Basic Statistics in Criminology and Criminal Justice

Preface
Acknowledgments
Contents
About the Authors
Chapter 1: Introduction: Statistics as a Research Tool
	The Purpose of Statistics Is to Clarify
	Statistics Are Used to Solve Problems
	Basic Principles Apply Across Statistical Techniques
	The Uses of Statistics
		Descriptive Statistics
		Inferential Statistics
	Chapter Summary
	Key Terms
	References
Chapter 2: Measurement: The Basic Building Block of Research
	Science and Measurement: Classification as a First Step in Research
	Levels of Measurement
		Nominal Scales
		Ordinal Scales
		Interval and Ratio Scales
	Relating Interval, Ordinal, and Nominal Scales: The Importance of Collecting Data at the Highest Level Possible
	What Is a Good Measure?
	Chapter Summary
	Key Terms
	Exercises
	Computer Exercises
		SPSS
		Stata
		R
		Problems
	References
Chapter 3: Representing and Displaying Data
	Frequency Distributions, Bar Charts, and Histograms
		The Bar Chart
		The Grouped Bar Chart
		Histograms for Continuous and Discrete Data
	Box plots for Interval and Ratio Data
	Time Series Data
	Chapter Summary
	Key Terms
	Symbols and Formulas
	Exercises
	Computer Exercises
		SPSS
			Frequency Distributions and Histograms
			Bar Charts
			Line Graphs
		Stata
			Frequency Distributions and Histograms
			Bar Charts
			Line Graphs
		R
			Frequency Distributions and Histograms
			Bar Charts
			Line Graphs
		Problems
	References
Chapter 4: Describing the Typical Case: Measures of Central Tendency
	The Mode: Central Tendency in Nominal Scales
	The Median: Taking into Account Position
	The Mean: Adding Value to Position
		Comparing Results Gained Using the Mean and Median
		Other Characteristics of the Mean
		Using the Mean for Non-interval/Ratio Scales
	Statistics in Practice: Comparing the Median and the Mean
	Chapter Summary
	Key Terms
	Symbols and Formulas
	Exercises
	Computer Exercises
		SPSS
			Recoding Variables in SPSS
			Identifying Outliers in SPSS
		Stata
			Recoding Variables in Stata
			Identifying Outliers in Stata
		R
			Recoding Variables and Missing Values in R
			Identifying Outliers in R
		Problems
	References
Chapter 5: How Typical Is the Typical Case? Measuring Dispersion
	Measures of Dispersion for Nominal- and Ordinal-Level Data
		The Proportion in the Modal Category
		The Percentage in the Modal Category
		The Variation Ratio
		Index of Qualitative Variation
	Measuring Dispersion in Interval/Ratio Scales: The Range, Interquartile Range, Variance, and Standard Deviation
		The Variance
		The Standard Deviation
		Characteristics of the Variance and Standard Deviation
		The Coefficient of Relative Variation
		A Note on the Mean Deviation
	Chapter Summary
	Key Terms
	Symbols and Formulas
	Exercises
	Computer Exercises
		SPSS
		Stata
		R
		Problems
	Reference
Chapter 6: The Logic of Statistical Inference: Making Statements About Populations from Sample Statistics
	The Dilemma: Making Statements About Populations from Sample Statistics
	The Research Hypothesis
	The Null Hypothesis
	Risks of Error in Hypothesis Testing
	Risks of Error and Statistical Levels of Significance
	Departing from Conventional Significance Criteria
	Chapter Summary
	Key Terms
	Symbols
	Exercises
	References
Chapter 7: Defining the Observed Significance Level of a Test: A Simple Example Using the Binomial Distribution
	The Fair Coin Toss
		Sampling Distributions and Probability Distributions
		The Multiplication Rule
	Different Ways of Getting Similar Results
	Solving More Complex Problems
	The Binomial Distribution
	Using the Binomial Distribution to Estimate the Observed Significance Level of a Test
	Chapter Summary
	Key Terms
	Symbols and Formulas
	Exercises
	Computer Exercises
		SPSS
		Stata
		R
		Problems
Chapter 8: Steps in a Statistical Test: Using the Binomial Distribution to Make Decisions About Hypotheses
	The Problem: The Impact of Problem-Oriented Policing on Disorderly Activity at Violent-Crime Hot Spots
	Assumptions: Laying the Foundations for Statistical Inference
		Level of Measurement
		Shape of the Population Distribution
		Sampling Method
		The Hypotheses
			Hypotheses
		Stating All of the Assumptions
			Assumptions
			Hypotheses
	Selecting a Sampling Distribution
	Significance Level and Rejection Region
		Choosing a One-Tailed or a Two-Tailed Rejection Region
	The Test Statistic
	Making a Decision
	Chapter Summary
	Key Terms
	Exercises
	Computer Exercises
		SPSS
		Stata
		R
		Problems
	References
Chapter 9: Chi-Square: A Test Commonly Used for Nominal-Level Measures
	Testing Hypotheses Concerning the Roll of a Die
		The Chi-Square Distribution
		Calculating the Chi-Square Statistic
		Linking the Chi-Square Statistic to Probabilities: The Chi-Square Table
		A Substantive Example: The Relationship Between Assault Victims and Offenders
