ANOVA for the Behavioral Sciences Researcher

Rudolf N. Cardinal, Michael R.F. Aitken

• Publisher: Psychology Press
• Year: 2013
• Print ISBN: 9780805855869
• eBook ISBN: 9781134814176
• Topic: Psychology
• Subtopic: History & Theory in Psychology
• Index: Psychology

This new book provides a theoretical and practical guide to analysis of variance (ANOVA) for those who have not had a formal course in this technique, but need to use this analysis as part of their research.

From their experience in teaching this material and applying it to research problems, the authors have created a summary of the statistical theory underlying ANOVA, together with important issues, guidance, practical methods, references, and hints about using statistical software. These have been organized so that the student can learn the logic of the analytical techniques but also use the book as a reference guide to experimental designs, realizing along the way what pitfalls are likely to be encountered.

CHAPTER 1: QUICK SUMMARY

1.1 Overview of this book

• First, in Chapter 1

, we'll summarize what most people want to know to get going—how to choose and perform an ANOVA. Few researchers read ANOVA theory before starting to analyse, much as statisticians may complain about this, so we might as well be pragmatic. Chapter 1 can be combined with Chapter 3, which talks about common things that are required in ANOVA analysis, and Chapter 5, which shows how to perform an ANOVA in SPSS.

• Then, in Chapter 2

, we'll cover what ANOVA does and what it assumes—things researchers should have known before running an ANOVA but quite possibly didn't.

• In Chapter 3

, we'll walk through what most people need to do to complete an ANOVA analysis.

• In Chapter 4

, we'll look at experimental design and analysis issues, such as how to analyse changes from previous or baseline values, and when and how to perform post hoc tests.

• In Chapter 5

, we'll look at how to use the SPSS software package to perform different ANOVAs.

• In Chapter 6

, we'll look at linear contrasts and trend analysis, two useful but probably under-used techniques of ANOVA.

• In Chapter 7

, we'll cover complex theory that most people will never need, but that may lead to a better general appreciation of ANOVA concepts.

• In Chapter 8

, we'll look at a variety of ANOVA models that can be used for different experimental designs. These will range from the very simple (one-way ANOVA) through the very useful (mixed designs with both between- and within-subject factors) to the very complicated. This material is for reference.

• In Chapter 9

, we'll revise mathematics that is touched on occasionally elsewhere, and cover advanced mathematics that underpins computerized calculations of complex ANOVAs.

• Chapter 10

gives statistical tables for reference.

• There's also a glossary

and suggestions for further reading

.

Key to symbols:

= fairly easy, and important

= important but not exciting

= reference material; look up the model that you need to use

= difficult mathematics in places; not necessary for basic analysis

Notes that are more advanced than the rest of the section they are in are usually placed at the end of their section and always marked by a vertical rule in the margin, like this. They may be safely ignored if you prefer!

1.2 Background knowledge

This book is aimed at graduate students and behavioural science researchers who need to perform analysis of variance (ANOVA). Covering the theory of ANOVA is one thing; putting it into practice in psychology and neuroscience research unfortunately requires using the technique at a level at which even statisticians debate the proper methods. This is depressing to the beginner; we hope this book helps. It covers simple ANOVA and also some complex techniques that are not often used but are rather powerful. It also provides reference material about different ANOVA designs. It assumes a basic knowledge of statistics. Explicit coverage of the background knowledge can be found in Aitken & Cardinal (2006), including:

1. Designing experiments and describing results. Basic mathematics; variables and measurement; populations and samples (and the concept of estimating population parameters from sample statistics); descriptive and inferential statistics; exerting control (independent and dependent variables, between- and within-subject experimental designs); measures of central tendency (mean, mode, median); measures of dispersion (including variance, standard deviation, range, interquartile range); example questions.

2. Probability and the normal distribution. Probability (including Bayes' theorem and Bayesian inference); discrete and continuous random variables; the normal distribution (Z scores, the one-sample Z test for scores of known variance, confidence intervals); the logic of null hypothesis testing (including the interpretation of p values, Type I and Type II error, power, Bayesian statistical inference, one- and two-tailed tests and how to choose between them, common fallacies); example questions.

3. Exploratory data analysis. Histograms; stem-and-leaf diagrams; Tukey box-plots (‘box-and-whiskers’ plots); outliers; testing for outliers; when to exclude outliers; non-normal distributions (skew, kurtosis); when and why to transform data; example questions.

4. Investigating sample means: t tests. Rationale behind ; tests; paired and unpaired tests for related and unrelated data; the one-sample t test; confidence intervals; the standard error of the mean; the two-sample, paired t test; the two-sample, unpaired t test (for equal and unequal sample variances); the standard error of the difference between means; assumptions of t tests; the F test for comparison of variances; derivations and the central limit theorem; graphical representation of within- and between-subject variability; power and things that affect it; example questions.

5. Nonparametric difference tests. Background; the Mann-Whitney U test for two independent samples; the Wilcoxon matched-pairs signed-rank test for two related samples; using the Wilcoxon signed-rank test as a one-sample test; how to choose between parametric and nonparametric approaches; supplementary material; example questions.

1. Binomial, sign, and χ² tests. Categorical data; the binomial distribution; the sign test; the goodness-of-fit χ² test for two and more than two categories; the contingency χ² test; assumptions of the χ² test and common errors; supplementary material (odds ratios, relative risk, multinomial distribution, derivations); example questions.

7. Correlation and regression. Scatter plots; correlation (Pearson's r); significance tests applied to correlation; nonparametric correlation (r...

Table of contents

• Cover
• Half Title
• Full Title
• Copyright
• Dedication
• CONTENTS
• PREFACE
• CHAPTER 1: QUICK SUMMARY
• CHAPTER 2: UNDERSTANDING THE BASICS
• CHAPTER 3: PRACTICAL ANALYSIS
• CHAPTER 4: PITFALLS AND COMMON ISSUES
• CHAPTER 5: USING SPSS FOR ANOVA
• CHAPTER 6: CONTRASTS AND TRENDS
• CHAPTER 7: ADVANCED TOPICS
• CHAPTER 8: SPECIFIC DESIGNS
• CHAPTER 9: MATHEMATICS
• CHAPTER 10: STATISTICAL TABLES
• GLOSSARY
• FURTHER READING
• REFERENCES
• INDEX