The authors 3 decades of experience in teaching has shown that biology students learn data analysis best in the context of interesting examples drawn from the medical and biological literature. Statistics is a means to an end, a tool to learn about the human and natural world. By emphasizing what we can learn about the science, the power and value of statistics becomes plain. Every chapter has several biological or medical examples of key concepts, and each example is prefaced by a substantial description of the biological setting. The examples are illustrated with photos of the real organisms, so that students can visualise the concepts they are learning about.
For the first time, this textbook comes with SaplingPlus, the best online resource to teach students the problem-solving skills they need to succeed in Statistics. SaplingPlus combines Sapling's acclaimed automatically-graded online homework with an extensive suite of engaging multimedia learning resources.
To learn more about SaplingPlus and how to purchase access, visit www.macmillanihe/sapling
Michael Whitlock is an evolutionary biologist and population geneticist. He is a professor of zoology at the University of British Columbia, where he has taught statistics to biology students since 1995. Whitlock is known for his work on the spatial structure of biological populations, genetic drift, and the genetics of adaptation. He has worked with fungus beetles, rhinos, and fruit flies; mathematical theory; and statistical genetics. He is a fellow of the American Academy of Arts and Sciences and a fellow of the American Association for the Advancement of Science. He is also the former editor-in-chief of The American Naturalist.
Dolph Schluter is a Professor and Canada Research Chair in the Zoology Department and Biodiversity Research Center at the University of British Columbia. He is known for his research on the ecology and evolution of Galapagos finches and threespine stickleback. He is a fellow of the Royal Societies of Canada and London and a foreign member of the Academy of Arts and Sciences.
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 Fisher's 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 can't 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 Spearman's 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
The authors 3 decades of experience in teaching has shown that biology students learn data analysis best in the context of interesting examples drawn from the medical and biological literature. Statistics is a means to an end, a tool to learn about the human and natural world. By emphasizing what we can learn about the science, the power and value of statistics becomes plain. Every chapter has several biological or medical examples of key concepts, and each example is prefaced by a substantial description of the biological setting. The examples are illustrated with photos of the real organisms, so that students can visualise the concepts they are learning about.
For the first time, this textbook comes with SaplingPlus, the best online resource to teach students the problem-solving skills they need to succeed in Statistics. SaplingPlus combines Sapling's acclaimed automatically-graded online homework with an extensive suite of engaging multimedia learning resources.
To learn more about SaplingPlus and how to purchase access, visit www.macmillanihe/sapling
Michael Whitlock is an evolutionary biologist and population geneticist. He is a professor of zoology at the University of British Columbia, where he has taught statistics to biology students since 1995. Whitlock is known for his work on the spatial structure of biological populations, genetic drift, and the genetics of adaptation. He has worked with fungus beetles, rhinos, and fruit flies; mathematical theory; and statistical genetics. He is a fellow of the American Academy of Arts and Sciences and a fellow of the American Association for the Advancement of Science. He is also the former editor-in-chief of The American Naturalist.
Dolph Schluter is a Professor and Canada Research Chair in the Zoology Department and Biodiversity Research Center at the University of British Columbia. He is known for his research on the ecology and evolution of Galapagos finches and threespine stickleback. He is a fellow of the Royal Societies of Canada and London and a foreign member of the Academy of Arts and Sciences.
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 Fisher's 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 can't 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 Spearman's 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
PART 1 INTRODUCTION TO STATISTICS
1. Statistics and samples 1
INTERLEAF 1 Biology and the history of statistics 23
2. Displaying data 25
3. Describing data 65
4. Estimating with uncertainty 95
INTERLEAF 2 Pseudoreplication 115
5. Probability 117
6. Hypothesis testing 149
INTERLEAF 3 Why statistical significance is not the same
as biological importance 176
PART 2 PROPORTIONS AND FREQUENCIES
7. Analyzing proportions 179
INTERLEAF 4 Correlation does not require causation 201
8. Fitting probability models to frequency data 203
INTERLEAF 5 Making a plan 233
9. Contingency analysis: associations between
categorical variables 235
Review Problems 1 269
vii
WS2_Frontmatter_pi-xxxiv_v2.indd 7 13/07/16 11:55 AM
viii Contents in brief
PART 3 COMPARING NUMERICAL VALUES10. The normal distribution 273
INTERLEAF 6 Controls in medical studies 301
11. Inference for a normal population 303
12. Comparing two means 327
INTERLEAF 7 Which test should I use? 366
13. Handling violations of assumptions 369
Review Problems 2 41714. Designing experiments 423
INTERLEAF 8 Data dredging 456
15. Comparing means of more than two groups 459
INTERLEAF 9 Experimental and statistical mistakes 500
PART 4 REGRESSION AND CORRELATION
16. Correlation between numerical variables 503
INTERLEAF 10 Publication bias 53517. Regression 539
INTERLEAF 11 Using species as data points 593
Review Problems 3 597
PART 5 MODERN STATISTICAL METHODS
18. Multiple explanatory variables 605
19. Computer-intensive methods 635
20. Likelihood 655
21. Meta-analysis: combining information from
multiple studies 681
Michael Whitlock is an evolutionary biologist and population geneticist. He is a professor of zoology at the University of British Columbia, where he has taught statistics to biology students since 1995. Whitlock is known for his work on the spatial structure of biological populations, genetic drift, and the genetics of adaptation. He has worked with fungus beetles, rhinos, and fruit flies; mathematical theory; and statistical genetics. He is a fellow of the American Academy of Arts and Sciences and a fellow of the American Association for the Advancement of Science. He is also the former editor-in-chief of The American Naturalist.
Dolph Schluter is a Professor and Canada Research Chair in the
Zoology Department and Biodiversity Research Center at the
University of British Columbia. He is known for his research on the
ecology and evolution of Galapagos finches and threespine
stickleback. He is a fellow of the Royal Societies of Canada and
London and a foreign member of the Academy of Arts and
Sciences.
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