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Statistics Success Stories and Cautionary Tales | |
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What is Statistics? | |
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Seven Statistical Stories with Morals | |
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The Common Elements in the Seven Stories | |
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Turning Data Into Information | |
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Raw Data | |
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Types of Data | |
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Summarizing One or Two Categorical Variables | |
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Finding Information in Quantitative Data | |
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Pictures for Quantitative Data | |
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Numerical Summaries of Quantitative Variables | |
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Bell-Shaped Distributions of Numbers | |
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Gathering Useful Information | |
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Description or Decision? | |
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Using Data Wisely | |
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Speaking the Language of Research Studies | |
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Designing a Good Experiment | |
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Designing a Good Observational Study | |
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Difficulties and Disasters in Experiments and Observational Studies | |
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Sampling: Surveys and How to Ask Questions | |
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The Beauty of Sampling | |
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Sampling Methods | |
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Difficulties and Disasters in Sampling | |
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How to Ask Survey Questions | |
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Relationships Between Quantitative Variables | |
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Looking for Patterns with Scatterplots | |
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Describing Linear Patterns with a Regression Line | |
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Measuring Strength and Direction with a Regression Line | |
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Why Answers May Not Make Sense | |
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Correlation Does Not Prove Causation | |
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Relationships Between Categorical Variables | |
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Displaying Relationships between Categorical Variables | |
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Risk, Relative Risk, Odds Ratio, and Increased Risk | |
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Misleading Statistics about Risk | |
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The Effect of a Third Variable and Simpson's Paradox | |
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Assessing the Statistical Significance of a 2 x 2 Table | |
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Probability | |
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Random Circumstances | |
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Interpretations of Probability | |
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Probability Definitions and Relationships | |
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Basic Rules for Finding Probabilities | |
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Strategies for Finding Complicated Probabilities | |
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Using Simulation to Estimate Probabilities | |
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Coincidences and Intuitive Judgments about Probability | |
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Random Varaibles | |
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What is a Random Variable? | |
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Discrete Random Variables | |
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Expectations for Random Variables | |
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Binomial Random Variables | |
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Continuous Random Variables | |
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Normal Random Variables | |
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Approximating Binominal Distribution Probabilities | |
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Sums, Differences, and Combinations of Random Variables | |
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Means and Proportions as Random Variables | |
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Understanding Dissimilarity among Samples | |
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Sampling Distributions for Sample Proportions | |
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What to Expect of Sample Means | |
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What to Expect in Other Situations: Central Limit Theorem | |
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Sampling Distribution for Any Statistic | |
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Standardized Statistics | |
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Student's t-Distribution: Replacing ? with s | |
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Statistical Inference | |
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Estimating Proportions with Confidence | |
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The Language and Notation of Estimation | |
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Margin of Error | |
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Confidence Intervals | |
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Calculating a Margin of Error for 95% Confidence | |
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General Theory of Confidence Intervals for a Proportion | |
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Choosing a Sample Size for a Survey | |
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Using Confidence Intervals to Guide Decisions | |
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Testing Hypotheses About Proportions | |
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Formulating Hypothesis Statements | |
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The Logic of Hypothesis Testing: What if the Null is True? | |
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Reaching a Conclusion about the Two Hypotheses | |
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Testing Hypotheses about a Proportion | |
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The Role of Sample Size in Statistical Significance | |
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Real Importance versus Statistical Significance | |
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What Can Go Wrong: The Two Types of Errors | |
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More About Confidence Intervals | |
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Examples of Different Estimation Situations | |
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Standard Errors | |
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Approximate 95% Confidence Intervals | |
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General Confidence Intervals for One Mean or Paired Data | |
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General Confidence Intervals for the Difference Between Two Means (Independent Samples) | |
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The Difference between Two Proportions (Independent Samples) | |
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Understanding Any Confidence Interval | |
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More About Significance Tests | |
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The General Ideas of Significance Testing | |
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Testing Hypotheses about One Mean or Paired Data | |
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Testing the Difference Between Two Means (Independent Samples) | |
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Testing the Difference between Two Population Proportions | |
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The Relationship between Significance Tests and Confidence Intervals | |
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The Two Types of Errors and Their Probabilities | |
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Evaluating Significance in Research Reports | |
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More About Regression | |
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Sample and Population Regression Models | |
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Estimating the Standard Deviation for Regression | |
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Inference about the Linear Regression Relationship | |
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Predicting the Value y for an Individual | |
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Estimating the Mean y at a Specified x | |
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Checking for Conditions for Using regression Models for Inference | |
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More About Categorical Variables | |
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The Chi-Square Test for Two-Way Tables | |
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Analyzing 2 x 2 Tables | |
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Testing Hypotheses about One Categorical Variable: Goodness of Fit | |
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Analysis of Variance | |
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Comparing Means with the ANOVA F-Test | |
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Details of One-Way Analysis of Variance | |
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Other Methods for Comparing Populations | |
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Two-Way Analysis of Variance | |
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Additional Discrete Random Variables | |
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Hypergeometric Distribution | |
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Poisson Distribution | |
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Multinomial Distribution | |
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Nonparametric Tests of Hypotheses | |
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The Sign Test | |
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The Two-Sample Rank-Sum Test | |
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The Wilcoxon Signed-Rank Test | |
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The Kruskal-Wallis Test | |
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Multiple Regression | |
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The Multiple Linear Regression Model | |
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Inference about Multiple Regression Models | |
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Checking Conditions for Multiple Linear Regression | |
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Two-Way Analysis of Variance | |
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Assumptions and Models for Two-Way ANOVA | |
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Testing for Main Effects and Interactions | |
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Ethics | |
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Ethical Treatment of Human and Animal Participants | |
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Assurance of Data Quality | |
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Appropriate Statistical Analysis | |
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Fair Reporting of Results | |
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Turning Information into Wisdom | |
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Beyond the Data | |
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Transforming Uncertainty into Wisdom | |
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Making Personal Decisions | |
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Control of Societal Risks | |
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Understanding Our World | |
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Getting to Know You | |
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Words to the Wise | |