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Principles & Methods of Statistical Analysis
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Principles & Methods of Statistical Analysis

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February 2017 | 528 pages | SAGE Publications, Inc
This unique intermediate/advanced statistics text uses real research on antisocial behaviors, such as cyberbullying, stereotyping, prejudice, and discrimination, to help readers across the social and behavioral sciences understand the underlying theory behind statistical methods. By presenting examples and principles of statistics within the context of these timely issues, the text shows how the results of analyses can be used to answer research questions. New techniques for data analysis and a wide range of topics are covered, including how to deal with “messy data” and the importance of engaging in exploratory data analysis.

 
Preface
 
About the Authors
 
Prologue
 
PART I • GETTING STARTED
 
Chapter 1: The Big Picture
Models  
The Classical Statistical Model  
Designing Experiments and Analyzing Data  
Summary  
Questions Raised by the Use of the Classical Statistical Model  
Conceptual Exercises  
 
Chapter 2: Examining Our Data: An Introduction to Some of the Techniques of Exploratory Data Analysis
Descriptive Statistics  
Histograms  
Exploratory Data Analysis  
Quantile Plots  
Stem-and-Leaf Displays  
Letter-Value Displays  
Box Plots  
Did My Data Come From a Normal Distribution?  
Why Should We Care About Looking at Our Data?  
Summary  
Conceptual Exercises  
 
PART II • THE BEHAVIOR OF DATA
 
Chapter 3: Properties of Distributions: The Building Blocks of Statistical Inference
The Effects of Adding a Constant or Multiplying by a Constant  
The Standard Score Transformation  
The Effects of Adding or Subtracting Scores From Two Different Distributions  
The Distribution of Sample Means  
The Central Limit Theorem  
Averaging Means and Variances  
Expected Value  
Theorems on Expected Value  
Summary  
Conceptual Exercises  
 
PART III • THE BASICS OF STATISTICAL INFERENCE: DRAWING CONCLUSIONS FROM OUR DATA
 
Chapter 4: Estimating Parameters of Populations From Sample Data
Statistical Inference With the Classical Statistical Model  
Criteria for Selecting Estimators of Population Parameters  
Maximum Likelihood Estimation  
Confidence Intervals  
Beyond Normal Distributions and Estimating Population Means  
Summary  
Conceptual Exercises  
 
Chapter 5: Resistant Estimators of Parameters
A Closer Look at Sampling From Non-Normal Populations  
The Sample Mean and Sample Median Are L-Estimators  
Measuring the Influence of Outliers on Estimates of Location and Spread  
?-Trimmed Means as Resistant and Efficient Estimators of Location  
Winsorizing: Another Way to Create a Resistant Estimator of Location  
Applying These Resistant Estimators to Our Data  
Resistant Estimators of Spread  
Applying These Resistant Estimators to Our Data (Part 2)  
M-Estimators: Another Approach to Finding Resistant Estimators of Location  
Which Estimator of Location Should I Use?  
Resampling Methods for Constructing Confidence Intervals  
A Final Caveat  
Summary  
Conceptual Exercises  
 
Chapter 6: General Principles of Hypothesis Testing
Experimental and Statistical Hypotheses  
Estimating Parameters  
The Criterion for Evaluating Our Statistical Hypotheses  
Creating Our Test Statistic  
Drawing Conclusions About Our Null Hypothesis  
But Suppose H0 Is False?  
Errors in Hypothesis Testing  
Power and Power Functions  
The Use of Power Functions  
p-Values, a, and Alpha (Type I) Errors: What They Do and Do Not Mean  
A Word of Caution About Attempting to Estimate the Power of a Hypothesis Test After the Data Have Been Collected  
Is It Ever Appropriate to Use a One-Tailed Hypothesis Test?  
What Should We Mean When We Say Our Results Are Statistically Significant?  
A Final Word  
Summary  
Conceptual Exercises  
 
