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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.
* 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.
Table of Contents
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