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