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Applied Statistics I
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Applied Statistics I
Basic Bivariate Techniques

Third Edition
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January 2020 | 648 pages | SAGE Publications, Inc
Rebecca M. Warner’s bestselling Applied Statistics: From Bivariate Through Multivariate Techniques has been split into two volumes for ease of use over a two-course sequence. Applied Statistics I: Basic Bivariate Techniques, Third Edition is an introductory statistics text based on chapters from the first half of the original book. 

The author's contemporary approach reflects current thinking in the field, with its coverage of the "new statistics" and reproducibility in research. Her in-depth presentation of introductory statistics follows a consistent chapter format, includes some simple hand-calculations along with detailed instructions for SPSS, and helps students understand statistics in the context of real-world research through interesting examples. Datasets are provided on an accompanying website.

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Applied Statistics I + Applied Statistics II: Basic Bivariate Techniques, Third Edition 
Bundle Volume I and II ISBN: 978-1-0718-1337-9
 
An R Companion for Applied Statistics I: Basic Bivariate Techniques + Applied Statistics I

Bundle ISBN: 978-1-0718-1325-6
 
Preface
 
Acknowledgments
 
About the Author
 
1. Evaluating Numerical Information
Introduction

 
Guidelines for Numeracy

 
Source Credibility

 
Message Content

 
Evaluating Generalizability

 
Making Causal Claims

 
Quality Control Mechanisms in Science

 
Biases of Information Consumers

 
Ethical Issues in Data Collection and Analysis

 
Lying with Graphs and Statistics

 
Degrees of Belief

 
Summary

 
 
2. Basic Research Concepts
Introduction

 
Types of Variables

 
Independent and Dependent Variables

 
Typical Research Questions

 
Conditions for Causal Inference

 
Experimental Research Design

 
Nonexperimental Research Design

 
Quasi-Experimental Research Designs

 
Other Issues in Design and Analysis

 
Choice of Statistical Analysis (Preview)

 
Populations and Samples: Ideal Versus Actual Situations

 
Common Problems in Interpretation of Results

 
Appendix 2A: More About Levels of Measurement

 
Appendix 2B: Justification for the Use of Likert and Other Rating Scales as Quantitative Variables (in Some Situations)

 
 
3. Frequency Distribution Tables
Introduction

 
Use of Frequency Tables for Data Screening

 
Frequency Tables for Categorical Variables

 
Elements of Frequency Tables

 
Using SPSS to Obtain a Frequency Table

 
Mode, Impossible Score Values, and Missing Values

 
Reporting Data Screening for Categorical Variables

 
Frequency Tables for Quantitative Variables

 
Frequency Tables for Categorical Versus Quantitative Variables

 
Reporting Data Screening for Quantitative Variables

 
What We Hope to See in Frequency Tables for Categorical Variables

 
What We Hope to See in Frequency Tables for Quantitative Variables

 
Summary

 
Appendix 3A: Getting Started in IBM SPSS® Version 25

 
Appendix 3B: Missing Values in Frequency Tables

 
Appendix 3C: Dividing Scores Into Groups or Bins

 
 
4. Descriptive Statistics
Introduction

 
Questions about Quantitative Variables

 
Notation

 
Sample Median

 
Sample Mean (M)

 
An Important Characteristic of M: The Sum of Deviations From M = 0

 
Disadvantage of M: It is Not Robust Against Influence of Extreme Scores

 
Behavior of Mean, Median, and Mode in Common Real-World Situations

 
Choosing Among Mean, Median, and Mode

 
Using SPSS to Obtain Descriptive Statistics for a Quantitative Variable

 
Minimum, Maximum, and Range: Variation among Scores

 
The Sample Variance s2

 
Sample Standard Deviation (s or SD)

 
How a Standard Deviation Describes Variation Among Scores in a Frequency Table

 
Why Is There Variance?

