# 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)

Additional resources:

March 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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