Statistics

Section I: COLLECTING DATA. 1. Collecting Data in Reasonable Ways. Statistics: It's All About Variability. Statistical Studies: Observation and Experimentation. Collecting Data: Planning an Observational Study. Collecting Data: Planning an Experiment. The Importance of Random Selection and Random Assignment: What Types of Conclusions Are Reasonable? Avoid These Common Mistakes. Chapter Activities. Explorations in Statistical Thinking. Section II: DESCRIBING DATA DISTRIBUTIONS. 2. Graphical Methods for Describing Data Distributions. Selecting an Appropriate Graphical Display. Displaying Categorical Data: Bar Charts and Comparative Bar Charts. Displaying Numerical Data: Dotplots, Stem-and-Leaf Displays, and Histograms. Displaying Bivariate Numerical Data: Scatterplots and Time-Series Plots. Graphical Displays in the Media. Bivariate and Multivariable Graphical Displays. Avoid These Common Mistakes. Chapter Activities. Explorations in Statistical Thinking. 3. Numerical Methods for Describing Data Distributions. Selecting Appropriate Numerical Summaries. Describing Center and Variability for Data Distributions that are Approximately Symmetric. Describing Center and Variability for Data Distributions that are Skewed or Have Outliers. Summarizing a Data Set: Boxplots. Measures of Relative Standing: z-scores and Percentiles. Avoid These Common Mistakes. Chapter Activities. Explorations in Statistical Thinking. 4. Describing Bivariate Numerical Data. Correlation. Linear Regression: Fitting a Line to Bivariate Data. Assessing the Fit of a Line. Describing Linear Relationships and Making Predictions--Putting it all Together. Avoid These Common Mistakes. Chapter Activities. Explorations in Statistical Thinking. Bonus Material on Logistic Regression (Online). Section III: A FOUNDATION FOR INFERENCE: REASONING ABOUT PROBABILITY. 5. Probability. Interpreting Probabilities. Computing Probabilities. Probabilities of More Complex Events: Unions, Intersections and Complements. Conditional Probability. Calculating Probabilities -- A More Formal Approach. Probability as a Basis for Making Decisions. Estimating Probabilities Empirically and Using Simulation (Optional). Chapter Activities. 6. Random Variables and Probability Distributions. Random Variables. Probability Distributions for Discrete Random Variables. Probability Distributions for Continuous Random Variables. The Mean and Standard Deviation of a Random Variable. Normal Distribution. Checking for Normality. Binomial and Geometric Distributions (Optional). Using the Normal Distribution to Approximate a Discrete Distribution (Optional). Chapter Activities. Bonus Material on Counting Rules, The Poisson Distribution (Online). Section IV: LEARNING FROM SAMPLE DATA. 7. An Overview of Statistical Inference -- Learning from Data. Statistical Inference -- What You Can Learn from Data. Selecting an Appropriate Method -- Four Key Questions. A Five-Step Process for Statistical Inference. 8. Sampling Variability and Sampling Distributions. Statistics and Sampling Variability. The Sampling Distribution of a Sample Proportion. How Sampling Distributions Support Learning from Data. Chapter Activities. 9. Estimating a Population Proportion. Selecting an Estimator. Estimating a Population Proportion -- Margin of Error. A Large Sample Confidence Interval for a Population Proportion. Choosing a Sample Size to Achieve a Desired Margin of Error. Bootstrap Confidence Intervals for a Population Proportion (Optional). Avoid These Common Mistakes. Chapter Activities. Explorations in Statistical Thinking. 10. Asking and Answering Questions about a Population Proportion. Hypotheses and Possible Conclusions. Potential Errors in Hypothesis Testing. The Logic of Hypothesis Testing -- An Informal Example. A Procedure for Carrying Out a Hypothesis Test. Large-Sample Hypothesis Tests for a Population Proportion. Randomization Tests and Exact Binomial Tests for One Proportion (Optional). Avoid These Common Mistakes. Chapter Activities. Explorations in Statistical