Statistics for economics, accounting, and business studies

Statistics for Economics,

Accounting and Business Studies

fourth edition

Michael Barrow

Additional student support at

www.pearsoned.co.uk/barrow Additional student support at

www.pearsoned.co.uk/barrow

9 780273 683087

ISBN 0-273-68308-X

www.pearson-books.com An imprint of

Statistics for Economics,

Accounting and Business Studies Barrow

fourth

edition

New to this edition:

More worked examples and real life business

applications show students how to use the

various techniques

Section exercises and end of chapter problems

allow for practice and testing

Chapters have been reorganised, making the

order more logical and flexible

Features:

Assumes no prior knowledge of statistics

or advanced level mathematics

Numerous real-life examples, problems

and applications are included, some

based on Excel

Use of computing in statistics is

explained and illustrated using industry￾based software, databases, etc.

Boxes highlight interesting issues, common

mistakes and give advice on using

computers in statistical analysis

A website accompanies the book with

resources for students and instructors

This fourth edition of Statistics for Economics, Accounting and Business Studies is written to provide a clear and

concise introduction to a range of statistical concepts and techniques. Throughout the text the author highlights

how and why these techniques can be used to solve real-life problems, ensuring that the material is relevant

to the experience of the student.

This is a core text for introductory courses in statistics

at undergraduate and MBA level. The book will be

particularly suitable for economics and accounting

students and will also appeal to those taking courses

in business studies.

Michael Barrow is Senior Lecturer in Economics at the

University of Sussex and has acted as a consultant for

major industrial, commercial and governmental bodies.

Statistics for Economics,

Accounting and Business Studies

fourth edition

Michael Barrow

‘An excellent reference book for the undergraduate student; filled

with examples and applications – both practical (i.e. computer

based) and traditional (i.e. pen and paper problems); wide-ranging

and sensibly ordered. The book is clearly written, easy to follow…

yet not in the least patronising. This is a particular strength.’

Christopher Gerry, UCL

Front cover image:

© Getty Images

027368308X_COVER 3/23/07 12:29 PM Page 1

Statistics for Economics,

Accounting and Business Studies

Visit the Statistics for Economics, Accounting and

Business Studies, fourth edition Companion Website at

www.pearsoned.co.uk/barrow to find valuable student

learning material including:

n Additional explanation of some topics with further

references

n Excel worksheets and demonstrations

n Annotated links to other useful websites

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Fourth Edition

Statistics for

Economics, Accounting

and Business Studies

Michael Barrow

University of Sussex

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Pearson Education Limited

Edinburgh Gate

Harlow

Essex CM20 2JE

England

and Associated Companies throughout the world

Visit us on the World Wide Web at:

www.pearsoned.co.uk

First published 1988

Fourth edition published 2006

© Pearson Education Limited 1988, 2006

The right of Michael Barrow to be identified as author of this work has been

asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

All rights reserved. No part of this publication may be reproduced, stored

in a retrieval system, or transmitted in any form or by any means, electronic,

mechanical, photocopying, recording or otherwise, without either the prior

written permission of the publisher or a licence permitting restricted copying

in the United Kingdom issued by the Copyright Licensing Agency Ltd,

90 Tottenham Court Road, London W1T 4LP.

All trademarks used herein are the property of their respective owners. The use

of any trademark in this text does not vest in the author or publisher any trademark

ownership rights in such trademarks, nor does the use of such trademarks imply any

affiliation with or endorsement of this book by such owners.

ISBN: 978-0-273-68308-7

British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library

Library of Congress Cataloging-in-Publication Data

Barrow, Michael.

Statistics for economics, accounting, and business studies / Michael Barrow.— 4th ed.

p. cm.

Includes index.

ISBN-13: 978-0-273-68308-7

ISBN-10: 0-273-68308-X

1. Economics–—Statistical methods. 2. Commercial statistics. I. Title.

HB137.B37 2006

519.5024'33—dc22

2005056640

10 9 8 7 6 5 4 3

10 09 08 07 06

Typeset in 9/12pt Stone Serif by 35

Printed and bound in Malaysia.

The publisher’s policy is to use paper manufactured from sustainable forests.