 
Reports of Descriptive Statistics in Journal Articles

 
Additional Issues in Reporting Descriptive Statistics

 
Summary

 
Appendix 4A: Order of Arithmetic Operations

 
Appendix 4B: Rounding

 
 
5. Graphs: Bar Charts, Histograms, and Boxplots
Introduction

 
Pie Charts for Categorical Variables

 
Bar Charts for Frequencies of Categorical Variables

 
Good Practice for Construction of Bar Charts

 
Deceptive Bar Graphs

 
Histograms for Quantitative Variables

 
Obtaining a Histogram Using SPSS

 
Describing and Sketching Bell-Shaped Distributions

 
Good Practices in Setting up Histograms

 
Boxplot (Box and Whiskers Plot)

 
Telling Stories About Distributions

 
Uses of Graphs in Actual Research

 
Data Screening: Separate Bar Charts or Histograms for Groups

 
Use of Bar Charts to Represent Group Means

 
Other Examples

 
Summary

 
 
6. The Normal Distribution and z Scores
Introduction

 
Locations of Individual Scores in Normal Distributions

 
Standardized or z Scores

 
Converting z Scores Back Into X Units

 
Understanding Values of z

 
Qualitative Description of Normal Distribution Shape

 
More Precise Description of Normal Distribution Shape

 
Areas Under the Normal Distribution Curve Can Be Interpreted as Probabilities

 
Reading Tables of Areas for the Standard Normal Distribution

 
Dividing the Normal Distribution Into Three Regions: Lower Tail, Middle, Upper Tail

 
Outliers Relative to a Normal Distribution

 
Summary of First Part of Chapter

 
Why We Assess Distribution Shape

 
Departure from Normality: Skewness

 
Another Departure from Normality: Kurtosis

 
Overall Normality

 
Practical Recommendations for Preliminary Data Screening and Descriptions of Scores for Quantitative Variables

 
Reporting Information About Distribution Shape, Missing Values, Outliers, and Descriptive Statistics for Quantitative Variables

 
Summary

 
Appendix 6A: The Mathematics of the Normal Distribution

 
Appendix 6B: How to Select and Remove Outliers in SPSS

 
Appendix 6C: Quantitative Assessments of Departure From Normality

 
Appendix 6D: Why Are Some Real-World Variables Approximately

 
 
7. Sampling Error and Confidence Intervals
Descriptive Versus Inferential Uses of Statistics

 
Notation for Samples Versus Populations

 
Sampling Error and the Sampling Distribution for Values of M

 
Prediction Error

 
Sample Versus Population (Revisited)

 
The Central Limit Theorem: Characteristics of the Sampling Distribution of M

 
Factors That Influence Population Standard Error (sM)

 
Effect of N on Value of the Population Standard Error

 
Describing the Location of a Single Outcome for M Relative to Population Sampling Distribution (Setting Up a z Ratio)

 
What We Do When s Is Unknown

 
The Family of t Distributions

 
Tables for t Distributions

 
Using Sampling Error to Set Up a Confidence Interval

 
How to Interpret a Confidence Interval

 
Empirical Example: Confidence Interval for Body Temperature

 
Other Applications for Confidence Intervals

 
Error Bars in Graphs of Group Means

 
Summary

 
 
8. The One-Sample t test: Introduction to Statistical Significance Tests
Introduction

 
Significance Tests as Yes/No Questions About Proposed Values of Population Means

 
Stating a Null Hypothesis

 
Selecting an Alternative Hypothesis

 
The One-Sample t Test

 
Choosing an Alpha (a) Level

 
Specifying Reject Regions on the Basis of a, Halt, and df

 
Questions for the One-Sample t Test

 
Assumptions for the Use of the One-Sample t Test

 
Rules for the Use of NHST

 
First Analysis of Mean Driving Speed Data (Using a Nondirectional Test)

 
SPSS Analysis: One-Sample t Test for Mean Driving Speed (Using a Nondirectional or Two-Tailed Test)

 
“Exact” p Values

 
Reporting Results for a Two-tailed One-Sample t Test

 
Second Analysis of Driving Speed Data Using a One-Tailed or Directional Test

 
Reporting Results for a One-tailed One-Sample t Test

 
Advantages and Disadvantages of One-Tailed Tests

 
Traditional NHST Versus New Statistics Recommendations

 
Things You Should Not Say About p Values

 
Summary

 
 
9. Issues in Significance Tests: Effect Size, Statistical Power, and Decision Errors
Beyond p Values

 
Cohen’s d: An Effect Size Index

 
Factors that Affect the Size of t Ratios

 
Statistical Significance Versus Practical Importance

 
Statistical Power

 
Type I and Type II Decision Errors

 
Meanings of “Error”