			The Sampling Distribution
			Significance Level and Rejection Region
			The Test Statistic
			The Decision
	Relating Two Nominal-Scale Measures in a Chi-Square Test
		A Substantive Example: Type of Sanction and Recidivism Among Convicted White-Collar Criminals
			The Sampling Distribution
			Significance Level and Rejection Region
			The Test Statistic
			The Decision
	Extending the Chi-Square Test to Multicategory Variables: The Example of Cell Allocations in Prison
		The Sampling Distribution
		Significance Level and Rejection Region
		The Test Statistic
		The Decision
	Extending the Chi-Square Test to a Relationship Between Two Ordinal Variables: Identification with Fathers and Delinquent Acts
		The Sampling Distribution
		Significance Level and Rejection Region
		The Test Statistic
		The Decision
	The Use of Chi-Square When Samples Are Small: A Final Note
	Chapter Summary
	Key Terms
	Symbols and Formulas
	Exercises
	Computer Exercises
		SPSS
		Stata
		R
		Problems
	References
Chapter 10: The Normal Distribution and Its Application to Tests of Statistical Significance
	The Normal Frequency Distribution (Normal Curve)
		Characteristics of the Normal Frequency Distribution
		z-Scores
		Developing Tests of Statistical Significance Based on the Standard Normal Distribution: The Single-Sample z-Test for Known Pop...
			The Sampling Distribution
			Significance Level and Rejection Region
			The Test Statistic
			The Decision
	Applying Normal Sampling Distributions to Non-normal Populations
	Comparing a Sample to an Unknown Population: The Single-Sample z-Test for Proportions
		Computing the Mean and Standard Deviation for the Sampling Distribution of a Proportion
		Testing Hypotheses with the Normal Distribution: The Case of a New Prison Program
			The Sampling Distribution
			Significance Level and Rejection Region
			The Test Statistic
			The Decision
	Limitations of the z-Test on a Proportion
	Comparing a Sample to an Unknown Population: The Single-Sample t-Test for Means
		Testing Hypotheses with the t Distribution
			The Sampling Distribution
			Significance Level and Rejection Region
			The Test Statistic
			The Decision
	Confidence Intervals
		Constructing Confidence Intervals
		Confidence Intervals for Sample Means
		Confidence Intervals for Sample Proportions
	Chapter Summary
	Key Terms
	Symbols and Formulas
	Exercises
	References
Chapter 11: Comparing Means and Proportions in Two Samples to Test Hypotheses About Population Parameters
	Comparing Means
		The Case of Anxiety Among Police Officers and Firefighters
		The Sampling Distribution
			Significance Level and Rejection Region
			The Test Statistic
			The Decision
		Constructing Confidence Intervals for Differences of Means
		Bail in Los Angeles County: Another Example of the Two-Sample t-Test for Hypotheses About Population Mean Differences
			The Sampling Distribution
			Significance Level and Rejection Region
			The Test Statistic
			The Decision
			Sensitivity Analysis
	Comparing Proportions: The Two-Sample z-Test for Differences Between Population Proportions
		The Case of Drug Testing and Pretrial Misconduct
			The Sampling Distribution
			Significance Level and Rejection Region
			The Decision
	The t-Test for Dependent (Paired) Samples
		The Effect of Police Presence on High-Crime Street Segments
			The Sampling Distribution
			Significance Level and Rejection Region
			The Test Statistic
			The Decision
	Nonparametric Alternative to the t-Test
		Mann-Whitney U: Nonparametric Test for Two Independent Samples
		Bail in Los Angeles County Redux: The Mann-Whitney U
		Wilcoxon Signed-Rank Test for Dependent Samples
		The Effect of Police Presence Near High-Crime Street Segments Redux: The Wilcoxon Signed-Rank Test
	Effect Size Measures for Comparing Two Means: Cohen´s d
	A Note on Using the t-Test for Ordinal Scales with a Limited Number of Categories
	Chapter Summary
	Key Terms
	Symbols and Formulas
	Exercises
	Computer Exercises
		SPSS
			Independent Sample t-Test
			Dependent Sample t-Test
		Stata
			Independent Sample t-Test
			Dependent Sample t-Test
		R
			Independent Sample t-Test
			Dependent Sample t-Test
		Problems
	References
Chapter 12: Comparing Means Among More Than Two Samples to Test Hypotheses about Populations: Analysis of Variance
	Analysis of Variance
		Computing the Variance Between and Within Groups
		A Substantive Example: Age and White-Collar Crimes
			The Sampling Distribution
			Significance Level and Rejection Region
			The Test Statistic
			The Decision
		Another ANOVA Example: Race and Bail Amounts Among Felony Drug Defendants
			The Sampling Distribution
			Significance Level and Rejection Region
			The Test Statistic
			The Decision
	Defining the Strength of the Relationship Observed
