Experimental Design and Data Analysis for Biologists 1st Edition by Gerry P Quinn, Michael J Keough ISBN 9780521811286 0521811287

1 Introduction

1.1 Scientific method

1.1.1 Pattern description

1.1.2 Models

1.1.3 Hypotheses and tests

1.1.4 Alternatives to falsification

1.1.5 Role of statistical analysis

1.2 Experiments and other tests

1.3 Data, observations and variables

1.4 Probability

1.5 Probability distributions

1.5.1 Distributions for variables

1.5.2 Distributions for statistics

2 Estimation

2.1 Samples and populations

2.2 Common parameters and statistics

2.2.1 Center (location) of distribution

2.2.2 Spread or variability

2.3 Standard errors and confidence intervals for the mean

2.3.1 Normal distributions and the Central Limit Theorem

2.3.2 Standard error of the sample mean

2.3.3 Confidence intervals for population mean

2.3.4 Interpretation of confidence intervals for population mean

2.3.5 Standard errors for other statistics

2.4 Methods for estimating parameters

2.4.1 Maximum likelihood (ML)

2.4.2 Ordinary least squares (OLS)

2.4.3 ML vs OLS estimation

2.5 Resampling methods for estimation

2.5.1 Bootstrap

2.5.2 Jackknife

2.6 Bayesian inference – estimation

2.6.1 Bayesian estimation

2.6.2 Prior knowledge and probability

2.6.3 Likelihood function

2.6.4 Posterior probability

2.6.5 Examples

2.6.6 Other comments

3 Hypothesis testing

3.1 Statistical hypothesis testing

3.1.1 Classical statistical hypothesis testing

3.1.2 Associated probability and Type I error

3.1.3 Hypothesis tests for a single population

3.1.4 One- and two-tailed tests

3.1.5 Hypotheses for two populations

3.1.6 Parametric tests and their assumptions

3.2 Decision errors

3.2.1 Type I and II errors

3.2.2 Asymmetry and scalable decision criteria

3.3 Other testing methods

3.3.1 Robust parametric tests

3.3.2 Randomization (permutation) tests

3.3.3 Rank-based non-parametric tests

3.4 Multiple testing

3.4.1 The problem

3.4.2 Adjusting significance levels and/or P values

3.5 Combining results from statistical tests

3.5.1 Combining P values

3.5.2 Meta-analysis

3.6 Critique of statistical hypothesis testing

3.6.1 Dependence on sample size and stopping rules

3.6.2 Sample space – relevance of data not observed

3.6.3 P values as measure of evidence

3.6.4 Null hypothesis always false

3.6.5 Arbitrary significance levels

3.6.6 Alternatives to statistical hypothesis testing

3.7 Bayesian hypothesis testing

4 Graphical exploration of data

4.1 Exploratory data analysis

4.1.1 Exploring samples

4.2 Analysis with graphs

4.2.1 Assumptions of parametric linear models

4.3 Transforming data

4.3.1 Transformations and distributional assumptions

4.3.2 Transformations and linearity

4.3.3 Transformations and additivity

4.4 Standardizations

4.5 Outliers

4.6 Censored and missing data

4.6.1 Missing data

4.6.2 Censored (truncated) data

4.7 General issues and hints for analysis

4.7.1 General issues

5 Correlation and regression

5.1 Correlation analysis

5.1.1 Parametric correlation model

5.1.2 Robust correlation

5.1.3 Parametric and non-parametric confidence regions

5.2 Linear models

5.3 Linear regression analysis

5.3.1 Simple (bivariate) linear regression

5.3.2 Linear model for regression

5.3.3 Estimating model parameters

5.3.4 Analysis of variance

5.3.5 Null hypotheses in regression

5.3.6 Comparing regression models

5.3.7 Variance explained

5.3.8 Assumptions of regression analysis

5.3.9 Regression diagnostics

5.3.10 Diagnostic graphics

5.3.11 Transformations

5.3.12 Regression through the origin

5.3.13 Weighted least squares

5.3.14 X random (Model II regression)

5.3.15 Robust regression

5.4 Relationship between regression and correlation

5.5 Smoothing

5.5.1 Running means

5.5.2 LO(W)ESS

5.5.3 Splines

