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by Jessica M. Utts and Robert F. Heckard

Edition: 2ND 04Copyright: 2004

Publisher: Brooks/Cole Publishing Co.

Published: 2004

International: No

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Emphasizing the conceptual development of statistical ideas, MIND ON STATISTICS actively engages students and explains topics in the context of excellent examples and case studies. This text balances the spirit of statistical literacy with statistical methodology taught in the introductory statistics course. Jessica Utts and Robert Heckard built the book on two learning premises: (1) New material is much easier to learn and remember if it is related to something interesting or previously known; (2) New material is easier to learn if you actively ask questions and answer them for yourself. More than any other text available, MIND ON STATISTICS motivates students to develop their statistical intuition by focusing on analyzing data and interpreting results as opposed to focusing on mathematical formulation. The new edition of this exciting text, enhanced with new material and features, appeals to a wide array of students and instructors alike.

**Utts, Jessica M. : University of California, Davis **

Jessica M. Utts is interested in applying statistics to issues of public interest and in educating students and others to be critical consumers of statistical information. Her research has focused on applications ranging from parapsychology to the impacts of transportation on air quality. In the area of statistics education, Professor Utts is the author of SEEING THROUGH STATISTICS (2nd Edition, 1999, Duxbury Press). She is also the Editor-In-Chief for CyberStats, a Web-based statistics course currently being used in classrooms across the United States. A recipient of two distinguished teaching awards, she frequently presents lectures and workshops on innovative methods for teaching statistics. She was a member of the College Board's Advanced Placement Statistics Development Committee from 1996-2002, serving as Chair from 1999-2002. Professor Utts has appeared on numerous television programs, including ABC's 20/20, Nightline, Larry King Live and CNN Morning News, discussing topics ranging from parapsychology to luck and lotteries. She has also served on numerous panels and advisory boards in government and industry. She is a Fellow of the American Statistical Association, the Institute of Mathematical Statistics, and the American Association for the Advancement of Science.

**Heckard, Robert F. : Pennsylvania State University **

Robert F. Heckard is a senior lecturer in statistics at the Pennsylvania State University, where he has taught for over 30 years. He has taught introductory and intermediate applied statistics to more than 15,000 college students. Heckard has been awarded several grants to develop multimedia and web-based instructional materials for teaching statistical concepts, and is a co-author of CyberStats, a Web-based introductory course. As a consultant, he is active in the statistical analysis and design of highway safety research and has frequently been a consultant in cancer treatment clinical trials.

1. STATISTICS SUCCESS STORIES AND CAUTIONARY TALES.

What is Statistics? Seven Statistical Stories with Morals. The Common Elements i n the Seven Stories.

2. TURNING DATA INTO INFORMATION.

Raw Data. Types of Data. Summarizing One or Two Categorical Variables. Finding I nformation in Quantitative Data. Pictures for Quantitative Data. Numerical Summa ries of Quantitative Variables. Bell-Shaped Distributions of Numbers.

3. GATHERING USEFUL INFORMATION.

Description or Decision? Using Data Wisely. Speaking the Language of Research St udies. Designing a Good Experiment. Designing a Good Observational Study. Diffic ulties 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 Regres sion 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, Odd s Ratio, and Increased Risk. Misleading Statistics About Risk. The Effect of a T hird Variable and Simpson's Paradox. Assessing the Statistical Significance of a 2 x 2 Table.

7. PROBABILITY.

Random Circumstances. Interpretations of Probability. Probability Definitions an d Relationships. Basic Rules for Finding Probabilities. Strategies for Finding C omplicated Probabilities. Using Simulation to Estimate Probabilities. Coincidenc es and Intuitive Judgments About Probability.

8. RANDOM VARAIBLES.

What is a Random Variable? Discrete Random Variables. Expectations for Random Va riables. Binomial Random Variables. Continuous Random Variables. Normal Random V ariables. 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 Pro portions. What to Expect of Sample Means. What to Expect in Other Situations: Ce ntral Limit Theorem. Sampling Distribution for Any Statistic. Standardized Stati stics. Student's t-Distribution: Replacing ó 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 percent Confidence. General Theory of Confi dence Intervals for a Proportion. Choosing a Sample Size For a Survey. Using Con fidence 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 I mportance versus Statistical Significance. What Can Go Wrong: The Two Types of E rrors.

