Elementary Statistics : Looking at the Big Picture
Publication Date 1 Jan 2010
Overview1. Introduction: Variables and Processes in Statistics. Types of Variables: Categorical or Quantitative. Students Talk Stats: Identifying Types of Variables. Handling. Data for Two Types of Variables. Roles of Variables: Explanatory or Response. Statistics as a Four-Stage Process. PART I: DATA PRODUCTION. 2. Sampling: Which Individuals Are Studied. Sources of Bias in Sampling: When Selected Individuals Are Not Representative. Probability Sampling Plans: Relying on Randomness. Role of Sample Size: Bigger Is Better if the Sample Is Representative. From Sample to Population: To What Extent Can We Generalize? Students Talk Stats: Seeking a Representative Sample. 3. Design: How Individuals Are Studied. Various Designs for Studying Variables. Sample Surveys: When Individuals Report Their Own Values. Observational Studies: When Nature Takes Its Course. Experiments: When Researchers Take Control. Students Talk Stats: Does TV Cause ADHD? Considering Study Design. PART II: DISPLAYING AND SUMMARIZING DATA. 4. Displaying and Summarizing Data for a Single Variable. Single Categorical Variable. Students Talk Stats: Biased Sample, Biased Assessment. Single Quantitative Variables and the Shape of a Distribution. Center and Spread: What's Typical for Quantitative Values, and How They Vary. Normal Distributions: The Shape of Things to Come. 5. Displaying and Summarizing Relationships. Relationship Between One Categorical and One Quantitative Variable. Students Talk Stats: Displaying and Summarizing Paired Data. Relationship Between Two Categorical Variables. Relationships Between Two Quantitative Variables. Students Talk Stats: How Outliers and Influential Observations Affect a Relationship. Students Talk Stats: Confounding in a Relationship Between Two Quantitative Variables. PART III: PROBABILITY. 6. Finding Probabilities. The Meaning of 'Probability' and Basic Rules. More General Probability Rules and Conditional Probability. Students Talk Stats: Probability as a Weighted Average of Conditional Probabilities. 7. Random Variables. Discrete Random Variables. Binomial Random Variables. Students Talk Stats: Calculating and Interpreting the Mean and Standard Deviation of Count or Proportion. Continuous Random Variables and the Normal Distribution. Students Talk Stats: Means, Standard Deviations, and Below-Average Heights. 8. Sampling Distributions. The Behavior of Sample Proportion in Repeated Random Samples. The Behavior of Sample Mean in Repeated Random Samples. Students Talk Stats: When Normal Approximations Are Appropriate. PART IV: STATISTICAL INFERENCE. 9. Inference for a Single Categorical Variable. Point Estimate and Confidence Interval: A Best Guess and a Range of Plausible Values for Population Proportion. Students Talk Stats: Interpreting a Confidence Interval. Test: Is a Proposed Population Proportion Plausible? Students Talk Stats: Interpreting a P-value. Students Talk Stats: What Type of Error Was Made? Students Talk Stats: The Correct Interpretation of a Small P-value. Students Talk Stats: The Correct Interpretation When a P-value Is Not Small. 10. Inference for a Single Quantitative Variable. Inference for a Mean when Population Standard Deviation Is Known or Sample Size Is Large. Students Talk Stats: Confidence Interval for a Mean. Students Talk Stats: Interpreting a Confidence Interval for the Mean Correctly. Inference for a Mean When the Population Standard Deviation Is Unknown and the Sample Size Is Small. Students Talk Stats: Practical Application of a t Test. A Closer Look at Inference for Means. 11. Inference for Relationships Between Categorical and Quantitative Variables. Inference for a Paired Design with t. Inference for a Two-Sample Design with t. Students Talk Stats: Ordinary Vs. Pooled Two-Sample t. Inference for a Several-sample Design with F: Analysis of Variance. Students Talk Stats: Reviewing Relationships between Categorical and Quantitative Variables. 12. Inference for Relationships Between Two Categorical Variables. Comparing Proportions with a z Test. Comparing Counts with a Chi-Square Test. 13.