# 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)

Models |

The Classical Statistical Model |

Designing Experiments and Analyzing Data |

Summary |

Questions Raised by the Use of the Classical Statistical Model |

Conceptual Exercises |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

### Supplements

**Calling all instructors!**

It’s easy to log on to SAGE’s password-protected Instructor Teaching Site for complete and protected access to all text-specific Instructor Resources. Simply provide your institutional information for verification and within 72 hours you’ll be able to use your login information for any SAGE title!

Password-protected

**Instructor Resources**include the following:

- A
**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.

- A

**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.

- Mobile-friendly

HEOA Compliance

####
**Available formats**

ISBN: 9781483358598 | Hardcover | Suggested Retail Price: $85.00 | Bookstore Price: $68.00 |

ISBN: 9781544334981 | Electronic Version | Suggested Retail Price: $32.00 | Bookstore Price: $25.60 |

ISBN: 9781506373461 | Electronic Version | Suggested Retail Price: $68.00 | Bookstore Price: $54.40 |

Should you need additional information or have questions regarding the HEOA information provided for this title, including what is new to this edition, please email sageheoa@sagepub.com. Please include your name, contact information, and the name of the title for which you would like more information. For information on the HEOA, please go to http://ed.gov/policy/highered/leg/hea08/index.html.

We hope you'll consider this SAGE text. Email us at info@sagepub.com, or click here to find your SAGE rep.

**SAGE**

2455 Teller Road

Thousand Oaks, CA 91320

www.sagepub.com