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chapter one 1

Introduction: Statistics as a Research Tool 1

The Purpose of Statistics Is to Clarify and Not Confuse 3

Statistics Are Used to Solve Problems 4

Basic Principles Apply Across Statistical Techniques 5

The Uses of Statistics 7

chapter two 13

Measurement: The Basic Building Block of Research 13

Science and Measurement: Classification as a First Step in Research 14

Levels of Measurement 15

Relating Interval, Ordinal, and Nominal Scales: The Importance of Collecting Data at the Highest Level Possible 22

What Is a Good Measure? 23

chapter three 33

Representing and Displaying Data 33

What Are Frequency Distributions and Histograms? 34

Extending Histograms to Multiple Groups: Using Bar Charts 40

Using Bar Charts with Nominal or Ordinal Data 47

Pie Charts 48

Time Series Data 49

chapter four 59

Describing the Typical Case: Measures of Central Tendency 59

The Mode: Central Tendency in Nominal Scales 60

The Median: Taking into Account Position 62

The Mean: Adding Value to Position 68

Statistics in Practice: Comparing the Median and the Mean 76

chapter five 86

How Typical Is the Typical Case?: Measuring Dispersion 86

Measures of Dispersion for Nominal-and Ordinal-Level Data 87

Measuring Dispersion in Interval Scales: The Range, Variance, and Standard Deviation 94

chapter six 115

The Logic of Statistical Inference: Making Statements About Populations from Sample Statistics 115

The Dilemma: Making Statements About Populations from Sample Statistics 116

The Research Hypothesis 119

The Null Hypothesis 121

Risks of Error in Hypothesis Testing 123

Risks of Error and Statistical Levels of Significance 125

Departing from Conventional Significance Criteria 127

chapter seven 135

Defining the Observed Significance Level of a Test:A Simple Example Using the Binomial Distribution 135

The Fair Coin Toss 137

DifferentWays of Getting Similar Results 141

Solving More Complex Problems 144

The Binomial Distribution 145

Using the Binomial Distribution to Estimate the Observed Significance Level of a Test 149

chapter eight 159

Steps in a Statistical Test: Using the Binomial Distribution to Make Decisions About Hypotheses 159

The Problem: The Impact of Problem-Oriented Policing on Disorderly Activity at Violent-Crime Hot Spots 160

Assumptions: Laying the Foundations for Statistical Inference 162

Selecting a Sampling Distribution 168

Significance Level and Rejection Region 170

The Test Statistic 175

Making a Decision 175

chapter nine 184

Chi-Square: A Test Commonly Used for Nominal-Level Measures 184

Testing Hypotheses Concerning the Roll of a Die 185

Relating Two Nominal-Scale Measures in a Chi-Square Test 193

Extending the Chi-Square Test to Multicategory Variables: The Example of Cell Allocations in Prison 199

Extending the Chi-Square Test to a Relationship Between Two Ordinal Variables: Identification with Fathers and Delinquent Acts 204

The Use of Chi-Square When Samples Are Small: A Final Note 209

chapter ten 219

The Normal Distribution and Its Application to Tests of Statistical Significance 219

The Normal Frequency Distribution,or Normal Curve 220

Applying Normal Sampling Distributions to Nonnormal Populations 232

Comparing a Sample to an Unknown Population: The Single-Sample z-Test for Proportions 237

Comparing a Sample to an Unknown Population: The Single-Sample t-Test for Means 242

chapter eleven 254

Comparing Means and Proportions in Two Samples 254

Comparing Sample Means 255

Comparing Sample Proportions: The Two-Sample t-Test for Differences of Proportions 267

The t-Test for Dependent Samples 273

A Note on Using the t-Test for Ordinal Scales 278

chapter twelve 290

Comparing Means Among More Than Two Samples: Analysis of Variance 290

Analysis of Variance 291

Defining the Strength of the Relationship Observed 312

Making Pairwise Comparisons Between the Groups Studied 315

A Nonparametric Alternative: The Kruskal-Wallis Test 318

chapter thirteen 333

Measures of Association for Nominal and Ordinal Variables 333

Distinguishing Statistical Significance and Strength of Relationship:The Example of the Chi-Square Statistic 334

Measures of Association for Nominal Variables 337

Measures of Association for Ordinal Variables 349

Choosing the Best Measure of Association for Nominal-and Ordinal-Level Variables 367

chapter fourteen 379

Measuring Association for Interval-Level Data:Pearson's Correlation Coefficient 379

Measuring Association Between Two Interval-Level Variables 380

Pearson's Correlation Coefficient 382

Spearman's Correlation Coefficient 400

Testing the Statistical Significance of Pearson's r 402

Testing the Statistical Significance of Spearman's r 409

chapter fifteen 419

An Introduction to Bivariate Regression 419

Estimating the Influence of One Variable on Another: The Regression Coefficient 420

Prediction in Regression: Building the Regression Line 425

Evaluating the Regression Model 433

The F-Test for the Overall Regression 447

chapter sixteen 459

Multivariate Regression 459

The Importance of Correct Model Specifications 460

Correctly Specifying the Regression Model 472

The Problem of Multicollinearity 482

chapter seventeen 494

Logistic Regression 494

Why Is It Inappropriate to Use OLS Regression for a Dichotomous Dependent Variable? 496

Logistic Regression 501

Interpreting Logistic Regression Coefficients 513

Comparing Logistic Regression Coefficients 523

Evaluating the Logistic Regression Model 529

Statistical Significance in Logistic Regression 533

chapter eighteen 546

Special Topics: Confidence Intervals 546

Confidence Intervals 548

Constructing Confidence Intervals 552

chapter nineteen 568

Special Topics: Statistical Power 568

Statistical Power 570

Parametric versus Nonparametric Tests 579

Estimating Statistical Power: What Size Sample Is Needed for a Statistically Powerful Study? 579

Summing Up: Avoiding Studies Designed for Failure 583

appendix 1 Factorials 590

appendix 2 Critical Values of x2 Distribution 591

appendix 3 Areas of the Standard Normal Distribution 592

appendix 4 Critical Values of Student's tDistribution 593

appendix 5 Critical Values of the F-Statistic 594

appendix 6 Critical Value forP (Pcrit), Tukey's HSD Test 597

appendix 7 Critical Values for Spearman's Rank-Order Correlation Coefficient 598

appendix 8 Fisher r-to-Z* Transformation 599

Glossary 601

Index 608