Choosing and Using Statistics E-Book

Calvin Dytham

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 528

Veröffentlichungsjahr: 2011

Beschreibung

Choosing and Using Statistics remains an invaluable guide for students using a computer package to analyse data from research projects and practical class work.  The text takes a pragmatic approach to statistics with a strong focus on what is actually needed.  There are chapters giving useful advice on the basics of statistics and guidance on the presentation of data. The book is built around a key to selecting the correct statistical test and then gives clear guidance on how to carry out the test and interpret the output from four commonly used computer packages: SPSS, Minitab, Excel, and (new to this edition) the free program, R. Only the basics of formal statistics are described and the emphasis is on jargon-free English but any unfamiliar words can be looked up in the extensive glossary. This new 3^rd edition of Choosing and Using Statistics is a must for all students who use a computer package to apply statistics in practical and project work.

Features new to this edition:

• Now features information on using the popular free program, R
• Uses a simple key and flow chart to help you choose the right statistical test
• Aimed at students using statistics for projects and in practical classes
• Includes an extensive glossary and key to symbols to explain any statistical jargon
• No previous knowledge of statistics is assumed

Leseprobe

Contents

Preface

The third edition

How to use this book

Acknowledgements for the first edition

1 Eight steps to successful data analysis

2 The basics

Observations

Hypothesis testing

P-values

Sampling

Experiments

Statistics

3 Choosing a test: a key

Remember: eight steps to successful data analysis

The art of choosing a test

A key to assist in your choice of statistical test

4 Hypothesis testing sampling and experimental design

Hypothesis testing

Acceptable errors

P-values

Sampling

Experimental design

5 Statistics, variables and distributions

What are statistics?

Types of statistics

What is a variable?

Types of variables or scales of measurement

Types of distribution

Discrete distributions

Continuous distributions

Non-parametric ‘distributions’

6 Descriptive and presentational techniques

General advice

Displaying data: summarizing a single variable

Displaying data: showing the distribution of a single variable

Descriptive statistics

Using the computer packages

Displaying data: summarizing two or more variables

Displaying data: comparing two variables

Displaying data: comparing more than two variables

7 The tests 1: tests to look at differences

Do frequency distributions differ?

Do the observations from two groups differ?

Do the observations from more than two groups differ?

There are two independent ways of classifying the data

More than one observation for each factor combination (with replication)

There are more than two independent ways to classify the data

Not all classifications are independent

Nested or hierarchical designs

8 The tests 2: tests to look at relationships

Is there a correlation or association between two variables?

Is there a cause-and-effect relationship between two variables?

Tests for more than two variables

9 The tests 3: tests for data exploration

Types of data

Observation, inspection and plotting

Symbols and letters used in statistics

Greek letters

Symbols

Upper-case letters

Lower-case letters

Glossary

Assumptions of the tests

What if the assumptions are violated?

Hints and tips

Using a computer

Sampling

Statistics

Displaying the data

Chapter 17

Index

This edition first published 2011, © 1999, 2003 by Blackwell Science, 2011 by Calvin Dytham

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Library of Congress Cataloging-in-Publication Data

Dytham, Calvin.

Choosing and using statistics: a biologist’s guide/by Calvin Dytham. - 3rd ed.

p. cm.

Includes bibliographical references and index.

ISBN 978-1-4051-9838-7 (hardback) - ISBN

1. Biometry. I. Title.

978-1-4051-9839-4 (pbk.)

QH323.5.D98 2011 001.4'22-dc22

2010030975

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

This book is published in the following electronic format: ePDF 978-1-4443-2843-1

Set in 9.5/12pt Berling by SPi Publisher Services, Pondicherry, India

1 2011

Preface

My aim was to produce a statistics book with two characteristics: to assume that the reader is using a computer to analyse data and to contain absolutely no equations.

This is a handbook for biologists who want to process their data through a statistical package on the computer, to select the most appropriate methods and extract the important information from the, often confusing, output that is produced. It is aimed, primarily, at undergraduates and masters students in the biological sciences who have to use statistics in practical classes and projects. Such users of statistics don’t have to understand exactly how the test works or how to do the actual calculations. These things are not covered in this book as there are more than enough books providing such information already. What is important is that the right statistical test is used and the right inferences made from the output of the test. An extensive key to statistical tests is included for the former and the bulk of the book is made up of descriptions of how to carry out the tests to address the latter.

