Foundational and Applied Statistics for Biologists Using R

FOUNDATIONS Philosophical and Historical Foundations Introduction Nature of Science Scientific Principles Scientific Method Scientific Hypotheses Logic Variability and Uncertainty in Investigations Science and Statistics Statistics and Biology Introduction to Probability Introduction: Models for Random Variables Classical Probability Conditional Probability Odds Combinatorial Analysis Bayes Rule Probability Density Functions Introduction Introductory Examples of pdfs Other Important Distributions Which pdf to Use? Reference Tables Parameters and Statistics Introduction Parameters Statistics OLS and ML Estimators Linear Transformations Bayesian Applications Interval Estimation: Sampling Distributions, Resampling Distributions, and Simulation Distributions Introduction Sampling Distributions Confidence Intervals Resampling Distributions Bayesian Applications: Simulation Distributions Hypothesis Testing Introduction Parametric Frequentist Null Hypothesis Testing Type I and Type II Errors Power Criticisms of Frequentist Null Hypothesis Testing Alternatives to Parametric Null Hypothesis Testing Alternatives to Null Hypothesis Testing Sampling Design and Experimental Design Introduction Some Terminology The Question Is: What Is the Question? Two Important Tenets: Randomization and Replication Sampling Design Experimental Design APPLICATIONS Correlation Introduction Pearson's Correlation Robust Correlation Comparisons of Correlation Procedures Regression Introduction Linear Regression Model General Linear Models Simple Linear Regression Multiple Regression Fitted and Predicted Values Confidence and Prediction Intervals Coefficient of Determination and Important Variants Power, Sample Size, and Effect Size Assumptions and Diagnostics for Linear Regression Transformation in the Context of Linear Models Fixing the Y-Intercept Weighted Least Squares Polynomial Regression Comparing Model Slopes Likelihood and General Linear Models Model Selection Robust Regression Model II Regression (X Not Fixed) Generalized Linear Models Nonlinear Models Smoother Approaches to Association and Regression Bayesian Approaches to Regression ANOVA Introduction One-Way ANOVA Inferences for Factor Levels ANOVA as a General Linear Model Random Effects Power, Sample Size, and Effect Size ANOVA Diagnostics and Assumptions Two-Way Factorial Design Randomized Block Design Nested Design Split-Plot Design Repeated Measures Design ANCOVA Unbalanced Designs Robust ANOVA Bayesian Approaches to ANOVA Tabular Analyses Introduction Probability Distributions for Tabular Analyses One-Way Formats Confidence Intervals for p Contingency Tables Two-Way Tables Ordinal Variables Power, Sample Size, and Effect Size Three-Way Tables Generalized Linear Models Appendix References Index A Summary and Exercises appear at the end of each chapter.