Efnisyfirlit

• About this Book
  • Cover Page
  • Halftitle Page
  • Title Page
  • Copyright Page
  • Dedication
  • Contents in brief
  • Contents
  • Preface
  • About the authors
  • Acknowledgments
  • SaplingPlus for Statistics: Course Resources
  • Online Resources for Students
• Chapter 1 Statistics and samples
  • 1.1 What is statistics?
  • 1.2 Sampling Populations
    • Populations and samples
    • Properties of good samples
    • Random sampling
    • How to take a random sample
    • The sample of convenience
    • Volunteer bias
    • Data in the real world
  • 1.3 Types of Data and Variables
    • Categorical and numerical variables
    • Explanatory and response variables
  • 1.4 Frequency distributions and probability distributions
  • 1.5 Types of studies
  • 1.6 Summary
  • Chapter 1 Problems
    • Practice problems
    • Assignment problems
• Interleaf 1 Correlation does not require causation
• Chapter 2 Displaying data
  • 2.1 Guidelines for effective graphs
    • How to draw a bad graph
    • How to draw a good graph
  • 2.2 Showing data for one variable
    • Showing categorical data: frequency table and bar graph
    • Making a good bar graph
    • A bar graph is usually better than a pie chart
    • Showing numerical data: frequency table and histogram
    • Describing the shape of a histogram
    • How to draw a good histogram
    • Other graphs for numerical data
  • 2.3 Showing association between two variables and differences between groups
    • Showing association between categorical variables
    • Showing association between numerical variables: scatter plot
    • Showing association between a numerical and a categorical variable
  • 2.4 Showing trends in time and space
  • 2.5 How to make good tables
    • Follow similar principles for display tables
  • 2.6 How to make data files
  • 2.7 Summary
  • Chapter 2 Problems
    • Practice problems
    • Assignment problems
• Chapter 3 Describing data
  • 3.1 Arithmetic mean and standard deviation
    • The sample mean
    • Variance and standard deviation
    • Rounding means, standard deviations, and other quantities
    • Coefficient of variation
    • Calculating mean and standard deviation from a frequency table
    • Effect of changing measurement scale
  • 3.2 Median and interquartile range
    • The median
    • The interquartile range
    • The box plot
  • 3.3 How measures of location and spread compare
    • Mean versus median
    • Standard deviation versus interquartile range
  • 3.4 Cumulative frequency distribution
    • Percentiles and quantiles
    • Displaying cumulative relative frequencies
  • 3.5 Proportions
    • Calculating a proportion
    • The proportion is like a sample mean
  • 3.6 Summary
  • 3.7 Quick formula summary
    • Table of formulas for descriptive statistics
  • Chapter 3 Problems
    • Practice problems
    • Assignment problems
• Chapter 4 Estimating with uncertainty
  • 4.1 The sampling distribution of an estimate
    • Estimating mean gene length with a random sample
    • The sampling distribution of Y¯
  • 4.2 Measuring the uncertainty of an estimate
    • Standard error
    • The standard error of Y¯
    • The standard error of Y¯ from data
  • 4.3 Confidence intervals
    • The 2SE rule of thumb
  • 4.4 Error bars
  • 4.5 Summary
  • 4.6 Quick formula summary
    • Standard error of the mean
  • Chapter 4 Problems
    • Practice problems
    • Assignment problems
• Interleaf 2 Pseudoreplication
• Chapter 5 Probability
  • 5.1 The probability of an event
  • 5.2 Venn diagrams
  • 5.3 Mutually exclusive events
  • 5.4 Probability distributions
    • Discrete probability distributions
    • Continuous probability distributions
  • 5.5 Either this or that: adding probabilities
    • The addition rule
    • The probabilities of all possible mutually exclusive outcomes add to one
    • The general addition rule
  • 5.6 Independence and the multiplication rule
    • Multiplication rule
    • “And” versus “or”
    • Independence of more than two events
  • 5.7 Probability trees
  • 5.8 Dependent events
  • 5.9 Conditional probability and Bayes’ theorem
    • Conditional probability
    • The general multiplication rule
    • Sampling without replacement
    • Bayes’ theorem
  • 5.10 Summary
  • Chapter 5 Problems
    • Practice problems
    • Assignment problems
• Chapter 6 Hypothesis testing
  • 6.1 Making and using statistical hypotheses
    • Null hypothesis
    • Alternative hypothesis
    • To reject or not to reject
  • 6.2 Hypothesis testing: an example
    • Stating the hypotheses
    • The test statistic
    • The null distribution
    • Quantifying uncertainty: the P-value
    • Draw the appropriate conclusion
    • Reporting the results
  • 6.3 Errors in hypothesis testing
    • Type I and Type II errors
  • 6.4 When the null hypothesis is not rejected
    • The test
    • Interpreting a nonsignificant result
  • 6.5 One-sided tests
  • 6.6 Hypothesis testing versus confidence intervals
  • 6.7 Summary
  • Chapter 6 Problems
    • Practice problems
    • Assignment problems
• Interleaf 3 Why statistical significance is not the same as biological importance
• Chapter 7 Analyzing proportions
  • 7.1 The binomial distribution
