Intermediate Statistics with R
Cover
Acknowledgments
1
Preface
1.1
Overview of methods
1.2
Getting started in R
1.3
Basic summary statistics, histograms, and boxplots using R
1.4
Chapter summary
1.5
Summary of important R code
1.6
Practice problems
2
(R)e-Introduction to statistics
2.1
Histograms, boxplots, and density curves
2.2
Pirate-plots
2.3
Models, hypotheses, and permutations for the two sample mean situation
2.4
Permutation testing for the two sample mean situation
2.5
Hypothesis testing (general)
2.6
Connecting randomization (nonparametric) and parametric tests
2.7
Second example of permutation tests
2.8
Reproducibility Crisis: Moving beyond p < 0.05, publication bias, and multiple testing issues
2.9
Confidence intervals and bootstrapping
2.10
Bootstrap confidence intervals for difference in GPAs
2.11
Chapter summary
2.12
Summary of important R code
2.13
Practice problems
3
One-Way ANOVA
3.1
Situation
3.2
Linear model for One-Way ANOVA (cell means and reference-coding)
3.3
One-Way ANOVA Sums of Squares, Mean Squares, and F-test
3.4
ANOVA model diagnostics including QQ-plots
3.5
Guinea pig tooth growth One-Way ANOVA example
3.6
Multiple (pair-wise) comparisons using Tukey’s HSD and the compact letter display
3.7
Pair-wise comparisons for the Overtake data
3.8
Chapter summary
3.9
Summary of important R code
3.10
Practice problems
4
Two-Way ANOVA
4.1
Situation
4.2
Designing a two-way experiment and visualizing results
4.3
Two-Way ANOVA models and hypothesis tests
4.4
Guinea pig tooth growth analysis with Two-Way ANOVA
4.5
Observational study example: The Psychology of Debt
4.6
Pushing Two-Way ANOVA to the limit: Un-replicated designs and Estimability
4.7
Chapter summary
4.8
Summary of important R code
4.9
Practice problems
5
Chi-square tests
5.1
Situation, contingency tables, and tableplots
5.2
Homogeneity test hypotheses
5.3
Independence test hypotheses
5.4
Models for R by C tables
5.5
Permutation tests for the
\(X^2\)
statistic
5.6
Chi-square distribution for the
\(X^2\)
statistic
5.7
Examining residuals for the source of differences
5.8
General protocol for
\(X^2\)
tests
5.9
Political party and voting results: Complete analysis
5.10
Is cheating and lying related in students?
5.11
Analyzing a stratified random sample of California schools
5.12
Chapter summary
5.13
Summary of important R commands
5.14
Practice problems
6
Correlation and Simple Linear Regression
6.1
Relationships between two quantitative variables
6.2
Estimating the correlation coefficient
6.3
Relationships between variables by groups
6.4
Inference for the correlation coefficient
6.5
Are tree diameters related to tree heights?
6.6
Describing relationships with a regression model
6.7
Least Squares Estimation
6.8
Measuring the strength of regressions: R
2
6.9
Outliers: leverage and influence
6.10
Residual diagnostics – setting the stage for inference
6.11
Old Faithful discharge and waiting times
6.12
Chapter summary
6.13
Summary of important R code
6.14
Practice problems
7
Simple linear regression inference
7.1
Model
7.2
Confidence interval and hypothesis tests for the slope and intercept
7.3
Bozeman temperature trend
7.4
Randomization-based inferences for the slope coefficient
7.5
Transformations part I: Linearizing relationships
7.6
Transformations part II: Impacts on SLR interpretations: log(y), log(x), & both log(y) & log(x)
7.7
Confidence interval for the mean and prediction intervals for a new observation
7.8
Chapter summary
7.9
Summary of important R code
7.10
Practice problems
8
Multiple linear regression
8.1
Going from SLR to MLR
8.2
Validity conditions in MLR
8.3
Interpretation of MLR terms
8.4
Comparing multiple regression models
8.5
General recommendations for MLR interpretations and VIFs
8.6
MLR inference: Parameter inferences using the t-distribution
8.7
Overall F-test in multiple linear regression
8.8
Case study: First year college GPA and SATs
8.9
Different intercepts for different groups: MLR with indicator variables
8.10
Additive MLR with more than two groups: Headache example
8.11
Different slopes and different intercepts
8.12
F-tests for MLR models with quantitative and categorical variables and interactions
8.13
AICs for model selection
8.14
Case study: Forced expiratory volume model selection using AICs
8.15
Chapter summary
8.16
Summary of important R code
8.17
Practice problems
9
Case studies
9.1
Overview of material covered
9.2
The impact of simulated chronic nitrogen deposition on the biomass and N2-fixation activity of two boreal feather moss–cyanobacteria associations
9.3
Ants learn to rely on more informative attributes during decision-making
9.4
Multi-variate models are essential for understanding vertebrate diversification in deep time
9.5
What do didgeridoos really do about sleepiness?
9.6
General summary
References
Published with bookdown
Intermediate Statistics with R
Intermediate Statistics with R
Version 2.0 – Published Fall 2019
Mark C Greenwood
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