 
Use of NHST in Exploratory Versus Confirmatory Research

 
Inflated Risk for Type I Decision Error for Multiple Tests

 
Interpretation of Null Outcomes

 
Interpretation of Statistically Significant Outcomes

 
Understanding Past Research

 
Planning Future Research

 
Guidelines for Reporting Results

 
What You Cannot Say

 
Summary

 
Appendix 9A: Further Explanation of Statistical Power

 
 
10. Bivariate Pearson Correlation
Research Situations Where Pearson’s r Is Used

 
Correlation and Causal Inference

 
How Sign and Magnitude of r Describe an X, Y Relationship

 
Setting Up Scatterplots

 
Most Associations Are Not Perfect

 
Different Situations in Which r = .00

 
Assumptions for Use of Pearson’s r

 
Preliminary Data Screening for Pearson’s r

 
Effect of Extreme Bivariate Outliers

 
Research Example

 
Data Screening for Research Example

 
Computation of Pearson’s r

 
How Computation of Correlation Is Related to Pattern of Data Points in the Scatterplot

 
Testing the Hypothesis That p0 = 0

 
Reporting Many Correlations and Inflated Risk for Type I Error

 
Obtaining Confidence Intervals for Correlations

 
Pearson’s r and r2 as Effect Sizes and Partition of Variance

 
Statistical Power and Sample Size for Correlation Studies

 
Interpretation of Outcomes for Pearson’s r

 
SPSS Example: Relationship Survey

 
Results Sections for One and Several Pearson’s r Values

 
Reasons to Be Skeptical of Correlations

 
Summary

 
Appendix 10A: Nonparametric Alternatives to Pearson’s r

 
Appendix 10B: Setting Up a 95% CI for Pearson’s r by Hand

 
Appendix 10C: Testing Significance of Differences Between Correlations

 
Appendix 10D: Some Factors That Artifactually Influence Magnitude of r

 
Appendix 10E: Analysis of Nonlinear Relationships

 
Appendix 10F: Alternative Formula to Compute Pearson’s r

 
 
11. Bivariate Regression
Research Situations Where Bivariate Regression Is Used

 
New Information Provided by Regression

 
Regression Equations and Lines

 
Two Versions of Regression Equations

 
Steps in Regression Analysis

 
Preliminary Data Screening

 
Formulas for Bivariate Regression Coefficients

 
Statistical Significance Tests for Bivariate Regression

 
Confidence Intervals for Regression Coefficients

 
Effect Size and Statistical Power

 
Empirical Example Using SPSS: Salary Data

 
SPSS Output: Salary Data

 
Results Section: Hypothetical Salary Data

 
Plotting the Regression Line: Salary Data

 
Using a Regression Equation to Predict Score for Individual (Joe’s Heart Rate Data)

 
Partition of Sums of Squares in Bivariate Regression

 
Why Is There Variance (Revisited)?

 
Issues in Planning a Bivariate Regression Study

 
Plotting Residuals

 
Standard Error of the Estimate

 
Summary

 
Appendix 11A: Review: How to Graph a Line From Two Points Obtained From an Equation

 
Appendix 11B: OLS Derivation of Equation for Regression Coefficients

 
Appendix 11C: Alternative Formula for Computation of Slope

 
Appendix 11D: Fully Worked Example: Deviations and SS

 
 
12. The Independent-Samples t Test
Research Situations Where the Independent-Samples t Test Is Used

 
Hypothetical Research Example

 
Assumptions for Use of Independent-Samples t Test

 
Preliminary Data Screening: Evaluating Violations of Assumptions and Getting to Know Your Data

 
Computation of Independent-Samples t Test

 
Statistical Significance of Independent-Samples t Test

 
Confidence Interval Around M1 – M2

 
SPSS Commands for Independent-Samples t Test

 
SPSS Output for Independent-Samples t Test

 
Effect Size Indexes for t

 
Factors that Influence the Size of t

 
Results Section

 
Graphing Results: Means and CIs

 
Decisions About Sample Size for the Independent-Samples t Test

 
Issues in Designing a Study

 
Summary

 
Appendix 12A: A Nonparametric Alternative to the Independent-Samples t Test

 
 