    • Formula for the binomial distribution
    • Number of successes in a random sample
    • Sampling distribution of the proportion
  • 7.2 Testing a proportion: the binomial test
    • Approximations for the binomial test
  • 7.3 Estimating proportions
    • Estimating the standard error of a proportion
    • Confidence intervals for proportions—the Agresti–Coull method
    • Confidence intervals for proportions—the Wald method
  • 7.4 Deriving the binomial distribution
  • 7.5 Summary
  • 7.6 Quick formula summary
    • Binomial distribution
    • Proportion
    • Agresti–Coull 95% confidence interval for a proportion
    • Binomial test
  • Chapter 7 Problems
    • Practice problems
    • Assignment problems
• Interleaf 4 Biology and the history of statistics
• Chapter 8 Fitting probability models to frequency data
  • 8.1 χ2 Goodness-of-fit test: the proportional model
    • Null and alternative hypotheses
    • Observed and expected frequencies
    • The χ2 test statistic
    • The sampling distribution of χ2 under the null hypothesis
    • Calculating the P-value
    • Critical values for the χ2 distribution
  • 8.2 Assumptions of the χ2 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
    • Formula for the Poisson distribution
    • Testing randomness with the Poisson distribution
    • Comparing the variance to the mean
  • 8.5 Summary
  • 8.6 Quick formula summary
    • χ2 Goodness-of-fit test
    • Test statistic: χ2
    • Poisson distribution
  • Chapter 8 Problems
    • Practice problems
    • Assignment problems
• Interleaf 5 Making a plan
• Chapter 9 Contingency analysis: Associations between categorical variables
  • 9.1 Associating two categorical variables
  • 9.2 Estimating association in 2×2 tables: relative risk
    • Relative risk
    • Reduction in risk
  • 9.3 Estimating association in 2×2 tables: the odds ratio
    • Odds
    • Odds ratio
    • Standard error and confidence interval for odds ratio
    • Odds ratio vs. relative risk
  • 9.4 The χ2 contingency test
    • Hypotheses
    • Expected frequencies assuming independence
    • The χ2 statistic
    • Degrees of freedom
    • P-value and conclusion
    • A shortcut for calculating the expected frequencies
    • The χ2 contingency test is a special case of the χ2 goodness-of-fit test
    • Assumptions of the χ2 contingency test
    • Correction for continuity
  • 9.5 Fisher’s exact test
  • 9.6 Summary
  • 9.7 Quick formula summary
    • Confidence interval for relative risk
    • Confidence interval for odds ratio
    • The χ2 contingency test
    • Fisher’s exact test
  • Chapter 9 Problems
    • Practice problems
    • Assignment problems
• Review Problems 1
• Chapter 10 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
    • Using the standard normal table
    • Using the standard normal to describe any normal distribution
  • 10.5 The normal distribution of sample means
    • Calculating probabilities of sample means
  • 10.6 Central limit theorem
  • 10.7 Normal approximation to the binomial distribution
  • 10.8 Summary
  • 10.9 Quick formula summary
    • Z-standardization
    • Normal approximation to the binomial distribution
  • Chapter 10 Problems
    • Practice problems
    • Assignment problems
• Interleaf 6 Controls in medical studies
• Chapter 11 Inference for a normal population
  • 11.1 The t-distribution for sample means
    • Student’s t-distribution
    • Finding critical values of the t-distribution
  • 11.2 The confidence interval for the mean of a normal distribution
    • The 95% confidence interval for the mean
    • The 99% confidence interval for the mean
  • 11.3 The one-sample t-test
    • The effects of larger sample size: body temperature revisited
  • 11.4 Assumptions of the one-sample t-test
  • 11.5 Estimating the standard deviation and variance of a normal population
    • Confidence limits for the variance
    • Confidence limits for the standard deviation
    • Assumptions
  • 11.6 Summary
  • 11.7 Quick formula summary
    • Confidence interval for a mean
    • One-sample t-test
    • Confidence interval for variance
  • Chapter 11 Problems
    • Practice problems
    • Assignment problems
• Chapter 12 Comparing two means
  • 12.1 Paired sample versus two independent samples
  • 12.2 Paired comparison of means
    • Estimating mean difference from paired data
    • Paired t-test
    • Assumptions
  • 12.3 Two-sample comparison of means
    • Confidence interval for the difference between two means
    • Two-sample t-test
    • Assumptions
    • Welch’s t-test
  • 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
    • The F-test of equal variances
    • Levene’s test for homogeneity of variances
  • 12.8 Summary
  • 12.9 Quick formula summary
    • Confidence interval for the mean difference (paired data)
    • Paired t-test
    • Standard error of difference between two means
    • Confidence interval for the difference between two means (two samples)
    • Two-sample t-test
    • Welch’s confidence interval for the difference between two means
    • Welch’s approximate t-test
    • F-test
    • Levene’s test
  • Chapter 12 Problems
    • Practice problems
    • Assignment problems
• Interleaf 7 Which test should I use?