12. MORE ABOUT CONFIDENCE INTERVALS.

Examples of Different Estimation Situations. Standard Errors. Approximate 95 per cent Confidence Intervals. General Confidence Intervals for One Mean or Paired D ata. General Confidence Intervals for the Difference Between Two Means (Independ ent Samples). The Difference Between Two Proportions (Independent Samples). Unde rstanding 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). Tes ting 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 R egression. Inference About the Linear Regression Relationship. Predicting the Va lue y for an Individual. Estimating the Mean y at a Specified x. Checking for Co nditions 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 Hypothes es 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. 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.

Summary

Emphasizing the conceptual development of statistical ideas, MIND ON STATISTICS actively engages students and explains topics in the context of excellent examples and case studies. This text balances the spirit of statistical literacy with statistical methodology taught in the introductory statistics course. Jessica Utts and Robert Heckard built the book on two learning premises: (1) New material is much easier to learn and remember if it is related to something interesting or previously known; (2) New material is easier to learn if you actively ask questions and answer them for yourself. More than any other text available, MIND ON STATISTICS motivates students to develop their statistical intuition by focusing on analyzing data and interpreting results as opposed to focusing on mathematical formulation. The new edition of this exciting text, enhanced with new material and features, appeals to a wide array of students and instructors alike.

Author Bio

**Utts, Jessica M. : University of California, Davis **

Jessica M. Utts is interested in applying statistics to issues of public interest and in educating students and others to be critical consumers of statistical information. Her research has focused on applications ranging from parapsychology to the impacts of transportation on air quality. In the area of statistics education, Professor Utts is the author of SEEING THROUGH STATISTICS (2nd Edition, 1999, Duxbury Press). She is also the Editor-In-Chief for CyberStats, a Web-based statistics course currently being used in classrooms across the United States. A recipient of two distinguished teaching awards, she frequently presents lectures and workshops on innovative methods for teaching statistics. She was a member of the College Board's Advanced Placement Statistics Development Committee from 1996-2002, serving as Chair from 1999-2002. Professor Utts has appeared on numerous television programs, including ABC's 20/20, Nightline, Larry King Live and CNN Morning News, discussing topics ranging from parapsychology to luck and lotteries. She has also served on numerous panels and advisory boards in government and industry. She is a Fellow of the American Statistical Association, the Institute of Mathematical Statistics, and the American Association for the Advancement of Science.

**Heckard, Robert F. : Pennsylvania State University **

Robert F. Heckard is a senior lecturer in statistics at the Pennsylvania State University, where he has taught for over 30 years. He has taught introductory and intermediate applied statistics to more than 15,000 college students. Heckard has been awarded several grants to develop multimedia and web-based instructional materials for teaching statistical concepts, and is a co-author of CyberStats, a Web-based introductory course. As a consultant, he is active in the statistical analysis and design of highway safety research and has frequently been a consultant in cancer treatment clinical trials.

Table of Contents

1. STATISTICS SUCCESS STORIES AND CAUTIONARY TALES.

What is Statistics? Seven Statistical Stories with Morals. The Common Elements i n the Seven Stories.

2. TURNING DATA INTO INFORMATION.

Raw Data. Types of Data. Summarizing One or Two Categorical Variables. Finding I nformation in Quantitative Data. Pictures for Quantitative Data. Numerical Summa ries of Quantitative Variables. Bell-Shaped Distributions of Numbers.

3. GATHERING USEFUL INFORMATION.

Description or Decision? Using Data Wisely. Speaking the Language of Research St udies. Designing a Good Experiment. Designing a Good Observational Study. Diffic ulties 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 Regres sion 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, Odd s Ratio, and Increased Risk. Misleading Statistics About Risk. The Effect of a T hird Variable and Simpson's Paradox. Assessing the Statistical Significance of a 2 x 2 Table.

7. PROBABILITY.

Random Circumstances. Interpretations of Probability. Probability Definitions an d Relationships. Basic Rules for Finding Probabilities. Strategies for Finding C omplicated Probabilities. Using Simulation to Estimate Probabilities. Coincidenc es and Intuitive Judgments About Probability.

8. RANDOM VARAIBLES.

What is a Random Variable? Discrete Random Variables. Expectations for Random Va riables. Binomial Random Variables. Continuous Random Variables. Normal Random V ariables. 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 Pro portions. What to Expect of Sample Means. What to Expect in Other Situations: Ce ntral Limit Theorem. Sampling Distribution for Any Statistic. Standardized Stati stics. Student's t-Distribution: Replacing ó 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 percent Confidence. General Theory of Confi dence Intervals for a Proportion. Choosing a Sample Size For a Survey. Using Con fidence 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 I mportance versus Statistical Significance. What Can Go Wrong: The Two Types of E rrors.