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For Patricia, Caroline and Nicolas

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Contents

Preface to the fourth edition xiii

Introduction 1

1 Descriptive statistics 7

Learning outcomes 8

Introduction 8

Summarising data using graphical techniques 10

Looking at cross-section data: wealth in the UK in 2001 15

Summarising data using numerical techniques 23

The box and whiskers diagram 41

Time-series data: investment expenditures 1970–2002 42

Graphing bivariate data: the scatter diagram 55

Data transformations 57

Guidance to the student: how to measure your progress 59

Summary 59

Key terms and concepts 60

Problems 60

Reference 66

Answers to exercises 66

Appendix 1A: Σ notation 70

Problems on Σ notation 71

Appendix 1B: E and V operators 72

Appendix 1C: Using logarithms 73

Problems on logarithms 74

2 Probability 75

Learning outcomes 75

Probability theory and statistical inference 76

The definition of probability 76

Probability theory: the building blocks 78

Bayes’ theorem 86

Decision analysis 88

Summary 92

Key terms and concepts 93

Problems 93

Answers to exercises 98

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viii Contents

3 Probability distributions 101

Learning outcomes 101

Introduction 101

Random variables 102

The Binomial distribution 103

The Normal distribution 109

The sample mean as a Normally distributed variable 116

The relationship between the Binomial and Normal distributions 122

The Poisson distribution 123

Summary 126

Key terms and concepts 126

Problems 126

Answers to exercises 131

4 Estimation and confidence intervals 133

Learning outcomes 133

Introduction 134

Point and interval estimation 134

Rules and criteria for finding estimates 135

Estimation with large samples 138

Precisely what is a confidence interval? 141

Estimation with small samples: the t distribution 148

Summary 153

Key terms and concepts 154

Problems 154

Answers to exercises 156

Appendix: Derivations of sampling distributions 158

5 Hypothesis testing 159

Learning outcomes 159

Introduction 160

The concepts of hypothesis testing 160

The Prob-value approach 167

Significance, effect size and power 168

Further hypothesis tests 169

Hypothesis tests with small samples 174

Are the test procedures valid? 176

Hypothesis tests and confidence intervals 176

Independent and dependent samples 177

Discussion of hypothesis testing 180

Summary 182

Key terms and concepts 182

Problems 183

Reference 186

Answers to exercises 187

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6 The χ2 and F distributions 190

Learning outcomes 190

Introduction 190

The χ2 distribution 191

The F distribution 205

Analysis of variance 207

Summary 214

Key terms and concepts 214

Problems 214

Answers to exercises 217

Appendix: Use of χ2 and F distribution tables 219

7 Correlation and regression 220

Learning outcomes 220

Introduction 221

What determines the birth rate in developing countries? 221

Correlation 223

Regression analysis 232

Inference in the regression model 238

Summary 251

Key terms and concepts 252

Problems 252

References 255

Answers to exercises 255

8 Multiple regression 258

Learning outcomes 258

Introduction 259

Principles of multiple regression 260

What determines imports into the UK? 261

Finding the right model 278

Summary 285

Key terms and concepts 286

Problems 286

References 289

Answers to exercises 290

9 Data collection and sampling methods 295

Learning outcomes 295

Introduction 296

Using secondary data sources 296

Using electronic sources of data 298

Collecting primary data 300

The meaning of random sampling 301

Contents ix

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x Contents

Calculating the required sample size 309

Collecting the sample 310

Case study: the UK Expenditure and Food Survey 313

Summary 314

Key terms and concepts 315

Problems 315

References 316

10 Index numbers 317

Learning outcomes 318

Introduction 318

A simple index number 318

A price index with more than one commodity 320

Using expenditures as weights 327

Quantity and expenditure indices 329

The Retail Price Index 334

Inequality indices 339

The Lorenz curve 340

The Gini coefficient 342

Concentration ratios 346

Summary 348

Key terms and concepts 349

Problems 349

Reference 354

Answers to exercises 354

Appendix: Deriving the expenditure share form of

the Laspeyres price index 357

Important formulae used in this book 359

Appendix: Tables 364

Table A1 Random number table 364

Table A2 The standard Normal distribution 366

Table A3 Percentage points of the t distribution 367

Table A4 Critical values of the χ2 distribution 368

Table A5(a) Critical values of the F distribution (upper 5% points) 370

Table A5(b) Critical values of the F distribution (upper 2.5% points) 372

Table A5(c) Critical values of the F distribution (upper 1% points) 374

Table A5(d) Critical values of the F distribution (upper 0.5% points) 376

Table A6 Critical values of Spearman’s rank correlation coefficient 378

Table A7 Critical values for the Durbin–Watson test at 5% 379

significance level

Answers to problems 380

Index 394

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Supporting resources

Visit www.pearsoned.co.uk/barrow to find valuable online resources

Companion Website for students

n Additional explanation of some topics with further references

n Excel worksheets and demonstrations

n Annotated links to other useful websites

For instructors

n Complete downloadable Instructors Manual, providing answers and

commentary on exercises

n Downloadable PowerPoint slides

For more information please contact your local Pearson Education sales

representative or visit www.pearsoned.co.uk/barrow

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Preface to the fourth edition

This text is aimed at students of economics and the closely related disciplines

of accountancy and business, and provides examples and problems relevant to

those subjects, using real data where possible. The book is at an elementary

level and requires no prior knowledge of statistics, nor advanced mathematics.

