Understanding and Using Statistics for Criminology and Criminal Justice

Understanding and Using Statistics for Criminology and Criminal Justice shows students how to critically examine the use and interpretation of statistics, covering not only the basics but also the essential probabilistic statistics that students will need in their future careers. Taking a conceptual approach, this unique text introduces students to the mindset of statistical thinking. It presents formulas in a step-by-step manner; explains the techniques using detailed, real-world examples; and encourages students to become insightful consumers of research.

FEATURES

* Assumes minimal knowledge of math and is accessible to students at all levels

* Incorporates examples from real journals, showing how statistics are used in practice

* Explains the purpose of hypothesis testing more clearly than any other text, clarifying the concept of probability and its relationship to statistics

* Call-out boxes provide more in-depth explanations of concepts

Jonathon A. Cooper is Assistant Professor of Criminology and Criminal Justice at Indiana University of Pennsylvania.

Peter A. Collins is Assistant Professor of Criminal Justice at Seattle University.

Anthony Walsh is Professor of Criminal Justice at Boise State University.

Preface
PART 1. THE BUILDING BLOCKS OF PROBABILISTIC STATISTICS
Chapter 1. Introduction to Statistical Analysis
Learning Objectives
Why Study Statistics?
Thinking Statistically
Descriptive and Inferential Statistics
Box 1-1. Galton's Quincux
Statistics and Error
Box 1-2. How do we know the drop in crime really happened?
Operationalization
--Validity and Reliability
Variables
--Dependent and Independent Variables
--Nominal Level
--Ordinal Level
--Interval Level
--Ratio Level
The Role of Statistics in Science
Box 1-3. The inductive process
Chapter 2. Presenting Data
Learning Objectives
Introduction
Standardizing Data
--Counts
Box 2-1. Coding data
Box 2-2. When to use N and n
-- Percentages
--Rates
Box 2-3. The difference between a rate and a ratio
Box 2-4. A cautionary note
Visualizing Data
--Bar Charts
--Pie Charts
--Line Charts
Frequency Distributions
Box 2-5. The difference between a bar chart and a histogram
Chapter 3. Central Tendency and Dispersion
Learning Objectives
Introduction
Measures of Central Tendency
--Mode
--Median
--The Mean
--Choosing a Measure of Central Tendency
--A Research Example
Measures of Dispersion
--Range
--The Sum of Squares, Variance, and the Standard Deviation
Box 3-1. N or n?
Computational Formula for s
More on Variability and Variance
Box 3-2. The coefficient of variation and the index of qualitative variation
Journal Table 3-1. Descriptive Statistics
Chapter 4. Probability and the Normal Curve
Learning Objectives
Probability
--The Multiplication Rule
--The Addition Rule
Box 4-1. When to multiply or add probabilities?
--A Research Example
Theoretical Probability Distributions
Box 4-2. What to do with 0!
Box 4-3. Do you have a "fair coin" or not?
--The Normal Curve
--The Standard Normal Curve
Z Scores
Practical Application: The Normal Curve and z Scores
Chapter 5. The Sampling Distribution and Estimation Procedures
Learning Objectives
Sampling
--Simple Random Sampling
--Stratified Random Sampling
The Sampling Distribution
Box 5-1. The central limit theorem
--The Standard Error of the Sampling Distribution
Box 5-2. Types of estimates
Confidence Intervals and Alpha Levels
--Calculating Confidence Intervals
--Confidence and Precision
--Sampling and Confidence Intervals
Estimating Sample Size
Practice Application: The Sampling Distribution and Estimation
Chapter 6. Hypothesis Testing: Interval/Ratio Data
Learning Objectives
Introduction
The Logic of Hypothesis Testing
Errors in Hypothesis Testing
One Sample Z Test
The t Test
--Directional Hypotheses: One- and Two-tailed Tests
--Computing t
--The Effects of Increasing Sample Size
--Placing Confidence Intervals around t
--T-test for Correlated (Dependent) Means
--Calculating t with Unequal Variances
Statistical vs. Substantive Significance, and Strength of Association
Large Sample t Test: A Computer Example
Journal Table 6-1. Hypothesis testing
Practice Application: t Test