12. MORE ABOUT CONFIDENCE INTERVALS.

Examples of Different Estimation Situations. Standard Errors. Approximate 95 per cent Confidence Intervals. General Confidence Intervals for One Mean or Paired D ata. General Confidence Intervals for the Difference Between Two Means (Independ ent Samples). The Difference Between Two Proportions (Independent Samples). Unde rstanding 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). Tes ting 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 R egression. Inference About the Linear Regression Relationship. Predicting the Va lue y for an Individual. Estimating the Mean y at a Specified x. Checking for Co nditions 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 Hypothes es 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. 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.

Publisher Info

Publisher: Brooks/Cole Publishing Co.

Published: 2004

International: No

Published: 2004

International: No

**Utts, Jessica M. : University of California, Davis **

Jessica M. Utts is interested in applying statistics to issues of public interest and in educating students and others to be critical consumers of statistical information. Her research has focused on applications ranging from parapsychology to the impacts of transportation on air quality. In the area of statistics education, Professor Utts is the author of SEEING THROUGH STATISTICS (2nd Edition, 1999, Duxbury Press). She is also the Editor-In-Chief for CyberStats, a Web-based statistics course currently being used in classrooms across the United States. A recipient of two distinguished teaching awards, she frequently presents lectures and workshops on innovative methods for teaching statistics. She was a member of the College Board's Advanced Placement Statistics Development Committee from 1996-2002, serving as Chair from 1999-2002. Professor Utts has appeared on numerous television programs, including ABC's 20/20, Nightline, Larry King Live and CNN Morning News, discussing topics ranging from parapsychology to luck and lotteries. She has also served on numerous panels and advisory boards in government and industry. She is a Fellow of the American Statistical Association, the Institute of Mathematical Statistics, and the American Association for the Advancement of Science.

**Heckard, Robert F. : Pennsylvania State University **

Robert F. Heckard is a senior lecturer in statistics at the Pennsylvania State University, where he has taught for over 30 years. He has taught introductory and intermediate applied statistics to more than 15,000 college students. Heckard has been awarded several grants to develop multimedia and web-based instructional materials for teaching statistical concepts, and is a co-author of CyberStats, a Web-based introductory course. As a consultant, he is active in the statistical analysis and design of highway safety research and has frequently been a consultant in cancer treatment clinical trials.

What is Statistics? Seven Statistical Stories with Morals. The Common Elements i n the Seven Stories.

2. TURNING DATA INTO INFORMATION.

Raw Data. Types of Data. Summarizing One or Two Categorical Variables. Finding I nformation in Quantitative Data. Pictures for Quantitative Data. Numerical Summa ries of Quantitative Variables. Bell-Shaped Distributions of Numbers.

3. GATHERING USEFUL INFORMATION.

Description or Decision? Using Data Wisely. Speaking the Language of Research St udies. Designing a Good Experiment. Designing a Good Observational Study. Diffic ulties 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 Regres sion 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, Odd s Ratio, and Increased Risk. Misleading Statistics About Risk. The Effect of a T hird Variable and Simpson's Paradox. Assessing the Statistical Significance of a 2 x 2 Table.

7. PROBABILITY.

Random Circumstances. Interpretations of Probability. Probability Definitions an d Relationships. Basic Rules for Finding Probabilities. Strategies for Finding C omplicated Probabilities. Using Simulation to Estimate Probabilities. Coincidenc es and Intuitive Judgments About Probability.

8. RANDOM VARAIBLES.

What is a Random Variable? Discrete Random Variables. Expectations for Random Va riables. Binomial Random Variables. Continuous Random Variables. Normal Random V ariables. 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 Pro portions. What to Expect of Sample Means. What to Expect in Other Situations: Ce ntral Limit Theorem. Sampling Distribution for Any Statistic. Standardized Stati stics. Student's t-Distribution: Replacing ó 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 percent Confidence. General Theory of Confi dence Intervals for a Proportion. Choosing a Sample Size For a Survey. Using Con fidence 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 I mportance versus Statistical Significance. What Can Go Wrong: The Two Types of E rrors.

12. MORE ABOUT CONFIDENCE INTERVALS.

Examples of Different Estimation Situations. Standard Errors. Approximate 95 per cent Confidence Intervals. General Confidence Intervals for One Mean or Paired D ata. General Confidence Intervals for the Difference Between Two Means (Independ ent Samples). The Difference Between Two Proportions (Independent Samples). Unde rstanding 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). Tes ting 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 R egression. Inference About the Linear Regression Relationship. Predicting the Va lue y for an Individual. Estimating the Mean y at a Specified x. Checking for Co nditions 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 Hypothes es 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. 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.