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

March 2017 | 528 pages | SAGE Publications, Inc
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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

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    •  Web resources include links to multimedia that appeal to students with different learning styles.

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Chapter 1

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