Introduction to Data Analysis for Criminal Justice
Edition: 2
Copyright: 2023
Pages: tbd
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This book is carefully constructed to allow students the chance to understand the research process. The first half of the class introduces students to general concepts and levels the playing field for those that may not have had a college-level statistics course before. Then we move to an analysis of the concepts of central tendency and the central limit theorem.
Once students are comfortable with these basic concepts, we begin discussing hypothesis testing, probability, and various tests using ordinary least squares (OLS) techniques. While not focusing extensively on the formulas for t-test, regression, and ANOVA, special attention is paid toward understanding where and how the means, standard deviations, and the size of the sample influence each of the models.
Students are also introduced to the concept of the mathematical null hypotheses. These are important because they let the student know upfront exactly what the formulas are doing and how the models are correctly interpreted. The book concludes with a discussion and presentation of non-parametric tests like the chi-square test for independence and several measures of association.
Chapter 1 Clearing the Deck
Introduction
Research Methods and Data Analysis: The Conjoined Twins
The Statistical Dragons
Book Organization
The Model: A Visual and Theoretical Approach
Basic Tools
Psychological Requirements From You
Conclusion
Key Terms
Discussion Questions
Chapter 2 In the Beginning
Introduction
Research Design
Quasi-Experimental Models
Sampling and Sample Size
Levels of Measurement
Nominal Level Data
Ordinal Level Data
Interval Level Data
Ratio Level Data
Reliability and Generalizability
Conclusion
Key Terms
Discussion Questions
Chapter 3 Distributions, Distributions, and More Distributions
Introduction
Arranging Data for Analysis
Frequency Distributions
Statistical Graphs Denoting Normality
Histograms
Box Plots
Steam-and-Leaf Plots
Skewed Distributions: Positive and Negative
Positively Skewed Distributions
Negatively Skewed Distributions
The Impact of Skewed Distributions
Data Transformations
Spotting the Skew Made Easy
Making a Decision and Distributional Skew
The Use of Multiple Measures to Assess Normality
Graphs Using a Graphing Calculator
Conclusion
Key Terms
Discussion Questions
Chapter 4 Measures of Central Tendency
Introduction
The Importance of Central Tendency
The Mean
The Median
The Mode
Integrating the Three Measures of Central Tendency
Conclusion
Key Terms
Discussion Questions
Chapter 5 Measures of Dispersion
Introduction
The Importance of Dispersion
Measures of Dispersion
The Range
The Variance
Differences Between the Sample and Population Statistics
Computing the Variance by Hand—An Example
The Standard Deviation
The Intrinsic Meaning and Value of the Standard Deviation
Relevance of Dispersion to Theoretical Distributions
Properties of Standard Deviation Units
Z-Scores and Areas of the Normal Curve
Conclusion
Key Terms
Discussion Questions
Chapter 6 Theoretical Distributions and Statistical Significance Testing
Introduction
The Different Types of Hypotheses
The Null Hypothesis
The Conceptual Null Hypothesis
The Mathematical Null Hypothesis
Types of Tests—One-and Two-Tailed Tests
P-Values, Sig Values, and Alphas
Setting Your Alpha Levels
Significance or P-Values
Rejecting or Failing to Your Null Hypothesis
Types of Error
Conclusion
Key Terms
Discussion Questions
Chapter 7 Simple Tests Between Groups
Introduction
Three Different Types of T-Tests
One-Sample T-Test
The Degrees of Freedom
Running a One-Sample T-Test on a Calculator
The Null Hypothesis and Test Interpretation
Two-Sample Independent T-Test
Variants of the Independent Two-Sample T-Tests
Two-Sample T-Test Using Variables
The Degrees of Freedom
Running an Independent Two-Sample T-Test on Your Calculator
Two-Sample T-Tests Using Groups
The Null Hypothesis and Test Interpretation
Paired or Pre-Post T-Test
Running a T-Test on the Computer
Calculating a Paired T-Test on Calculator
The Degrees of Freedom
The Null Hypothesis and Test Interpretation
Conclusion
Key Terms
Discussion Questions
Chapter 8 Advanced Tests Between Groups
Introduction
The Variety of ANOVA Tests
The One-Way ANOVA
The Null Hypotheses
The ANOVA Table
The Sources of Variation in ANOVA
The Sum of Squares
The Between Group Sum of Squares in ANOVA
The Within Group Sum of Squares in ANOVA
The Total Group Sum of Squares in ANOVA
The Degrees of Freedom
The F Test
Post Hoc Test
Running a One-Way ANOVA on Your Calculator
Differences Between ANOVA Table on the Computer and Your Calculator
Conclusion
Key Terms
Discussion Questions
Chapter 9 Correlation and Simple Functional Regression
Introduction
The Underlying Data Element Principles
History and Null Hypotheses
Exploring Correlation and Pearson’s R
The Formula for Pearson’s R and Its Properties
Cohen’s Effect Size or Pearson’s R
Determining Correlation Strength and Direction Using Scatterplots
Simple Functional Regression
The ANOVA Table in Regression
The Model or Explained Sum of Squares
The Residual or Sum of Squares Error
The Total Sum of Squares
The Value of F and R2 in the Regression ANOVA Table
Computing the Value of R2 Using the ANOVA Table
The Regression Formula
The Computation of the Regression Line
Additional Considerations in Regression
The Standardized Regression Coeffecient
The Assumptions of Regression Analysis
Using Your Calculator to Run a Regression Analysis
Conclusion
Key Terms
Discussion Questions
Chapter 10 Non-Parametric Tests: The Chi-Square Test of Independence
Introduction
History of Chi-Square and the Null Hypothesis
Yates Correction for Small Cell Counts
Running a Chi-Square Model on Your Calculator
Computing a Chi-Square on the Computer
Measures of Association With Chi-Square
The Contingency Coefficient—Equal Number of Rows and Columns
Phi—For 2 × 2 Tables
Cramer’s V—No Limitations and Generalizable Upper and Lower Limits
Comparing Nominal Level Measures of Association to Pearson’s R
Conclusion
Key Terms
Discussion Questions