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Summary: MIND ON STATISTICS is designed to help students learn statistical ideas by encouraging them to actively think about those ideas. The authors blend the spirit of statistical literacy (the conceptual development of statistical ideas) with the statistical methodology taught in the Introductory Statistics course. By focusing on ideas instead of mathematical formulation, this book generates student excitement, motivation, and understanding. Using a wide variety of applica ...show moretions, the book clearly demonstrates the relevance of statistics. As students master the material, they see how statistics influences their daily lives. The text also helps students develop statistical intuition and learn how to interpret the results of statistical studies.
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.
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 Data.
Description of 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.
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 Correlation.
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 2x2 Table.
Interpretations of Probability.
Probability Definitions and Relations.
Basic Rules for Finding Probabilities.
Strategies for Finding Complicated Probabilities.
Using Simulation to Estimate Probabilities.
Coincidences and Intuitive Judgments about Probability.
8. Random Variables.
What is a Random Variable?.
Discrete Random Variables.
Expectations for Random Variables.
Binomial Random Variables.
Continuous Random Variables.
Normal Random Variables.
Approximating Binomial 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.
Student's t-distribution: Replacing s with s.
10. Estimating Proportions with Confidence.
The Language and Notation of Estimation.
Margin of Error.
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 Proprtions.
Formulating Hypothesis Statements.
The Logic of Hypothesis Testing: What if the Null is True?.
Deciding Between 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.
Approximate 95% Confidence Intervals.
General Confidence Interval Procedures for One Mean or Paired Data.
General Confidence Interval for the Difference in 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 Test and Confidence Intervals.
The Two Types of Errors and Their Probabilities.
Evaluating Significance in Research Reports.
14. More About Regression.
The Sample and Population Regression Lines.
Estimating the Standard Deviation from the Mean.
Inference about the Linear Regression Relationship.
Predicting the Value of Y for an Individual. Estimating the Mean Y at a Specified X.
Checking Conditions for Using Regression Models for Inference.
15. More About Categorical Variables.
The Chi-Square Test for Two-way Tables.
Analyzing 2x2 Tables.
Testing Hypotheses about One Categorical Variable: Goodness of Fit.
16. Analysis of Variance.
Comparing Means with an ANOVA F-test.
Details of One-way Analysis of Variance.
Other Methods for Comparing Populations.
Two-way Analysis of Variance.
17. 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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