# Principles & Methods of Statistical Analysis

- Jerome Frieman - Kansas State University, USA
- Donald A. Saucier - Kansas State University, USA
- Stuart S. Miller - Kansas State University (Student)

January 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

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