PART 2. HYPOTHESIS TESTING WITH PROBABILISTIC STATISTICS
Chapter 7. Analysis of Variance
Learning Objectives
Introduction
Assumptions of Analysis of Variance
The Basic Logic of ANOVA
The Idea of Variance Revisited
Box 7-1. The grand mean
ANOVA and the F Distribution
Calculating ANOVA
Box 7-2. Calculating SSwithin
Box 7-3. Reading the F table
Box 7-4. Eta squared
--Multiple Comparisons: The Scheffé Test
Box 7-5. The advantage of ANOVA over multiple tests
Two-Way Analysis of Variance
--Understanding Interaction
--A Research Example of a Significant Interaction Effect
Journal Table 7-1. ANOVA
Practice Application: ANOVA
Chapter 8. Hypothesis Testing with Categorical Data: Chi square
Learning Objectives
Introduction
Table Construction
--Putting Percentages in Tables
Assumptions of the Use of Chi square
Box 8-1. Yate's correction for continuity
The Chi square Distribution
Chi square with a 3 x 2 Table
Box 8-2. The relationship between z, t, F, and chi square
Chi square-based Measures of Association
Box 8-3. More on phi
--Sample Size, Chi square, and phi
--Other Measures of Association for Chi square: Contingency Coefficient; Cramer's V
A Computer Example of Chi square
Journal Table 8-1. Cross-tabulations and chi square
Practice Application: Chi square
Chapter 9. Non-parametric Measures of Association
Learning Objectives
Introduction
Establishing Association
--Does an Association Exist?
--What is the Strength of the Association?
--What is the Direction of the Association?
Proportional Reduction in Error
The Concept of Paired Cases
Box 9-1. Different types of pairs for any data set
--A Computer Example
--Gamma
--Lambda
--Somer's d
Tau b
The Odds Ratio and Yule's Q
Box 9-2. The odds and probability
Spearman's Rank Order Correlation
Which Test of Association Should We Use?
Journal Table 9-1. Non-parametric measures of association
Practice Application: Nonparametric Measures of Association
Chapter 10. Elaboration of Tabular Data and the Nature of Causation
Learning Objectives
Introduction
Criteria for Causality
--Association
--Temporal Order
--Spuriousness
Box 10-1. Variables versus constants
Necessary and Sufficient Causes
Multivariate Contingency Analysis
Explanation and Interpretation
Illustrating Elaboration Outcomes
Box 10-2. Replication and specification
--Controlling for One Variable
Box 10-3. Simpson's Paradox
--Further Elaboration: Two Control Variables
--Partial Gamma
Box 10-4. When not to compute partial gamma
Problems with Tabular Elaboration
Practice Application: Bivariate Elaboration
Chapter 11. Bivariate Correlation and Regression
Learning Objectives
Introduction
Linear Relationships
Box 11-1. The scatterplot
--Linearity in Social Science Data
The Pearson Correlation Coefficient (r)
Box 11-2. Calculating covariance
--r squared as a Proportionate Reduction in Error
--Significance Testing for Pearson's r
Box 11-3. Standard error of r
The Interrelationship of b, r, and ?
Box 11-4. Summarizing the properties of r, b, and ?
Standard Error of the Estimate
A Computer Example of Bivariate Correlation and Regression
Journal Table 11-1. Bivariate correlation
Practice Application: Bivariate Correlation and Regression
Chapter 12. Multivariate Regression and Regression
Learning Objectives
Introduction
Partial Correlation
Computer Example
Second-order Partials: Controlling for Two Independent Variables
The Multiple Correlation Coefficient
Multiple Regression
A Computer Example of Multiple Regression
--Interpreting the Printout
Box 12-1. The adjusted R squared
Box 12-2. The y-intercept
--A Visual Representation of Multiple Regression
Regression and Interaction
Journal Table 12-1. OLS regression
Practice Application: Partial Correlation
Appendix A: Introduction to Regression with Categorical and Limited Dependent Variables
The Generalized Linear Model
Binary Outcomes: The Logit
Box A-1. About the pseudo-R squared
Nominal Outcomes: The Multinomial Model
Box A-2. What about the reference category?
Ordinal Outcomes: The Ordered Logit
Count Outcomes: Heavily Skewed Distributions
Appendix B: A Brief Primer on Statistical Software
SPSS
SAS
Stata
R
Conclusions
Distribution Tables
Distribution of t
Distribution of F
Distribution of Chi square
Glossary
Formula Index
Subject Index