PART IV • SPECIFIC TECHNIQUES TO ANSWER SPECIFIC QUESTIONS
 
Chapter 7: The Independent Groups t-Tests for Testing for Differences Between Population Means
Student’s t-test  
Distribution of the Independent Groups t-Statistic when H0 Is True  
Distribution of the Independent Groups t-Statistic When H0 Is False  
Factors That Affect the Power of the Independent Groups t-Test  
The Assumption Behind the Homogeneity of Variance Assumption  
Graphical Methods for Comparing Two Groups  
Suppose the Population Variances Are Not Equal?  
Standardized Group Differences as Estimators of Effect Size  
Robust Hypothesis Testing  
Resistant Estimates of Effect Size  
Summary  
Conceptual Exercises  
 
Chapter 8: Testing Hypotheses When the Dependent Variable Consists of Frequencies of Scores in Various Categories
Classifying Data  
Testing Hypotheses When the Dependent Variable Consists of Only Two Possibilities  
The Binomial Distribution  
Testing Hypotheses About the Parameter p in a Binomial Experiment  
The Normal Distribution Approximation to the Binomial Distribution  
Testing Hypotheses About the Difference Between Two Binomial Parameters (p1 – p2)  
Testing Hypotheses in Which the Dependent Variable Consists of Two or More Categories  
Summary  
Conceptual Exercises  
 
Chapter 9: The Randomization/Permutation Model: An Alternative to the Classical Statistical Model for Testing Hypotheses About Treatment Effects
The Assumptions Underlying the Classical Statistical Model  
The Assumptions Underlying the Randomization Model  
Hypotheses for Both Models  
The Exact Randomization Test for Testing Hypotheses About the Effects of Different Treatments on Behavior  
The Approximate Randomization Test for Testing Hypotheses About the Effects of Different Treatments on Behavior  
Using the Randomization Model to Investigate Possible Effects of Treatments  
Single-Participant Experimental Designs  
Summary  
Conceptual Exercises  
Additional Resources  
 
Chapter 10: Exploring the Relationship Between Two Variables: Correlation
Measuring the Degree of Relationship Between Two Interval-Scale Variables  
Randomization (Permutation) Model for Testing Hypotheses About the Relationship Between Two Variables  
The Bivariate Normal Distribution Model for Testing Hypotheses About Population Correlations  
Creating a Confidence Interval for the Population Correlation Using the Bivariate Normal Distribution Model  
Bootstrap Confidence Intervals for the Population Correlation  
Unbiased Estimators of the Population Correlation  
Robust Estimators of Correlation  
Assessing the Relationship Between Two Nominal Variables  
The Fisher Exact Probability Test for 2 x 2 Contingency Tables With Small Sample Sizes  
Correlation Coefficients for Nominal Data in Contingency Tables  
Summary  
Conceptual Exercises  
 
Chapter 11: Exploring the Relationship Between Two Variables: The Linear Regression Model
Assumptions for the Linear Regression Model  
Estimating Parameters With the Linear Regression Model  
Regression and Prediction  
Variance and Correlation  
Testing Hypotheses With the Linear Regression Model  
Summary  
Conceptual Exercises  
 
Chapter 12: A Closer Look at Linear Regression
The Importance of Looking at Our Data  
Using Residuals to Check Assumptions  
Testing Whether the Relationship Between Two Variables Is Linear  
The Correlation Ratio: An Alternate Way to Measure the Degree of Relationship and Test for a Linear Relationship  
Where Do We Go From Here?  
When the Relationship Is Not Linear  
The Effects of Outliers on Regression  
Robust Alternatives to the Method of Least Squares  
A Quick Peek at Multiple Regression  
Summary  
Conceptual Exercises  
 
Chapter 13: Another Way to Scale the Size of Treatment Effects
The Point Biserial Correlation Coefficient and the t-Test  
Advantages and Disadvantages of Estimating Effect Sizes With Correlation Coefficients or Standardized Group Difference Measures  
Confidence Intervals for Effect Size Estimates  
Final Comments on the Use of Effect Size Estimators  
Summary  
Conceptual Exercises  
 
