A Primer of Ecological Statistics
Part I: FundamentaIs of Probability and Statistical Thinking. Chapter 1: An lntroduction to Probability. What Is Probability? Measuring Probability. The Probability of a Single Event. Prey Capture by Carnivorous Plants. Estimating Probabilities by Sampling . Problems in the Definition Probability The Mathematics of Probability. Defining the Sample Space. Complex and Shared Events: Combining Simple Probabilities. Probability Calcu1ations: Milkweeds and Caterpillars. Complex and Shared Events: Rules for Combining Sets, Conditional Probabilities. Bayes' Theorem. Chapter 2: Random Variables and Probability Distributions. Discrete Random Variables. Bernoulli Random Variables. An Example of a Bernoulli Trial. Many Bernoulli Trials = A Binomial Randorn Variable. The Binomial Distribution. Poisson Random Variables. An Example of a Poisson Random Variable: Distribution of aRare Plant. The Expected Value of a Discrete Random Variable. The Variance of a Discrete Random Variable. Continuous Random Variables. Uniform Random Variables. The Expected Value of a Continuous Random Variable. Normal Random Variables. Useful Properties of the Normal Distribution. Other Continuous Random Variables. The Central Limit Theorem. Chapter 3: Summary Statistics: Measuresof Location and Spread. Measures of Location. The Arithmetic Mean Other Means. Other Measures of Location: The Median and the Mode. When to Use Each Measure of Location. Measures of Spread. The Variance and the Standard Deviation. The Standard Error of the Mean. Skewness, Kurtosis, and Central Moments. Quantiles. Using Measures of Spread. Some Philosophical Issues Surrounding Summary Statistics. Confidence Intervals. Generalized Confidence lntervals. Chapter 4: Framing and Testing Hypotheses. Scientific Methods. Deduction and lnduction. Moderrn-Day lnduction: Bayesian lnference. The Hypothetico-Deductive Method. Testing Statistical Hypotheses. Statistical Hypotheses versus Scientific Hypotheses. Statistical Significance and P - Values. Errors in Hypothesis Testing. Parameter Estimation and Prediction. Chapter 5:Three Frameworks for Statistical Analysis. Sample Problem. Monte Carlo Analysis. Step 1: Specifying the Test Statistic. Step 2: Creating the Null Distribution. Step 3: Deciding on a One- or Two- Tailed Test. Step 4: Calculating the Tail Probability. Assumptions of the Monte Carlo Method. Advantages and Disadvantages of the Monte Carlo Method. Parametric Analysis. Step 1: Specifyjng the Test Statistic. Step 2: Specifying the Null Distribution. Step 3: Calculating the Tail Probability. Assumptions of the Parametric Method. Advantages and Disadvantages of the Parametric Method. Least-Squares Parameter Estimates 246 Variance Components and the Coefficient of Determination. Hypothesis Tests with Regression. The Anatomy of an ANOVA Table. Other Tests and Confidence IntervaIs. Assumptions of Regression. Diagnostic Tests For Regression. Plotting ResiduaIs. Other Diagnostic Plots. The lnfluence Function. Monte Cado and Bayesian Analyses. Linear Regression Using Monte Cado Methods. Linear Regression Using Bayesian Methods. Other Kinds of Regression Analyses. Robust Regression. Quantile Regression. Logistic Regression. Non-Linear Regression. Multiple Regression. Path AnaIysis. Model Selection Cri teria. Model Selection Methods for Multiple Regression. Model Selection Methods in Path Analysis. Bayesian Model Selection. Chapter 10: The Analysis Of VarianceSymbols and Labels in ANOVA. ANOVA and Partitioning of the Sum of Squares. The Assumptions of ANOVA. Hypothesis Tests with ANOVA. Constructing F- Ratios. A Bestiary of ANOVA Tables. Randomized Block. Nested ANOVA. Two- Way ANOVA. ANOVA for Three- Way and n- Way Designs. Split-Plot ANOVA. Repeated Measures ANOVA. ANCOVA. Random versus Fixed Factors in ANOVA. Partitioning the Variance in ANOVA. After ANOVA: Plotting and Understanding Interaction Terms. Plotting Results from One-Way ANOVAs. Plotting Results from Two- Way ANOVAs. Understanding the lnteraction Term. Plotting Results fram ANCOVAs. Comparing Means. A Posteriori Comparisons. A Priori Contrasts. Bonferroni Corrections and the Problem of Multiple Tests. Chapter 11: The Analysis of Categorical Data. Two- Way Contingency Tables. Organizing the Data. Are the Variables lndependent? Testing the Hypothesis: Pearson's Chi-square Test. An Alternative to Pearson's Chi-Square: The G- Test. The Chi-square Test and the G- Test for R x C Tables. Which Test To Choose? Multi- Way Contingency Tables. Organizing the Data. On to Multi- Way Tables! Bayesian Approaches to Contingency Tables. Tests for Goodness-of-Fit. Goodness-of- Fit Tests for Discrete Distributions. Testing Goodness-of-Fit for Continuous. Distributions: The Kolmogorov-Smirnov Test. Chapter 12: The Analysis Of Multivariate Data. Approaching Multivariate Data. The Need for Matrix Algebra. Comparing Multivariate Means. Comparing Multivariate Means of Two Samples: Hotelling's y2 Test. Comparing Multivariate Means of More Than Two Samples: A Simple MANOVA. The Multivariate Normal Distribution. Testing for Multivariate Normality. Measurements of Multivariate Distance. Measuring Distances between Two IndividuaIs. Measuring Distances Between Two Groups. Other Measurements of Distance. Ordination. Principal Component Analysis 406 Factor Analysis. Principal Coordinates Analysis. Correspondence Analysis. Non-Metric Multidimensional Scaling. Advantages and Disadvantages of Ordination.Classification . Cluster Analysis. Choosing a Clustering Method. Discriminant Analysis. Advantages and Disadvantages of Classification. Multivariate Multiple Regression. Redundancy Analysis.