The Analysis of Biological Data

PART 1 INTRODUCTION TO STATISTICS
1.0 Statistics and samples
1.1 What is statistics?
1.2 Sampling populations
1.3 Types of data and variables
1.4 Frequency distributions and probability distributions
1.5 Types of studies
1.6 Summary
Interleaf 1 Correlation does not require causation

2.0 Displaying data
2.1 Guidelines for effective graphs
2.2 Showing data for one variable
2.3 Showing association between two variables and differences between groups
2.4 Showing trends in time and space
2.5 How to make good tables
2.6 How to make data files
2.7 Summary

3.0 Describing data
3.1 Arithmetic mean and standard deviation
3.2 Median and interquartile range
3.3 How measures of location and spread compare
3.4 Cumulative frequency distribution
3.5 Proportions
3.6 Summary
3.7 Quick Formula Summary

4.0 Estimating with uncertainty
4.1 The sampling distribution of an estimate
4.2 Measuring the uncertainty of an estimate
4.3 Confidence intervals
4.4 Error bars
4.5 Summary
4.6 Quick Formula Summary
Interleaf 2 Pseudoreplication

5.0 Probability
5.1 The probability of an event
5.2 Venn Diagrams
5.3 Mutually exclusive events
5.4 Probability distributions
5.5 Either this or that: adding probabilities
5.6 Independence and the multiplication rule
5.7 Probability trees
5.8 Dependent events
5.9 Conditional probability and Bayes theorem
5.10 Summary

6.0 Hypothesis testing
6.1 Making and using hypotheses
6.2 Hypothesis testing: an example
6.3 Errors in hypothesis testing
6.4 When the null hypothesis is not rejected
6.5 One-sided tests
6.6 Hypothesis testing versus confidence intervals
6.7 Summary
Intereaf 3 Why statistical significance is not the same as biological importance

PART 2 PROPORTIONS AND FREQUENCIES
7.0 Analyzing proportions
7.1 The binomial distribution
7.2 Testing a proportion: the binomial test
7.3 Estimating proportions
7.4 Deriving the binomial distribution
7.5 Summary
7.6 Quick Formula Summary
Interleaf 4 Biology and the history of statistics

8.0 Fitting probability models to frequency data
8.1 X^2 goodness-of-fit test: the proportional model
8.2 Assumptions of the X^2 goodness-of-fit test
8.3 Goodness-of-fit tests when there are only two categories
8.4 Random in space or time: the Poisson distribution
8.5 Summary
8.6 Quick Formula Summary
Interleaf 5 Making a plan

9.0 Contingency analysis: Associations between categorical variables
9.1 Associating two categorical variables
9.2 Estimating association in 2 × 2 tables: relative risk
9.3 Estimating association in 2x2 tables: the odds ratio
9.4 The x^2 contingency test
9.5 Fishers exact test
9.6 Summary
9.7 Quick Formula Summary
PR1 Review Problems 1

PART 3 COMPARING NUMERICAL VALUES
10.0 The normal distribution
10.1 Bell-shaped curves and the normal distribution
10.2 The formula for the normal distribution
10.3 Properties of the normal distribution
10.4 The standard normal distribution and statistical tables
10.5 The normal distribution of sample means
10.6 Central limit theorem
10.7 Normal approximation to the binomial distribution
10.8 Summary
10.9 Quick Formula Summary
Interleaf 6 Controls in medical studies

11.0 Inference for a normal population
11.1 The t-distribution for sample means
11.2 The confidence interval for the mean of a sample distribution
11.3 The one-sample t-test
11.4 Assumptions of the one-sample t-test
11.5 Estimating the standard deviation and variance of a normal population
11.6 Summary
11.7 Quick Formula Summary

12.0 Comparing two means
12.1 Paired sample versus two independent samples
12.2 Paired comparison of means
12.3 Two-sample comparison of means
12.4 Using the correct sampling units
12.5 The fallacy of indirect comparison
12.6 Interpreting overlap of confidence intervals
12.7 Comparing variances
12.8 Summary
12.9 Quick Formula Summary
Interleaf 7 Which test should I use?

13.0 Handling violations of assumptions
13.1 Detecting deviations from normality
13.2 When to ignore violations of assumptions
13.3 Data transformations
13.4 Nonparametric alternatives to one-sample and paired t-tests
13.5 Comparing two groups: the Mann-Whitney U-test
13.6 Assumptions of nonparametric tests
13.7 Type I and Type II error rates of nonparametric methods
13.8 Permutation tests
13.9 Summary
13.10 Quick Formula Summary
RP2 Review Problems 2

14.0 Designing experiments
14.1 Lessons from clinical trials
14.2 How to reduce bias
14.3 How to reduce the influence of sampling error
14.4 Experiments with more than one factor
14.5 What if you cant do experiments?
14.6 Choosing a sample size
14.7 Summary
14.8 Quick Formula Summary
Interleaf 8 Data dredging

15.0 Comparing means of more than two groups
15.1 The analysis of variance
15.2 Assumptions and alternatives
15.3 Planned comparisons
15.4 Unplanned comparisons
15.5 Fixed and random effects
15.6 ANOVA with randomly chosen groups
15.7 Summary
15.8 Quick Formula Summary
Interleaf 9 Experimental and statistical mistakes

PART 4 REGRESSION AND CORRELATION
16.0 Correlation between numerical variables
16.1 Estimating a linear correlation coefficient
16.2 Testing the null hypothesis of zero correlation
16.3 Assumptions
16.4 The correlation coefficient depends on the range
16.5 Spearmans rank correlation
16.6 The effects of measurement error on correlation
16.7 Summary
16.8 Quick Formula Summary
Interleaf 10 Publication bias

17.0 Regression
17.1 Linear Regression
17.2 Confidence in predictions
17.3 Testing hypotheses about a slope
17.4 Regression toward the mean
17.5 Assumptions of regression
17.6 Transformations
17.7 The effects of measurement error on regression
17.8 Regression with nonlinear relationships
17.9 Logistic regression: fitting a binary response variable
17.10 Summary
17.11 Quick Formula Summary
Interleaf 11 Meta-analysis
RP3 Review Problems 3

PART 5 MODERN STATISTICAL METHODS
18.0 Multiple explanatory variables
18.1 ANOVA and linear regression are linear models
18.2 Analyzing experiments with blocking
18.3 Analyzing factorial designs
18.4 Adjusting for the effects of a covariate
18.5 Assumptions of general linear models
18.6 Summary
Interleaf 12 Using species as data points

19.0 Computer-intensive methods
19.1 Hypothesis testing using simulation
19.2 Bootstrap standard errors and confidence intervals
19.3 Summary

20.0 Likelihood
20.1 What is the likelihood?
20.2 Two uses of likelihood in biology
20.3 Maximum likelihood estimation
20.4 Versatility of maximum likelihood estimation
20.5 Log-likelihood ratio test
20.6 Summary
20.7 Quick Formula Summary

21.0 Survivorship analysis
21.1 Survival curves
21.2 Comparing two survival curves
21.3 Summary
21.4 Quick Formula Summary

BACK MATTER 
 Statistical tables
 Literature cited
 Answers to practice problems
 Index