13. One-Way Between-Subjects Analysis of Variance
Research Situations Where One-Way ANOVA Is Used

 
Questions in One-Way Between-S ANOVA

 
Hypothetical Research Example

 
Assumptions and Data Screening for One-Way ANOVA

 
Computations for One-Way Between-S ANOVA

 
Patterns of Scores and Magnitudes of SSbetween and SSwithin

 
Confidence Intervals for Group Means

 
Effect Sizes for One-Way Between-S ANOVA

 
Statistical Power Analysis for One-Way Between-S ANOVA

 
Planned Contrasts

 
Post Hoc or “Protected” Tests

 
One-Way Between-S ANOVA in SPSS

 
Output From SPSS for One-Way Between-S ANOVA

 
Reporting Results From One-Way Between-S ANOVA

 
Issues in Planning a Study

 
Summary

 
Appendix 13A: ANOVA Model and Division of Scores Into Components

 
Appendix 13B: Expected Value of F When H0 Is True

 
Appendix 13C: Comparison of ANOVA and t Test

 
Appendix 13D: Nonparametric Alternative to One-Way Between-S ANOVA: Independent-Samples Kruskal-Wallis Test

 
 
14. Paired-Samples t Test
Independent- Versus Paired-Samples Designs

 
Between-S and Within-S or Paired-Groups Designs

 
Types of Paired Samples

 
Hypothetical Study: Effects of Stress on Heart Rate

 
Review: Data Organization for Independent Samples

 
New: Data Organization for Paired Samples

 
A First Look at Repeated-Measures Data

 
Calculation of Difference (d) Scores

 
Null Hypothesis for Paired-Samples t Test

 
Assumptions for Paired-Samples t Test

 
Formulas for Paired-Samples t Test

 
SPSS Paired-Samples t Test Procedure

 
Comparison Between Results for Independent-Samples and Paired-Samples t Tests

 
Effect Size and Power

 
Some Design Problems in Repeated-Measures Analyses

 
Results for Paired-Samples t Test: Stress and Heart Rate

 
Further Evaluation of Assumptions

 
Summary

 
Appendix 14A: Nonparametric Alternative to Paired-Samples t: Wilcoxon Signed Rank Test

 
 
15. One-Way Repeated-Measures Analysis of Variance
Introduction

 
Null Hypothesis for Repeated-Measures ANOVA

 
Preliminary Assessment of Repeated-Measures Data

 
Computations for One-Way Repeated-Measures ANOVA

 
Use of SPSS Reliability Procedure for One-Way Repeated-Measures ANOVA

 
Partition of SS in Between-S Versus Within-S ANOVA

 
Assumptions for Repeated-Measures ANOVA

 
Choices of Contrasts in GLM Repeated Measures

 
SPSS GLM Procedure for Repeated-Measures ANOVA

 
Output of GLM Repeated-Measures ANOVA

 
Paired-Samples t Tests as Follow-Up

 
Results

 
Effect Size

 
Statistical Power

 
Counterbalancing in Repeated-Measures Studies

 
More Complex Designs

 
Summary

 
Appendix 15A: Test for Person-by-Treatment Interaction

 
Appendix 15B: Nonparametric Analysis for Repeated Measures (Friedman Test)

 
 
16. Factorial Analysis of Variance
Research Situations Where Factorial Design Is Used

 
Questions in Factorial ANOVA

 
Null Hypotheses in Factorial ANOVA

 
Screening for Violations of Assumptions

 
Hypothetical Research Situation

 
Computations for Between-S Factorial ANOVA

 
Computation of SS and df in Two-Way Factorial ANOVA

 
Effect Size Estimates for Factorial ANOVA

 
Statistical Power

 
Follow-Up Tests

 
Factorial ANOVA Using the SPSS GLM Procedure

 
SPSS Output

 
Results

 
Design Decisions and Magnitudes of SS Terms

 
Summary

 
Appendix 16A: Fixed Versus Random Factors

 
Appendix 16B: Weighted Versus Unweighted Means

 
Appendix 16C: Unequal Cell n’s in Factorial ANOVA: Computing Adjusted Sums of Squares

 
Appendix 16D: Model for Factorial ANOVA

 
Appendix 16E: Computation of Sums of Squares by Hand

 
 
17. Chi-Square Analysis of Contingency Tables
Evaluating Association Between Two Categorical Variables

 
First Example: Contingency Tables for Titanic Data

 
What Is Contingency?

