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Data Matters. Conceptual Statistics for a Random World

  • ID: 2241483
  • Book
  • September 2008
  • Region: Global
  • 626 Pages
  • John Wiley and Sons Ltd
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With an analytical approach that emphasizes concepts and comprehension, Data Matters provides a crucial introduction to statistics by preparing readers to think critically about the most common statistics found in the natural and social sciences. Real data and events taken from the daily news media bring relevance to the subject and turn the general reader into a critical and capable consumer of everyday statistics. With its pleasant, conversational style, Data Matters engages and interests readers while it covers the basics and lays a foundation for further study in statistics.
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Foreword by George Cobb vii


To the Instructor ix

To the Student xiii

Acknowledgments xiv

Introduction: Why Data Matters 1

Part I Statistics in the News 7

Basic Concepts of Statistical Thinking Presented

in the Context of Categorical Data

Chapter 1 Proportions in Samples, Proportions in Populations 8

1.1 The Most Popular News Statistics 9

Percentage, Proportions, Raw Counts, Pie Charts, Bar Charts

1.2 How Many People Are There? 36

U.S. and World Populations, Population Growth,

Proportional Changes, The Unemployment Rate, X–Y Plots

1.3 Things Vary, and Small Samples Vary the Most 54

The Law of Large Numbers

Chapter 2 The Pattern in Random Sample Proportions 73

2.1 Taking a Good Sample of a Population 74

Representative and Biased Samples, Random Sampling,

Self–Selected Samples

2.2 How Samples Vary 94

Histograms, Bell Curves

2.3 How Widely Samples Vary 111

The Standard Error of a Proportion, The Normal Distribution

Chapter 3 Making Inferences 132

3.1 Forecasting the Future 133

Prediction Intervals for Sample Proportions

3.2 What a Sample Reveals About a Population 150

Confidence Intervals for Proportions in Populations

3.3 The Story of Statistical Inference 170

Null Hypothesis, P–Value, Alpha, Significance

Chapter 4 Testing Locations and Differences of Proportions 194

4.1 Testing Where a Proportion Is 195

The Z–Test

4.2 How to Look for Differences in Chances 213

Cross–Tabulations, Correlation, The Null Hypothesis

of the Chi–Square Test

4.3 Checking for No Correlation with the Chi–Square Test 234

Chi–Square Distribution, Degrees of Freedom,

Correlation Is Not Causation

Chapter 5 Averages and Other Number Line Statistics in the News 257

5.1 Incomes and Other Quantities 258

Medians, Number Line Observations,Means

5.2 Which Tells the Truth The Mean, the Median . . . or 281

the Weighted Mean?

Standard Deviation, Spread,Weighted Means

5.3 Inflation and the Consumer Price Index 302

Adjusting for Inflation

Part II Statistics in Science 317

Descriptive and Inferential Statistics for Continuous Data

Chapter 6 What Sample Data Distribution Reveals About the Population 318

6.1 Exploratory Data Analysis 319

Histograms, Stem–and–Leaf Plots, Box Plots

6.2 Describing Number Line Variation 338

Standard Deviation of Samples,Variance

6.3 How to See the Future 360

Prediction Intervals for Number Line Observations

and Sample Means, Standard Error of Means, Confidence

Intervals for Population Means, Central Limit Theorem

Chapter 7 Testing Treatments 378

7.1 A Cautionary Tale 380

William Gosset s Troubles with the Z–Test and the T–Distribution,

The T–Test

7.2 How to Test Whether a Treatment Works 399

The Logic of Experiments, Correlational Studies

7.3 Variances Between and Within 413

Estimating the Population Variance from Variation

Within Groups and from Variation Between Group Means

Chapter 8 Analysis of Variance 431

8.1 Fisher s Analysis of Variance 432

Calculating Fisher s F–Value

8.2 What If the Data Are Not Normally Distributed? 451

The Effect of Nonconstant Variances and Non–normality on

ANOVA, Nonparametric Tests

8.3 American Counties 471

Correlation, Scatter Plots

Chapter 9 Best Lines 495

9.1 Lines 496

How to Calculate the Equation of a Line

9.2 Finding Best–Fitting Lines 512

The Least Squares Line

9.3 An Excellent Line 522

Calculating the Slope of the Regression Equation,

Standard Error and Confidence Interval for the Regression Equation

Chapter 10 Tests of Regression 544

10.1 How to Test the Regression Models 545

R2, Pearson s r, A T–Test for the Regression Slope

10.2 What If the Assumptions of the Regression Test Are Not Valid? 568

Spearman s Rho, Effect of Nonconstant Variances on

Correlation Tests, Effect of Non–normality on

Correlation Tests, Nonlinear Regression

Postscript: A Statistical Life 592

References 599

Index 609

Some Useful Equations 624

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Nicholas Maxwell
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