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Intermediate Statistics with R
Introductory statistics courses prepare students to think statistically but cover relatively few statistical methods. Building on the basic statistical thinking emphasized in an introductory course, a second course in statistics at the undergraduate level can explore a large number of statistical methods. This text covers more advanced graphical summaries, One-Way ANOVA with pair-wise comparisons, Two-Way ANOVA, Chi-square testing, and simple and multiple linear regression models.
- Author
- Mark Greenwood
- Publisher
- Montana State University
- Source
- LibreTexts
- License
- CC BY-NC
- Language
- EN
- Category
- Basic Sciences
Contents· 114 sections
- 01: Preface
- 1.01: Overview of methods
- 1.02: Getting started in R
- 1.03: Basic summary statistics histograms and boxplots using R
- 1.04: R Markdown
- 1.05: Grammar of Graphics
- 1.06: Exiting RStudio
- 1.07: Chapter summary
- 1.08: Summary of important R code
- 1.09: Practice problems
- 02: (R)e-Introduction to statistics
- 2.01: Data wrangling and density curves
- 2.02: Pirate-plots
- 2.03: Models hypotheses and permutations for the two sample mean situation
- 2.04: Permutation testing for the two sample mean situation
- 2.05: Hypothesis testing (general)
- 2.06: Connecting randomization (nonparametric) and parametric tests
- 2.07: Second example of permutation tests
- 2.08: Reproducibility Crisis - Moving beyond p 0.05 publication bias and multiple testing issues
- 2.09: 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
- 03: One-Way ANOVA
- 3.01: Situation
- 3.02: Linear model for One-Way ANOVA (cell means and referencecoding)
- 3.03: One-Way ANOVA Sums of Squares Mean Squares and F-test
- 3.04: ANOVA model diagnostics including QQ-plots
- 3.05: Guinea pig tooth growth One-Way ANOVA example
- 3.06: Multiple (pair-wise) comparisons using Tukeys HSD and the compact letter display
- 3.07: Pair-wise comparisons for the Overtake data
- 3.08: Chapter summary
- 3.09: Summary of important R code
- 3.10: Practice problems
- 04: Two-Way ANOVA
- 4.01: Situation
- 4.02: Designing a two-way experiment and visualizing results
- 4.03: Two-Way ANOVA models and hypothesis tests
- 4.04: Guinea pig tooth growth analysis with Two-Way ANOVA
- 4.05: Observational study example - The Psychology of Debt
- 4.06: Pushing Two-Way ANOVA to the limit - Un-replicated designs and Estimability
- 4.07: Chapter summary
- 4.08: Summary of important R code
- 4.09: Practice problems
- 05: Chi-square tests
- 5.01: Situation contingency tables and tableplots
- 5.02: Homogeneity test hypotheses
- 5.03: Independence test hypotheses
- 5.04: Models for R by C tables
- 5.05: Permutation tests for the X2 statistic
- 5.06: Chi-square distribution for the X2 statistic
- 5.07: Examining residuals for the source of differences
- 5.08: General protocol for X2 tests
- 5.09: 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 code
- 5.14: Practice problems
- 06: Correlation and Simple Linear Regression
- 6.01: Relationships between two quantitative variables
- 6.02: Estimating the correlation coefficient
- 6.03: Relationships between variables by groups
- 6.04: Inference for the correlation coefficient
- 6.05: Are tree diameters related to tree heights
- 6.06: Describing relationships with a regression model
- 6.07: Least Squares Estimation
- 6.08: Measuring the strength of regressions - R2
- 6.09: 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
- 07: Simple linear regression inference
- 7.01: Model
- 7.02: Confidence interval and hypothesis tests for the slope and intercept
- 7.03: Bozeman temperature trend
- 7.04: Randomization-based inferences for the slope coefficient
- 7.05: Transformations part I - Linearizing relationships
- 7.06: Transformations part II - Impacts on SLR interpretations - log(y) log(x) and both log(y) and log(x)
- 7.07: Confidence interval for the mean and prediction intervals for a new observation
- 7.08: Chapter summary
- 7.09: Summary of important R code
- 7.10: Practice problems
- 08: Multiple linear regression
- 8.01: Going from SLR to MLR
- 8.02: Validity conditions in MLR
- 8.03: Interpretation of MLR terms
- 8.04: Comparing multiple regression models
- 8.05: General recommendations for MLR interpretations and VIFs
- 8.06: MLR inference - Parameter inferences using the t-distribution
- 8.07: Overall F-test in multiple linear regression
- 8.08: Case study - First year college GPA and SATs
- 8.09: 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
- 09: Case studies
- 9.01: Overview of material covered
- 9.02: The impact of simulated chronic nitrogen deposition on the biomass and N2-fixation activity of two boreal feather mosscyanobacteria associations
- 9.03: Ants learn to rely on more informative attributes during decision-making
- 9.04: Multi-variate models are essential for understanding vertebrate diversification in deep time
- 9.05: What do didgeridoos really do about sleepiness
- 9.06: General summary
- 10: Appendix
- 10.01: A- Bibliography
- 10.02: B- Index