In several years of teaching statistics to biology students it is clear to me that most students don’t really care how or why the test works. They do care a great deal that they are using an appropriate test and interpreting the results properly. I think that this is a fair aim to have for occasional users of statistics. Of course, anyone going on to use statistics frequently should become familiar with the way that calculations manipulate the data to produce the output as this will give a better understanding of the test.

If this book has a message it is this: think about the statistics before you collect the data! So many times I have seen rather distraught students unable to analyse their precious data because the experimental design they used was inappropriate. On such occasions I try to find a compromise test that will make the best of a bad job but this often leads to a weaker conclusion than might have been possible if more forethought had been applied from the outset. There is no doubt that if experiments or sampling strategies are designed with the statistics in mind better science will result.

Statistics are often seen by students as the ‘thing you must do to data at the end’. Please try to avoid falling into this trap yourself. Thought experiments producing dummy data are a good way to try out experimental designs and are much less labour-intensive than real ones!

Although there are almost no equations in this book I’m afraid there was no way to totally avoid statistical jargon. To ease the pain somewhat, an extensive Glossary and key to symbols are included. So when you are navigating your way through the key to choosing a test you should look up any words you don’t understand.

In this book I have given extensive instructions for the use of four commonly encountered software packages: SPSS, R, Excel and MINITAB. However, the key to choosing a statistical test is not at all package-specific, so if you use a software package other than the four I focus on or if you are using a calculator you will still be able to get a good deal out of this book.

If every sample gave the same result there would be no need for statistics. However, all aspects of biology are filled with variation. It is statistics that can be used to penetrate the haze of experimental error and the inherent variability of the natural world to reach the underlying causes and processes at work. So, try not to hate statistics, they are merely a tool that, when used wisely and properly, can make the life of a biologist much simpler and give conclusions a sound basis.

The third edition

In the 8 years since I wrote the second edition of this book there have, of course, been several new versions of the software produced. I have received many comments about the previous editions and I am grateful for the many suggestions on how to improve the text and coverage. Requests to add further statistical packages have been the most common suggestion for change. There was surprisingly little consensus on the packages to add for the second edition, but since 2000 the freely available, and very powerful, package R has become extremely widely used so I have added that to the mix this time.

How to use this book

This is definitely not a book that should be read from cover to cover. It is a book to refer to when you need assistance with statistical analysis, either when choosing an appropriate test or when carrying it out. The basics of statistical analysis and experimental design are covered briefly but those sections are intended mostly as a revision aid, or to outline of some of the more important concepts. The reviews of other statistics books may help you choose those that are most appropriate for you if you want or need more details.

The heart of the book is the key. The rest of the book hinges on the key, explaining how to carry out the tests, giving assistance with the statistical terms in the Glossary or giving tips on the use of computers and packages.

Packages used

MINITAB® version 15, MINITAB Inc.

SPSS® versions 16 and 17, SPSS Inc.

Excel™ version 2007 and 2008 for Mac, Microsoft Corporation

Running on:

Windows® versions XP, 2000, 7 and Vista, Microsoft Corporation

Mac OS 10, Apple Inc.

Example data

In the spirit of dummy data collection, all example data used throughout this book have been fabricated. Any similarity to data alive or dead is purely coincidental.

Acknowledgements for the first edition

Thanks to Sheena McNamee for support during the writing process, to Andrea Gillmeister and two anonymous reviewers for commenting on an early version of the manuscript and to Terry Crawford, Jo Dunn, David Murrell and Josephine Pithon for recommending and lending various books. Thanks also to Ian Sherman and Susan Sternberg at Blackwell and to many of my colleagues who told me that the general idea of a book like this was a sound one. Finally, I would especially like to thank the students at the University of York, UK, who brought me the problems that provided the inspiration for this book.