• Chapter 13 Handling violations of assumptions
  • 13.1 Detecting deviations from normality
    • Graphical methods
    • Formal test of normality
  • 13.2 When to ignore violations of assumptions
    • Violations of normality
    • Unequal standard deviations
  • 13.3 Data transformations
    • Log transformation
    • Other transformations
    • Confidence intervals with transformations
    • Avoid multiple testing with transformations
  • 13.4 Nonparametric alternatives to one-sample and paired t-tests
    • Sign test
    • The Wilcoxon signed-rank test
  • 13.5 Comparing two groups: the Mann–Whitney U-test
    • Tied ranks
    • Large samples and the normal approximation
  • 13.6 Assumptions of nonparametric tests
  • 13.7 Type I and Type II error rates of nonparametric methods
  • 13.8 Permutation tests
    • Assumptions of permutation tests
  • 13.9 Summary
  • 13.10 Quick formula summary
    • Transformations
    • Back-transformations
    • Sign test
    • Mann–Whitney U-test
  • Chapter 13 Problems
    • Practice problems
    • Assignment problems
• Review Problems 2
• Chapter 14 Designing experiments
  • 14.1 Lessons from clinical trials
    • Design components
  • 14.2 How to reduce bias
    • Simultaneous control group
    • Randomization
    • Blinding
  • 14.3 How to reduce the influence of sampling error
    • Replication
    • Balance
    • Blocking
    • Extreme treatments
  • 14.4 Experiments with more than one factor
  • 14.5 What if you can’t do experiments?
    • Match and adjust
  • 14.6 Choosing a sample size
    • Plan for precision
    • Plan for power
    • Plan for data loss
  • 14.7 Summary
  • 14.8 Quick formula summary
    • Planning for precision
    • Planning for power
  • Chapter 14 Problems
    • Practice problems
    • Assignment problems
• Interleaf 8 Data dredging
• Chapter 15 Comparing means of more than two groups
  • 15.1 The analysis of variance
    • Hypotheses
    • ANOVA in a nutshell
    • ANOVA tables
    • Partitioning the sum of squares
    • Calculating the mean squares
    • The variance ratio, F
    • Variation explained: R^2
    • ANOVA with two groups
  • 15.2 Assumptions and alternatives
    • The robustness of ANOVA
    • Data transformations
    • Nonparametric alternatives to ANOVA
  • 15.3 Planned comparisons
    • Planned comparison between two means
  • 15.4 Unplanned comparisons
    • Testing all pairs of means using the Tukey–Kramer method
    • Assumptions
  • 15.5 Fixed and random effects
  • 15.6 ANOVA with randomly chosen groups
    • ANOVA calculations
    • Variance components
    • Repeatability
    • Assumptions
  • 15.7 Summary
  • 15.8 Quick formula summary
    • Analysis of variance (ANOVA)
    • Kruskal–Wallis test
    • Planned confidence interval for the difference between two of k means
    • Planned test of the difference between two of k means
    • Tukey–Kramer test of all pairs of means
    • Repeatability and variance components
  • Chapter 15 Problems
    • Practice problems
    • Assignment problems
• Interleaf 9 Experimental and statistical mistakes
• Chapter 16 Correlation between numerical variables
  • 16.1 Estimating a linear correlation coefficient
    • The correlation coefficient
    • Standard error
    • Approximate confidence interval
  • 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
    • Procedure for large n
    • Assumptions of Spearman’s correlation
  • 16.6 The effects of measurement error on correlation
  • 16.7 Summary
  • 16.8 Quick formula summary
    • Shortcuts
    • Covariance
    • Correlation coefficient
    • Confidence interval (approximate) for a population correlation
    • The t-test of zero linear correlation
    • Spearman’s rank correlation
    • Spearman’s rank correlation test
    • Correlation corrected for measurement error
  • Chapter 16 Problems
    • Practice problems
    • Assignment problems
• Interleaf 10 Publication bias
• Chapter 17 Regression
  • 17.1 Linear regression
    • The method of least squares
    • Formula for the line
    • Calculating the slope and intercept
    • Populations and samples
    • Predicted values
    • Residuals
    • Standard error of slope
    • Confidence interval for the slope
  • 17.2 Confidence in predictions
    • Confidence intervals for predictions
    • Extrapolation
  • 17.3 Testing hypotheses about a slope
    • The t-test of regression slope
    • The ANOVA approach