5.5.4 Kernels

5.5.5 Other issues

5.6 Power of tests in correlation and regression

5.7 General issues and hints for analysis

5.7.1 General issues

5.7.2 Hints for analysis

6 Multiple and complex regression

6.1 Multiple linear regression analysis

6.1.1 Multiple linear regression model

6.1.2 Estimating model parameters

6.1.3 Analysis of variance

6.1.4 Null hypotheses and model comparisons

6.1.5 Variance explained

6.1.6 Which predictors are important?

6.1.7 Assumptions of multiple regression

6.1.8 Regression diagnostics

6.1.9 Diagnostic graphics

6.1.10 Transformations

6.1.11 Collinearity

6.1.12 Interactions in multiple regression

6.1.13 Polynomial regression

6.1.14 Indicator (dummy) variables

6.1.15 Finding the “best” regression model

6.1.16 Hierarchical partitioning

6.1.17 Other issues in multiple linear regression

6.2 Regression trees

6.3 Path analysis and structural equation modeling

6.4 Nonlinear models

6.5 Smoothing and response surfaces

6.6 General issues and hints for analysis

6.6.1 General issues

6.6.2 Hints for analysis

7 Design and power analysis

7.1 Sampling

7.1.1 Sampling designs

7.1.2 Size of sample

7.2 Experimental design

7.2.1 Replication

7.2.2 Controls

7.2.3 Randomization

7.2.4 Independence

7.2.5 Reducing unexplained variance

7.3 Power analysis

7.3.1 Using power to plan experiments (a priori power analysis)

7.3.2 Post hoc power calculation

7.3.3 The effect size

7.3.4 Using power analyses

7.4 General issues and hints for analysis

7.4.1 General issues

7.4.2 Hints for analysis

8 Comparing groups or treatments – analysis of variance

8.1 Single factor (one way) designs

8.1.1 Types of predictor variables (factors)

8.1.2 Linear model for single factor analyses

8.1.3 Analysis of variance

8.1.4 Null hypotheses

8.1.5 Comparing ANOVA models

8.1.6 Unequal sample sizes (unbalanced designs)

8.2 Factor effects

8.2.1 Random effects: variance components

8.2.2 Fixed effects

8.3 Assumptions

8.3.1 Normality

8.3.2 Variance homogeneity

8.3.3 Independence

8.4 ANOVA diagnostics

8.5 Robust ANOVA

8.5.1 Tests with heterogeneous variances

8.5.2 Rank-based (“non-parametric”) tests

8.5.3 Randomization tests

8.6 Specific comparisons of means

8.6.1 Planned comparisons or contrasts

8.6.2 Unplanned pairwise comparisons

8.6.3 Specific contrasts versus unplanned pairwise comparisons

8.7 Tests for trends

8.8 Testing equality of group variances

8.9 Power of single factor ANOVA

8.10 General issues and hints for analysis

8.10.1 General issues

8.10.2 Hints for analysis

9 Multifactor analysis of variance

9.1 Nested (hierarchical) designs

9.1.1 Linear models for nested analyses

9.1.2 Analysis of variance

9.1.3 Null hypotheses

9.1.4 Unequal sample sizes (unbalanced designs)

9.1.5 Comparing ANOVA models

9.1.6 Factor effects in nested models

9.1.7 Assumptions for nested models

9.1.8 Specific comparisons for nested designs

9.1.9 More complex designs

9.1.10 Design and power

9.2 Factorial designs

9.2.1 Linear models for factorial designs

9.2.2 Analysis of variance

9.2.3 Null hypotheses

9.2.4 What are main effects and interactions really measuring?

9.2.5 Comparing ANOVA models

9.2.6 Unbalanced designs

9.2.7 Factor effects

9.2.8 Assumptions

9.2.9 Robust factorial ANOVAs

9.2.10 Specific comparisons on main effects

9.2.11 Interpreting interactions

9.2.12 More complex designs

9.2.13 Power and design in factorial ANOVA

9.3 Pooling in multifactor designs

9.4 Relationship between factorial and nested designs

9.5 General issues and hints for analysis

9.5.1 General issues

9.5.2 Hints for analysis

10 Randomized blocks and simple repeated measures: unreplicated two factor designs

10.1 Unreplicated two factor experimental designs

10.1.1 Randomized complete block (RCB) designs

