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Statistical Ideas and Methods


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1. STATISTICS SUCCESS STORIES AND CAUTIONARY TALES. What is Statistics? Seven Statistical Stories with Morals. The Common Elements in the Seven Stories. 2. TURNING DATA INTO INFORMATION. Raw Data. Types of Data. Summarizing One or Two Categorical Variables. Finding Information in Quantitative Data. Pictures for Quantitative Data. Numerical Summaries of Quantitative Variables. Bell-Shaped Distributions of Numbers. 3. GATHERING USEFUL INFORMATION. Description or Decision? Using Data Wisely. Speaking the Language of Research Studies. Designing a Good Experiment. Designing a Good Observational Study. Difficulties and Disasters in Experiments and Observational Studies. 4. SAMPLING: SURVEYS AND HOW TO ASK QUESTIONS. The Beauty of Sampling. Sampling Methods. Difficulties and Disasters in Sampling. How to Ask Survey Questions. 5. RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES. Looking for Patterns with Scatterplots. Describing Linear Patterns with a Regression Line. Measuring Strength and Direction with a Regression Line. Why Answers May Not Make Sense. Correlation Does Not Prove Causation. 6. RELATIONSHIPS BETWEEN CATEGORICAL VARIABLES. Displaying Relationships between Categorical Variables. Risk, Relative Risk, Odds Ratio, and Increased Risk. Misleading Statistics about Risk. The Effect of a Third Variable and Simpson's Paradox. Assessing the Statistical Significance of a 2 x 2 Table. 7. PROBABILITY. Random Circumstances. Interpretations of Probability. Probability Definitions and Relationships. Basic Rules for Finding Probabilities. Strategies for Finding Complicated Probabilities. Using Simulation to Estimate Probabilities. Coincidences and Intuitive Judgments about Probability 8. RANDOM VARAIBLES. What is a Random Variable? Discrete Random Variables. Expectations for Random Variables. Binomial Random Variables. Continuous Random Variables. Normal Random Variables. Approximating Binominal Distribution Probabilities. Sums, Differences, and Combinations of Random Variables. 9. MEANS AND PROPORTIONS AS RANDOM VARIABLES. Understanding Dissimilarity among Samples. Sampling Distributions for Sample Proportions. What to Expect of Sample Means. What to Expect in Other Situations: Central Limit Theorem. Sampling Distribution for Any Statistic. Standardized Statistics. Student's t-Distribution: Replacing o with s. Statistical Inference. 10. ESTIMATING PROPORTIONS WITH CONFIDENCE. The Language and Notation of Estimation. Margin of Error. Confidence Intervals. Calculating a Margin of Error for 95% Confidence. General Theory of Confidence Intervals for a Proportion. Choosing a Sample Size for a Survey. Using Confidence Intervals to Guide Decisions. 11. TESTING HYPOTHESES ABOUT PROPORTIONS. Formulating Hypothesis Statements. The Logic of Hypothesis Testing: What if the Null is True? Reaching a Conclusion about the Two Hypotheses. Testing Hypotheses about a Proportion. The Role of Sample Size in Statistical Significance. Real Importance versus Statistical Significance. What Can Go Wrong: The Two Types of Errors. 12. MORE ABOUT CONFIDENCE INTERVALS. Examples of Different Estimation Situations. Standard Errors. Approximate 95% Confidence Intervals. General Confidence Intervals for One Mean or Paired Data. General Confidence Intervals for the Difference Between Two Means (Independent Samples). The Difference between Two Proportions (Independent Samples). Understanding Any Confidence Interval. 13. MORE ABOUT SIGNIFICANCE TESTS. The General Ideas of Significance Testing. Testing Hypotheses about One Mean or Paired Data. Testing the Difference Between Two Means (Independent Samples). Testing the Difference between Two Population Proportions. The Relationship between Significance Tests and Confidence Intervals. The Two Types of Errors and Their Probabilities. Evaluating Significance in Research Reports. 14. MORE ABOUT REGRESSION. Sample and Population Regression Models. Estimating the Standard Deviation for Regression. Inference about the Linear Regression Relationship. Predicting the Value y for an Individual. Estimating the Mean y at a Specified x. Checking for Conditions for Using regression Models for Inference. 15. MORE ABOUT CATEGORICAL VARIABLES. The Chi-Square Test for Two-Way Tables. Analyzing 2 x 2 Tables. Testing Hypotheses about One Categorical Variable: Goodness of Fit. 16. ANALYSIS OF VARIANCE. Comparing Means with the ANOVA F-Test. Details of One-Way Analysis of Variance. Other Methods for Comparing Populations. Two-Way Analysis of Variance. 17. ADDITIONAL DISCRETE RANDOM VARIABLES. Hypergeometric Distribution. Poisson Distribution. Multinomial Distribution. 18. NONPARAMETRIC TESTS OF HYPOTHESES. The Sign Test. The Two-Sample Rank-Sum Test. The Wilcoxon Signed-Rank Test. The Kruskal-Wallis Test. 19. MULTIPLE REGRESSION. The Multiple Linear Regression Model. Inference about Multiple Regression Models. Checking Conditions for Multiple Linear Regression. 20. TWO-WAY ANALYSIS OF VARIANCE. Assumptions and Models for Two-Way ANOVA. Testing for Main Effects and Interactions. 21. ETHICS. Ethical Treatment of Human and Animal Participants. Assurance of Data Quality. Appropriate Statistical Analysis. Fair Reporting of Results. 22. TURNING INFORMATION INTO WISDOM.Beyond the Data. Transforming Uncertainty into Wisdom. Making Personal Decisions. Control of Societal Risks. Understanding Our World. Getting to Know You. Words to the Wise.

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