  • 17.4 Regression toward the mean
  • 17.5 Assumptions of regression
    • Outliers
    • Detecting nonlinearity
    • Detecting non-normality and unequal variance
  • 17.6 Transformations
  • 17.7 The effects of measurement error on regression
  • 17.8 Regression with nonlinear relationships
    • A curve with an asymptote
    • Quadratic curves
    • Formula-free curve fitting
  • 17.9 Logistic regression: fitting a binary response variable
  • 17.10 Summary
  • 17.11 Quick formula summary
    • Shortcuts
    • Regression slope
    • Regression intercept
    • Confidence interval for the regression slope
    • Confidence interval for the predicted mean Y at a given X (confidence bands)
    • Confidence interval for the predicted individual Y at a given X (prediction intervals)
    • The t-test of a regression slope
    • The ANOVA method for testing zero slope
  • Chapter 17 Problems
    • Practice problems
    • Assignment problems
• Interleaf 11 Meta-analysis
• Review Problems 3
• Chapter 18 Analyzing multiple factors
  • 18.1 ANOVA and linear regression are linear models
    • Modeling with linear regression
    • Generalizing linear regression
    • Linear models
  • 18.2 Analyzing experiments with blocking
    • Analyzing data from a randomized block design
    • Model formula
    • Fitting the model to data
  • 18.3 Analyzing factorial designs
    • Model formula
    • Testing the factors
    • The importance of distinguishing fixed and random factors
  • 18.4 Adjusting for the effects of a covariate
    • Testing interaction
    • Fitting a model without an interaction term
  • 18.5 Assumptions of linear models
  • 18.6 Summary
  • Chapter 18 Problems
    • Practice problems
    • Assignment problems
• Interleaf 12 Using species as data points
• Chapter 19 Computer-intensive methods
  • 19.1 Hypothesis testing using simulation
  • 19.2 Bootstrap standard errors and confidence intervals
    • Bootstrap standard error
    • Confidence intervals by bootstrapping
    • Bootstrapping with multiple groups
    • Assumptions and limitations of the bootstrap
  • 19.3 Summary
  • Chapter 19 Problems
    • Practice problems
    • Assignment problems
• Chapter 20 Likelihood
  • 20.1 What is likelihood?
  • 20.2 Two uses of likelihood in biology
    • Phylogeny estimation
    • Gene mapping
  • 20.3 Maximum likelihood estimation
    • Probability model
    • The likelihood formula
    • The maximum likelihood estimate
    • Likelihood-based confidence intervals
  • 20.4 Versatility of maximum likelihood estimation
    • Probability model
    • The likelihood formula
    • The maximum likelihood estimate
    • Bias
  • 20.5 Log-likelihood ratio test
    • Likelihood ratio test statistic
    • Testing a population proportion
  • 20.6 Summary
  • 20.7 Quick formula summary
    • Likelihood
    • Likelihood-based confidence interval for a single parameter
    • Log-likelihood ratio test for a single parameter
  • Chapter 20 Problems
    • Practice problems
    • Assignment problems
• Chapter 21 Survival analysis
  • 21.1 Survival curves
    • Calculation summary
    • Confidence intervals
    • Median survival time
    • Assumptions
  • 21.2 Compare survival curves
    • Hazard ratio
    • Hazard ratio calculation
    • Logrank test
    • Assumptions
  • 21.3 Summary
  • 21.4 Quick formula summary
    • Hazard ratio
    • 95% Confidence interval for the hazard ratio
    • Logrank test
  • Chapter 21 Problems
    • Practice problems
    • Assignment problems
• Notes
• Statistical tables
  • Using statistical tables
  • Statistical Table A: The χ2 distribution
  • Statistical Table B: The standard normal (Z) distribution
  • Statistical Table C: Student’s t-distribution
  • Statistical Table D: The F-distribution
  • Statistical Table E: Mann–Whitney U-distribution
  • Statistical Table F: Tukey–Kramer q-distribution
  • Statistical Table G: Critical values for the Spearman’s rank correlation
• Literature cited
• Answers to practice problems
  • Chapter 1
  • Chapter 2
  • Chapter 3
  • Chapter 4
  • Chapter 5
  • Chapter 6
  • Chapter 7
  • Chapter 8
  • Chapter 9
  • Review 1
  • Chapter 10
  • Chapter 11
  • Chapter 12
  • Chapter 13
  • Review 2
  • Chapter 14
  • Chapter 15
  • Chapter 16
  • Chapter 17
  • Review 3
  • Chapter 18
  • Chapter 19
  • Chapter 20
  • Chapter 21
• Index
• glossary
• Back Cover

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