10.1.2 Repeated measures (RM) designs

10.2 Analyzing RCB and RM designs

10.2.1 Linear models for RCB and RM analyses

10.2.2 Analysis of variance

10.2.3 Null hypotheses

10.2.4 Comparing ANOVA models

10.3 Interactions in RCB and RM models

10.3.1 Importance of treatment by block interactions

10.3.2 Checks for interaction in unreplicated designs

10.4 Assumptions

10.4.1 Normality, independence of errors

10.4.2 Variances and covariances – sphericity

10.4.3 Recommended strategy

10.5 Robust RCB and RM analyses

10.6 Specific comparisons

10.7 Efficiency of blocking (to block or not to block?)

10.8 Time as a blocking factor

10.9 Analysis of unbalanced RCB designs

10.10 Power of RCB or simple RM designs

10.11 More complex block designs

10.11.1 Factorial randomized block designs

10.11.2 Incomplete block designs

10.11.3 Latin square designs

10.11.4 Crossover designs

10.12 Generalized randomized block designs

10.13 RCB and RM designs and statistical software

10.14 General issues and hints for analysis

10.14.1 General issues

10.14.2 Hints for analysis

11 Split-plot and repeated measures designs: partly nested analyses of variance

11.1 Partly nested designs

11.1.1 Split-plot designs

11.1.2 Repeated measures designs

11.1.3 Reasons for using these designs

11.2 Analyzing partly nested designs

11.2.1 Linear models for partly nested analyses

11.2.2 Analysis of variance

11.2.3 Null hypotheses

11.2.4 Comparing ANOVA models

11.3 Assumptions

11.3.1 Between plots/subjects

11.3.2 Within plots/subjects and multisample sphericity

11.4 Robust partly nested analyses

11.5 Specific comparisons

11.5.1 Main effects

11.5.2 Interactions

11.5.3 Profile (i.e. trend) analysis

11.6 Analysis of unbalanced partly nested designs

11.7 Power for partly nested designs

11.8 More complex designs

11.8.1 Additional between-plots/subjects factors

11.8.2 Additional within-plots/subjects factors

11.8.3 Additional between-plots/subjects and within-plots/subjects factors

11.8.4 General comments about complex designs

11.9 Partly nested designs and statistical software

11.10 General issues and hints for analysis

11.10.1 General issues

11.10.2 Hints for individual analyses

12 Analyses of covariance

12.1 Single factor analysis of covariance (ANCOVA)

12.1.1 Linear models for analysis of covariance

12.1.2 Analysis of (co)variance

12.1.3 Null hypotheses

12.1.4 Comparing ANCOVA models

12.2 Assumptions of ANCOVA

12.2.1 Linearity

12.2.2 Covariate values similar across groups

12.2.3 Fixed covariate (X)

12.3 Homogeneous slopes

12.3.1 Testing for homogeneous within-group regression slopes

12.3.2 Dealing with heterogeneous within-group regression slopes

12.3.3 Comparing regression lines

12.4 Robust ANCOVA

12.5 Unequal sample sizes (unbalanced designs)

12.6 Specific comparisons of adjusted means

12.6.1 Planned contrasts

12.6.2 Unplanned comparisons

12.7 More complex designs

12.7.1 Designs with two or more covariates

12.7.2 Factorial designs

12.7.3 Nested designs with one covariate

12.7.4 Partly nested models with one covariate

12.8 General issues and hints for analysis

12.8.1 General issues

12.8.2 Hints for analysis

13 Generalized linear models and logistic regression

13.1 Generalized linear models

13.2 Logistic regression

13.2.1 Simple logistic regression

13.2.2 Multiple logistic regression

13.2.3 Categorical predictors

13.2.4 Assumptions of logistic regression

13.2.5 Goodness-of-fit and residuals

13.2.6 Model diagnostics

13.2.7 Model selection

13.2.8 Software for logistic regression

13.3 Poisson regression

13.4 Generalized additive models

13.5 Models for correlated data

13.5.1 Multi-level (random effects) models

13.5.2 Generalized estimating equations

13.6 General issues and hints for analysis

13.6.1 General issues

