A Student's Guide to Analysis of Variance

Analysis of Variance (ANOVA) is one of the most widely used statistical tests in psychology and other behavioral sciences.A Student's Guide to Analysis of Varianceclearly and simply explains how to conduct and interpret ANOVA. It includes information on how to conduct ANOVA for a range of research designs, use follow-up tests, make sense of interactions and write formal reports. It also offers many valuable hints on how to make the best of the techniques available and how best to avoid pitfalls.

Maxwell J. Roberts and Riccardo Russo are experienced teachers of research methods and statistics. Both are lecturers in psychology at the University of Essex

List of figures

x

List of tables

xiii

List of boxes

xv

Preface

xvii

Acknowlegements

xx

Introduction

1

(8)

Averages, measures of dispersal and the t-test

9

(21)

Summarising data

9

(1)

Distribution

10

(3)

Variability

13

(4)

Testing for differences with the t-test

17

(5)

Intuitive statistics

22

(1)

Using one- and two-tailed tests

23

(4)

A note on statistical power

27

(3)

Using variance to test hypotheses

30

(11)

Calculating F rations for one-factor between-subjects designs

41

(21)

One-factor between-subjects ANOVA: advance topics

62

(20)

ANOVA and the central limit theorem

62

(7)

Assumptions underlying ANOVA

69

(6)

Dealing with rogue data

75

(7)

Following up a one-factor between-subject Anova

82

(28)

The meanings of Anova outcomes

82

(2)

Pairwise comparisons for single-factor designs: planned comparisons and post-hoc testing

84

(8)

Making comparisons between every possible pair of means

92

(6)

Linear contrast analysis for single-factor designs

98

(12)

Calculating F ratios for one-factor within-subjects designs

110

(24)

Sources of error variability

112

(6)

Calculating F for a within-subjects design

118

(10)

Planned comparisons and post-hoc testing

128

(6)

An introduction to factorial designs and interactions

134

(19)

Outcomes of factorial designs

137

(11)

Managing factorial designs

148

(5)

Calculating F rations for two-factor between-subjects designs

153

(19)

Analysing a 2 X 2 between-subjects factorial design

156

(16)

Following up a two-factor between-subjects Anova

172

(22)

Some pitfalls in interpreting interactions

191

(3)

Interpreting two-factor mixed and within-subjects designs

194

(17)

Interpreting a three-factor Anova

211

(13)

Summary and frequently asked questions

224

(9)

A summary of follow-up tests for Analysis of Variance

224

(3)

Frequently asked questions

227

(6)

Appendix A: Writing up the results of Analysis of Variance

233

(11)

Appendix B: Statistical tables

244

(14)

Notes

258

(2)

References

260

(1)

Index

261

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A Student's Guide to Analysis of Variance

Summary

Author Biography

Table of Contents

Supplemental Materials