Acknowledgements for the second edition

Thanks to all the many people who contacted me with suggestions and comments about the first edition. I hope you can see that many of the corrections and improvements have come directly from you. Five anonymous reviewers provided many useful comments about the proposal for a second edition. Thanks to Sarah Shannon, Cee Brandston, Katrina McCallum and many others at Blackwell for seeing this book through and especially for producing a second superb and striking cover. S’Albufera Natural Parc and Nick Riddiford provided a very convenient bolt-hole for writing. Once again, I give special thanks to Sheena and to my colleagues, PhD students and undergraduate students at the University of York. Finally, thanks to everyone on the MRes EEM course over the last 4 years.

Acknowledgements for the third edition

It’s been thanks to the pushing of Ward Cooper at Wiley-Blackwell and Sheena McNamee that this third edition has seen the light of day. Thanks to Emma Rand, Olivier Missa and Frank Schurr for encouraging me to enter the brave new world of R. Thanks to Nik Prowse for guiding me through the final editing.

Calvin Dytham,

York 1998, 2002 and 2010

1

Eight steps to successful data analysis

This is a very simple sequence that, if you follow it, will integrate the statistics you use into the process of scientific investigation. As I make clear here, statistical tests should be considered very early in the process and not left until the end.

1 Decide what you are interested in.

2 Formulate a hypothesis or several hypotheses (see Chapters 2 and 3 for guidance).

3 Design the experiment, manipulation or sampling routine that will allow you to test the hypotheses (see Chapters 2 and 4 for some hints on how to go about this).

4Collect dummy data (i.e. make up approximate values based on what you expect to obtain). The collection of ‘dummy data’ may seem strange but it will convert the proposed experimental design or sampling routine into something more tangible. The process can often expose flaws or weaknesses in the datacollection routine that will save a huge amount of time and effort.

5 Use the key presented in Chapter 3 to guide you towards the appropriate test or tests.

6 Carry out the test(s) using the dummy data. (Chapters 6–9 will show you how to input the data, use the statistical packages and interpret the output.)

7 If there are problems go back to step 3 (or 2); otherwise, proceed to the collection of real data.

8 Carry out the test(s) using the real data. Report the findings and/or return to step 2.

I implore you to use this sequence. I have seen countless students who have spent a long time and a lot of effort collecting data only to find that the experimental or sampling design was not quite right. The test they are forced to use is much less powerful than one they could have used with only a slight change in the experimental design. This sort experience tends to turn people away from statistics and become ‘scared’ of them. This is a great shame as statistics are a hugely useful and vital tool in science.

The rest of the book follows this eight-step process but you should use it for guidance and advice when you become unsure of what to do.

3

Choosing a test: a key

I hope that you are not reading this chapter with your data already collected and the experiment or sampling programme ‘finished’. If you have finished collecting your data I strongly advise you to approach your next experiment or survey in a different way. As you will see below, I hope that you will be using this key before you start collecting real data.

Remember: eight steps to successful data analysis

1 Decide what you are interested in.

2 Formulate a hypothesis or hypotheses.

3 Design the experiment or sampling routine.

4 Collect dummy data. Make up approximate values based on what you expect.

5Use the key here to decide on the appropriate test or tests.

6 Carry out the test(s) using the dummy data.

7 If there are problems go back to step 3 (or 2), otherwise collect the real data.

8 Carry out the test(s) using the real data.

The art of choosing a test

It may be a surprising revelation, but choosing a statistical test is not an exact science. There is nearly always scope for considerable choice and many decisions will be made based on personal judgements, experience with similar problems or just a simple hunch. There are many circumstances under which there are several ways that the data could be analysed and yet each of the possible tests could be justified.

A common tendency is to force the data from your experiment into a test you are familiar with even if it is not the best method. Look around for different tests that may be more appropriate to the hypothesis you are testing. In this way you will expand your statistical repertoire and add power to your future experiments.

A key to assist in your choice of statistical test

Starting at step 1 in the list above move through the key following the path that best describes your data. If you are unsure about any of the terms used then consult the glossary or the relevant sections of the next two chapters. This is not a true dichotomous key and at several points there are more than two routes or end points.