: Crohn's disease and cornflakes

Comparing the means of small samples

The t distribution

The one sample t method

The means of two independent samples

The use of transformations

Deviations from the assumptions of t methods

What is a large sample?

* Serial data

* Comparing two variances by the F test

* Comparing several means using analysis of variance

* Assumptions of the analysis of variance

* Comparison of means after analysis of variance

* Random effects in analysis of variance

* Units of analysis and clusterrandomized trials

Appendix: The ratio mean/standard error

Multiple choice questions 50 to 56

Exercise: The paired t method

Regression and correlation

Scatter diagrams

Regression

The method of least squares

* The regression of X on Y

The standard error of the regression coefficient

* Using the regression line for prediction

* Analysis of residuals

* Deviations from assumptions in regression

Correlation

Significance test and confidence interval for r

Uses of the correlation coefficient

* Using repeated observations

* Intraclass correlation

Appendix: The least squares estimates

Appendix: The variance about the regression line

Appendix: The standard error of b

Multiple choice questions 57 to 61

Exercise: Comparing two regression lines

Methods based on rank order

* Nonparametric methods

* The Mann Whitney U Test

* The Wilcoxon matched pairs test

* Spearman's rank correlation coefficient, rho

* Kendall's rank correlation coefficient, tau

* Continuity corrections

* Parametric or nonparametric methods?

Multiple choice questions 62 to 66

Exercise: Application of rank methods

The analysis of crosstabulations

The chisquared test for association

Tests for 2 by 2 tables

The chisquared test for small samples

Fisher's exact test

Yates' continuity correction for the 2 by 2 table

* The validity of Fisher's and Yates' methods

Odds and odds ratios

* The chisquared test for trend

* Methods for matched samples

* The chisquared goodness of fit test

Appendix: Why the chisquared test works

Appendix: The formula for Fisher's exact test

Appendix: Standard error for the odds ratio

Multiple choice questions 67 to 73

Exercise: Admissions to hospital in a heatwave

Choosing the statistical method

* Method oriented and problem oriented teaching

* Types of data

* Comparing two groups

* One sample and paired samples

* Relationship between two variables

Multiple choice questions 74 to 80

* Exercise: Choosing a statistical method

Clinical measurement

Making measurements

* Repeatability and measurement error

* Comparing two methods of measurement

Sensitivity and specificity

Normal range or reference interval

* Survival data

* Computer aided diagnosis

* Number needed to treat

Multiple choice questions 81 to 86

Exercise: A reference interval

Mortality statistics and population structure

Mortality rates

Age standardization using the direct method

Age standardization by the indirect method

Demographic life tables

Vital statistics

The population pyramid

Multiple choice questions 87 to 92

Exercise: Deaths from volatile substance abuse

Multifactorial methods

* Multiple Regression

* Significance tests and estimation in multiple regression

* Interaction in multiple regression

* Polynomial regression

* Assumptions of multiple regression

* Qualitative predictor variables

* Multiway analysis of variance

* Logistic regression

* Survival data using Cox regression

* Stepwise regression

* Metaanalysis: data from several studies

* Other multifactorial methods

* Multiple choice questions 93 to 97

* Exercise: A multiple regression analysis

Determination of sample size

* Estimation of a population mean

* Estimation of a population proportion

* Sample size for significance tests

* Comparison of two means

* Comparison of two proportions

* Detecting a correlation

* Accuracy of the estimated sample size

* Trials randomized in clusters

* Multiple choice questions 98 to 100

* Exercise: Estimation of sample sizes

Solutions to exercises

References

Index
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Last updated: 19 September, 2009.
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