Introduction to Statistics and Data Analysis

1. THE ROLE OF STATISTICS AND THE DATA ANALYSIS PROCESS: Why Study Statistics? The Nature and Role of Variability. Statistics and the Data Analysis Process. Types of Data and Some Simple Graphical Displays. 2. COLLECTING DATA SENSIBLY: Statistical Studies: Observation and Experimentation. Sampling. Simple Comparative Experiments. More on Experimental Design. Interpreting and Communicating the Results of Statistical Analyses. More on Observational Studies: Designing Surveys (online). 3. GRAPHICAL METHODS FOR DESCRIBING DATA: Displaying Categorical Data: Comparative Bar Charts and Pie Charts. Displaying Numerical Data: Stem-and-Leaf Displays. Displaying Numerical Data: Frequency Distributions and Histograms. Displaying Bivariate Numerical Data. Interpreting and Communicating the Results of Statistical Analyses. 4. NUMERICAL METHODS FOR DESCRIBING DATA: Describing the Center of a Data Set. Describing Variability in a Data Set. Summarizing a Data Set: Boxplots. Interpreting Center and Variability: Chebyshev's Rule, the Empirical Rule, and z Scores. Interpreting and Communicating the Results of Statistical Analyses. 5. SUMMARIZING BIVARIATE DATA: Correlation. Linear Regression: Fitting a Line to Bivariate Data. Assessing the Fit of a Line. Nonlinear Relationships and Transformations. Interpreting and Communicating the Results of Statistical Analyses. Logistic Regression (online). 6. PROBABILITY: Chance Experiments and Events. Definition of Probability. Basic Properties of Probability. Conditional Probability. Independence. Some General Probability Rules. Estimating Probabilities Empirically Using Simulation. 7. RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS: Random Variables. Probability Distributions for Discrete Random Variables. Probability Distributions for Continuous Random Variables. Mean and Standard Deviation of a Random Variable. Binomial and Geometric Distributions. Normal Distributions. Checking for Normality and Normalizing Transformations. Using the Normal Distribution to Approximate a Discrete Distribution. 8. SAMPLING VARIABILITY AND SAMPLING DISTRIBUTIONS: Statistics and Sampling Variability. The Sampling Distribution of a Sample Mean. The Sampling Distribution of a Sample Proportion. 9. Estimation Using a Single Sample: Point Estimation. Large-Sample Confidence Interval for a Population Proportion. Confidence Interval for a Population Mean. Interpreting and Communicating the Results of Statistical Analyses. Bootstrap Confidence Intervals for a Population Proportion (optional). Bootstrap Confidence Intervals for a Population Mean (optional). 10. HYPOTHESIS TESTING USING A SINGLE SAMPLE: Hypotheses and Test Procedures. Errors in Hypothesis Testing. Large-Sample Hypothesis Tests for a Population Proportion. Hypothesis Tests for a Population Mean. Power and Probability of Type II Error. Interpreting and Communicating the Results of Statistical Analyses. Exact Binomial Test and Randomization Test for a Population Proportion (optional). Randomization Test for a Population Mean (optional). 11. COMPARING TWO POPULATIONS OR TREATMENTS: Inferences Concerning the Difference Between Two Population or Treatment Means Using Independent Samples. Inferences Concerning the Difference Between Two Population or Treatment Means Using Paired Samples. Large-Sample Inferences Concerning the Difference Between Two Population or Treatment Proportions. Interpreting and Communicating the Results of Statistical Analyses. Randomization-Based Inference for a Difference in Proportions (optional). Randomization-Based Inference for a Difference in Means (optional). 12. THE ANALYSIS OF CATEGORICAL DATA AND GOODNESS-OF-FIT TESTS: Chi-Square Tests for Univariate Data. Tests for Homogeneity and Independence in a Two-way Table. Interpreting and Communicating the Results of Statistical Analyses. 13. SIMPLE LINEAR REGRESSION AND CORRELATION: INFERENTIAL METHODS: Simple Linear Regression Model. Inferences about the Slope of the Population Regression Line. Checking Model Adequacy. Inferences Based on the Estimated Regression Line