13.6.2 Hints for analysis

14 Analyzing frequencies

14.1 Single variable goodness-of-fit tests

14.2 Contingency tables

14.2.1 Two way tables

14.2.2 Three way tables

14.3 Log-linear models

14.3.1 Two way tables

14.3.2 Log-linear models for three way tables

14.3.3 More complex tables

14.4 General issues and hints for analysis

14.4.1 General issues

14.4.2 Hints for analysis

15 Introduction to multivariate analyses

15.1 Multivariate data

15.2 Distributions and associations

15.3 Linear combinations, eigenvectors and eigenvalues

15.3.1 Linear combinations of variables

15.3.2 Eigenvalues

15.3.3 Eigenvectors

15.3.4 Derivation of components

15.4 Multivariate distance and dissimilarity measures

15.4.1 Dissimilarity measures for continuous variables

15.4.2 Dissimilarity measures for dichotomous (binary) variables

15.4.3 General dissimilarity measures for mixed variables

15.4.4 Comparison of dissimilarity measures

15.5 Comparing distance and/or dissimilarity matrices

15.6 Data standardization

15.7 Standardization, association and dissimilarity

15.8 Multivariate graphics

15.9 Screening multivariate data sets

15.9.1 Multivariate outliers

15.9.2 Missing observations

15.10 General issues and hints for analysis

15.10.1 General issues

15.10.2 Hints for analysis

16 Multivariate analysis of variance and discriminant analysis

16.1 Multivariate analysis of variance (MANOVA)

16.1.1 Single factor MANOVA

16.1.2 Specific comparisons

16.1.3 Relative importance of each response variable

16.1.4 Assumptions of MANOVA

16.1.5 Robust MANOVA

16.1.6 More complex designs

16.2 Discriminant function analysis

16.2.1 Description and hypothesis testing

16.2.2 Classification and prediction

16.2.3 Assumptions of discriminant function analysis

16.2.4 More complex designs

16.3 MANOVA vs discriminant function analysis

16.4 General issues and hints for analysis

16.4.1 General issues

16.4.2 Hints for analysis

17 Principal components and correspondence analysis

17.1 Principal components analysis

17.1.1 Deriving components

17.1.2 Which association matrix to use?

17.1.3 Interpreting the components

17.1.4 Rotation of components

17.1.5 How many components to retain?

17.1.6 Assumptions

17.1.7 Robust PCA

17.1.8 Graphical representations

17.1.9 Other uses of components

17.2 Factor analysis

17.3 Correspondence analysis

17.3.1 Mechanics

17.3.2 Scaling and joint plots

17.3.3 Reciprocal averaging

17.3.4 Use of CA with ecological data

17.3.5 Detrending

17.4 Canonical correlation analysis

17.5 Redundancy analysis

17.6 Canonical correspondence analysis

17.7 Constrained and partial “ordination”

17.8 General issues and hints for analysis

17.8.1 General issues

17.8.2 Hints for analysis

18 Multidimensional scaling and cluster analysis

18.1 Multidimensional scaling

18.1.1 Classical scaling – principal coordinates analysis (PCoA)

18.1.2 Enhanced multidimensional scaling

18.1.3 Dissimilarities and testing hypotheses about groups of objects

18.1.4 Relating MDS to original variables

18.1.5 Relating MDS to covariates

18.2 Classification

18.2.1 Cluster analysis

18.3 Scaling (ordination) and clustering for biological data

18.4 General issues and hints for analysis

18.4.1 General issues

18.4.2 Hints for analysis

19 Presentation of results

19.1 Presentation of analyses

19.1.1 Linear models

19.1.2 Other analyses

19.2 Layout of tables

19.3 Displaying summaries of the data

19.3.1 Bar graph

19.3.2 Line graph (category plot)

19.3.3 Scatterplots

19.3.4 Pie charts

19.4 Error bars

19.4.1 Alternative approaches

19.5 Oral presentations

19.5.1 Slides, computers, or overheads?

19.5.2 Graphics packages

19.5.3 Working with color

19.5.4 Scanned images

19.5.5 Information content

19.6 General issues and hints

References

Index