For those with a weak mathematical background and in need of some revision,

some recommended texts are given at the end of this preface.

This is not a cookbook of statistical recipes; it covers all the relevant con￾cepts so that an understanding of why a particular statistical test should be used

is gained. These concepts are introduced naturally in the course of the text as

they are required, rather than having sections to themselves. The book can

form the basis of a one- or two-term course, depending upon the intensity of

the teaching.

As well as explaining statistical concepts and methods, the different schools

of thought about statistical methodology are discussed, giving the reader some

insight into some of the debates that have taken place in the subject. The book

uses the methods of classical statistical analysis, for which some justification is

given in Chapter 5, as well as presenting criticisms which have been made of

these methods.

There have been some substantial changes to this edition in the light of my

own experience and comments from students and reviewers. There has been

some rearrangement of the chapters of the book, although the content remains

similar with a few changes to encourage better learning of the subject. The

main changes are:

n The old Chapters 2 (Index numbers) and 7 (Data collection and sampling

methods) have been moved to the end of the book. This allows a continuous

development from descriptive statistics, through probability concepts, to sta￾tistical inference in the first part of the book. This will suit many courses

which concentrate on the use of statistics and which do not wish to focus on

data collection. Index numbers and data collection now form the final two

chapters which may be thought of as covering the collection and prepara￾tion of data.

n The previous edition’s final chapter on time-series methods (covering sea￾sonal adjustment) has been dropped, but this chapter is available on the

website for those who wish to make use of it. It was apparent that not many

teachers used this chapter, so it has been dropped in order to keep the book

relatively concise.

n In most chapters, exercises have been added within the chapter, at the end

of each section, so that students can check that they have understood the

material (answers are at the end of each chapter). The previous edition’s

exercises (at the end of each chapter) are renamed ‘Problems’ and are mostly

Changes in this

edition

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xiv Preface to the fourth edition

unchanged (with answers to odd-numbered problems at the end of the

book). The new exercises are relatively straightforward and usually require

the student to replicate the calculations in the text, but using different data.

There is thus a distinction drawn between the exercises which check under￾standing and the problems which encourage deeper thinking and discussion.

n Some of the more challenging problems are indicated by highlighting the

problem number in colour. This warns that the problem might require

some additional insight or effort to solve, beyond what is learned from the

text. This may be because a proof or demonstration is demanded, or that the

problem is open-ended and requires interpretation.

n In a few places I have included some worked examples, but, in general, most

of the book uses examples to explain the various techniques. The new exer￾cises may be treated as worked examples if desired, as worked-out answers

are given at the end of each chapter.

n Where appropriate, the examples used in the text have been updated using

more recent data.

n There is a website (www.pearsoned.co.uk/barrow) accompanying the text.

For this edition the website contains:

– Powerpoint slides for lecturers to use (these contain most of the key

tables, formulae and diagrams, but omit the text). Lecturers can adapt

these for their own use.

– An instructor’s manual giving hints and guidance on some of the teaching

issues, including those that come up in response to some of the problems.

– Answers to even-numbered problems (available to lecturers).

– The chapter on seasonal adjustment of time-series data, mentioned above.

No more than elementary algebra is assumed in this text, any extensions being

covered as they are needed in the book. It is helpful if students are comfortable

manipulating equations so if some revision is required I recommend one of the

following books:

I. Jacques, Mathematics for Economics and Business, Prentice Hall, 2003.

E.T. Dowling, Mathematics for Economists, Schaum’s Outline Series in

Economics, McGraw-Hill, 1986.

J. Black and J. Bradley, Essential Mathematics for Economists, 2nd edn, Wiley,

1980.

Author acknowledgements

I would like to thank the anonymous reviewers who made suggestions for this

new edition and the many colleagues and students who have passed on

comments or pointed out errors or omissions in previous editions. I would like

to thank all those at Pearson Education who have encouraged me, responded

to my various queries and reminded me of impending deadlines! Finally, I

would like to thank my family for giving me encouragement and the time to

complete this new edition.

Mathematics

requirements and

texts

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