Chapter 14: Analysis of Variance for Testing for Differences Between Population Means
What Are the Sources of Variation in Our Experiments?  
Experimental and Statistical Hypotheses  
Estimating Variances  
When There Are More Than Two Conditions in Your Experiment  
Assumptions for Analysis of Variance  
Testing Hypotheses About Differences Among Population Means With Analysis of Variance  
Factors That Affect the Power of the F-Test in Analysis of Variance  
Relational Effect Size Measures for Analysis of Variance  
Randomization Tests for Testing for Differential Effects of Three or More Treatments  
Using ANOVA to Study the Effects of More Than One Factor on Behavior  
Partitioning Variance for a Two-Factor Analysis of Variance  
Testing Hypotheses With Two-Factor Analysis of Variance  
Testing Hypotheses About Differences Among Population Means With Analysis of Variance  
Dealing With Unequal Sample Sizes in Factorial Designs  
Summary  
Conceptual Exercises  
 
Chapter 15: Multiple Regression and Beyond
Overview of the General Linear Model Approach  
Regression  
Simple Versus Multiple Regression  
Multiple Regression  
Types of Multiple Regression  
Interactions in Multiple Regression  
Continuous x Continuous Interactions  
Categorical x Continuous Interactions  
Categorical x Categorical Interactions: ANOVA Versus Regression  
Summary  
Conceptual Exercises  
 
Epilogue
 
Appendices
 
A. Some Useful Rules of Algebra
 
B. Rules of Summation
 
C. Logarithms
 
D. The Inverse of the Cumulative Normal Distribution
 
E. The Unit Normal Distribution
 
F. The t-Distribution
 
G. The Fisher r to zr Transformation
 
H. Critical Values for F With Alpha = .05
 
I. The Chi Square Distribution
 
References
 
Index

Supplements

Instructor Resource Site
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Instructor Resources include the following:
    • Microsoft® Word test bank is available containing multiple choice, true/false, short answer, and essay questions for each chapter. The test bank provides you with a diverse range of pre-written options as well as the opportunity for editing any question and/or inserting your own personalized questions to effectively assess students’ progress and understanding.
    • Editable, chapter-specific Microsoft® PowerPoint® slides offer you complete flexibility in easily creating a multimedia presentation for your course. Highlight essential content and features.
    • Discussion questions help launch classroom interaction by prompting students to engage with the material and by reinforcing important content.
    • Lively and stimulating class activities that can be used in class to reinforce active learning. The activities apply to individual or group projects.
    • EXCLUSIVE! Access to certain full-text SAGE journal articles that have been carefully selected for each chapter. Each article supports and expands on the concepts presented in the chapter. This feature also provides questions to focus and guide student interpretation. Combine cutting-edge academic journal scholarship with the topics in your course for a robust classroom experience.
    • Web resources include links to multimedia that appeal to students with different learning styles.
Student Resource Site
Use the Student Study Site to get the most out of your course!
Our Student Study Site is completely open-access and offers a wide range of additional features.

The open-access
 Student Study Site includes the following:
    • Mobile-friendly web quizzes allow for independent assessment of progress made in learning course material.
    • EXCLUSIVE! Access to certain full-text SAGE journal articles that have been carefully selected for each chapter. Each article supports and expands on the concepts presented in the chapter. This feature also provides questions to focus and guide student interpretation. Combine cutting-edge academic journal scholarship with the topics in your course for a robust classroom experience.
    •  Web resources include links to multimedia that appeal to students with different learning styles.
Key features
KEY FEATURES:

  • Coverage of traditional concepts in statistics includes expected value operators, likelihood functions, maximum likelihood estimation, and least squares estimation, preparing students for concepts they will continue to encounter in more advanced material.
  • Real research on specific antisocial behaviors provides consistent context for answering research questions in an interesting and intuitive way.
  • Discussion of statistical inference in an easy-to-understand manner ensures that students have the foundation they need to avoid misusing hypothesis tests.
  • A detailed presentation of resampling methods and randomization tests for experiments and correlation provides a better way to analyze data when the assumptions of the classical tests are not met.
  • A number of current techniques for data analysis not included in other textbooks are introduced, including quantile plots, quantile-quantile plots, normal quantile plots, analysis of residuals in scatter plots, bootstrap methods, robust estimators, robust regression, and the use of randomization (permutation) tests for experiments and correlation.

Sample Materials & Chapters

Chapter 1

Chapter 6

Chapter 11


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