	Making Pairwise Comparisons Between the Groups Studied
		Tukey´s Honestly Significant Difference (HSD) Test
		Bonferroni Post Hoc Pairwise t-Tests
	A Nonparametric Alternative: The Kruskal-Wallis Test
		The Sampling Distribution
		Significance Level and Rejection Region
		The Test Statistic
		The Decision
	Chapter Summary
	Key Terms
	Symbols and Formulas
	Exercises
	Computer Exercises
		SPSS
			ANOVA
			Tukey´s HSD
			Kruskal-Wallis Test
		Stata
			ANOVA
			Tukey´s HSD
			Kruskal-Wallis Test
		R
			ANOVA
			Tukey´s HSD
			Kruskal-Wallis Test
		Problems
	References
Chapter 13: Measures of Association for Nominal and Ordinal Variables
	Distinguishing Statistical Significance and Strength of Relationship: The Example of the Chi-Square Statistic
	Measures of Association for Nominal Variables
		Measures of Association Based on the Chi-Square Statistic
			The Phi Coefficient
			The Risk Ratio and Odds Ratio
			Cramer´s V
		Proportional Reduction in Error Measures: Tau and Lambda
		Statistical Significance of Measures of Association for Nominal Variables
			The Sampling Distribution
			Significance Level and Rejection Region
			The Test Statistic
			The Decision
	Measures of Association for Ordinal-Level Variables
		Gamma
		Kendall´s τb and τc
		Somers´ d
		A Substantive Example: Affectional Identification with Father and Level of Delinquency
		Note on the Use of Measures of Association for Ordinal Variables
		Statistical Significance of Measures of Association for Ordinal Variables
			The Sampling Distribution
			Significance Level and Rejection Region
			The Test Statistic
			The Decision
	Choosing the Best Measure of Association for Nominal- and Ordinal-Level Variables
	Chapter Summary
	Key Terms
	Symbols and Formulas
	Exercises
	Computer Exercises
		SPSS
		Stata
		R
		Problems
	References
Chapter 14: Measuring Association for Scaled Data: Pearson´s Correlation Coefficient
	Measuring Association Between Two Interval- or Ratio-Level Variables
	Pearson´s Correlation Coefficient
		The Calculation
		A Substantive Example: Crime and Unemployment in California
		Nonlinear Relationships and Pearson´s r
		Beware of Outliers
	Spearman´s Correlation Coefficient
	Testing the Statistical Significance of Pearson´s r
		Statistical Significance of r: The Case of Age and Number of Arrests
			The Sampling Distribution
			Significance Level and Rejection Region
			The Test Statistic
			The Decision
		Statistical Significance of r: Unemployment and Crime in California
			The Sampling Distribution
			Significance Level and Rejection Region
			The Test Statistic
			The Decision
	Testing the Statistical Significance of Spearman´s r
		The Sampling Distribution
		Significance Level and Rejection Region
		The Test Statistic
		The Decision
	Using Pearson´s r When One or Both Variables are Dichotomous or Ordinal
		The Correlation Coefficient for Two Dichotomous Variables
		The Correlation Coefficient for One Dichotomous Variable and One Interval- or Ratio-level Variable
	Confidence Intervals for the Correlation Coefficient
	Chapter Summary
	Key Terms
	Symbols and Formulas
	Exercises
	Computer Exercises
		SPSS
			Correlation Coefficients
			Scatter plots
		Stata
			Correlation Coefficients
			Scatter plots
		R
			Correlation Coefficients
			Scatter plots
		Problems
	References
Chapter 15: An Introduction to Bivariate Regression
	Estimating the Influence of One Variable on Another: The Regression Coefficient
		Calculating the Regression Coefficient
		A Substantive Example: Unemployment and Burglary in California
	Prediction in Regression: Building the Regression Line
		The Y-Intercept
		The Regression Line
	Predictions Beyond the Distribution Observed in a Sample
	Predicting Burglary Rates from Unemployment Rates in California
		Choosing the Best Line of Prediction Based on Regression Error
	Evaluating the Regression Model
		Percent of Variance Explained
		Percent of Variance Explained: Unemployment Rates and Burglary Rates in California
		Statistical Significance of the Regression Coefficient: The Case of Age and Number of Arrests
			The Sampling Distribution
			Significance Level and Rejection Region
			The Test Statistic
			The Decision
		Testing the Statistical Significance of the Regression Coefficient for Unemployment Rates and Burglary Rates in California
			The Sampling Distribution
			Significance Level and Rejection Region
			The Test Statistic
			The Decision
	The F-Test for the Overall Regression
		Age and Number of Arrests
		Unemployment Rates and Burglary Rates in California
	Chapter Summary
	Key Terms
	Symbols and Formulas
	Exercises
	Computer Exercises
		SPSS
		Stata
		R
		Problems
	Reference
Appendix 1: Factorials
Appendix 2:
Appendix 3: Areas of the
Appendix 4:
Appendix 5:
Appendix 6: Critical
Appendix 7:
Appendix 8: Fisher
Index