 
Conditional and Unconditional Probabilities

 
Null Hypothesis for Contingency Table Analysis

 
Second Empirical Example: Dog Ownership Data

 
Preliminary Examination of Dog Ownership Data

 
Expected Cell Frequencies If H0 Is True

 
Computation of Chi Squared Significance Test

 
Evaluation of Statistical Significance of x2

 
Effect Sizes for Chi Squared

 
Chi Squared Example Using SPSS

 
Output From Crosstabs Procedure

 
Reporting Results

 
Assumptions and Data Screening for Contingency Tables

 
Other Measures of Association for Contingency Tables

 
Summary

 
Appendix 17A: Margin of Error for Percentages in Surveys

 
Appendix 17B: Contingency Tables With Repeated Measures: McNemar Test

 
Appendix 17C: Fisher Exact Test

 
Appendix 17D: How Marginal Distributions for X and Y Constrain Maximum Value of f

 
Appendix 17E: Other Uses of x2

 
 
18. Selection of Bivariate Analyses and Review of Key Concepts
Selecting Appropriate Bivariate Analyses

 
Types of Independent and Dependent Variables (Categorical Versus Quantitative

 
Parametric Versus Nonparametric Analyses

 
Comparisons of Means or Medians Across Groups (Categorical IV and Quantitative DV)

 
Problems With Selective Reporting of Evidence and Analyses

 
Limitations of Statistical Significance Tests and p Values

 
Statistical Versus Practical Significance

 
Generalizability Issues

 
Causal Inference

 
Results Sections

 
Beyond Bivariate Analyses: Adding Variables

 
Some Multivariable or Multivariate Analyses

 
Degree of Belief

 
 
Appendices
Appendix A: Proportions of Area Under a Standard Normal Curve

 
Appendix B: Critical Values for t Distribution

 
Appendix C: Critical Values of F

 
Appendix D: Critical Values of Chi-Square

 
Appendix E: Critical Values of the Pearson Correlation Coefficient

 
Appendix F: Critical Values of the Studentized Range Statistic

 
Appendix G: Transformation of r (Pearson Correlation) to Fisher’s Z

 
 
Glossary
 
References
 
Index

Supplements

Instructor Teaching Site
study.sagepub.com/warner3e
Password-protected Instructor Resources include the following:
  • Editable, chapter-specific Microsoft® PowerPoint® slides offer you complete flexibility in easily creating a multimedia presentation for your course. 
  • Test banks in Word and LMS-ready formats provide a diverse range of pre-written options as well as the opportunity to edit any question and/or insert your own personalized questions to effectively assess students’ progress and understanding.
  • Tables and figures from the printed book are available in an easily-downloadable format for use in papers, hand-outs, and presentations.
  • Answers to comprehension questions from the text.

Open-access Student Resources include flashcards, web resources, and data sets provided by the author for student download for completing in-chapter exercises.

 

“Combined, these texts provide both simplistic explanations of analyses, and also in-depth exploration of them with examples. Thus, they prove to be a useful resource to beginning statistics students all the way through the dissertation level, and even for faculty conducting research.”

Karla Hamlen Mansour
Cleveland State University

“This book presents statistical complexity in a friendly and uncomplicated way with friendly text and plenty of helpful diagrams and tables.”

Beverley Hale
University of Chichester, U.K.

“Well-written, comprehensive statistics book. A very valuable resource for advanced undergraduate and graduate students.”

Dan Ispas
Illinois State University

“Warner's textbook is ideal for graduate or advanced undergraduate students providing extensive, yet highly accessible, coverage of important issues in fundamental research design and statistical analysis and newer recommendations in how to conduct statistical analysis and report results ethically. She writes extremely well and my students find her book very readable and useful.”

Paul F. Tremblay
University of Western Ontario

“The book is well-written and focuses on practical applications of the concepts rather than typical ‘textbook’ applications. The focus on meaning rather than the mechanics of computation is also a strength.”

Linda M. Bajdo
Wayne State University

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