Statistics translated : a step-by-step guide to analyzing and interpreting data

Description

Cover Half Title Page Title Page Copyright Dedication Acknowledgments Brief Contents Introduction: You Do Not Need to Be a Statistician to Understand Statistics! 1. Identifying a Research Problem and Stating Hypotheses 2. Identifying the Independent and Dependent Variables in a Hypothesis 3. Measures of Dispersion and Measures of Relative Standing 4. Graphically Describing the Dependent Variable 5. Choosing the Right Statistical Test 6. The One-Sample t-Test 7. The Independent-Sample t-Test 8. The Dependent-Sample t-Test 9. Analysis of Variance and Multivariate Analysis of Variance 10. The Chi-Square Tests 11. The Correlational Procedures Conclusion: Have We Accomplished What We Set Out to Do? Appendix A. Area under the Normal Curve Table (Critical Values of z) Appendix B. Critical Values of t Appendix C. Critical Values of F When Alpha = .01 Appendix D. Critical Values of F When Alpha = .05 Appendix E. Critical Values of F When Alpha = .10 Appendix F. Critical Values of Chi-Square Appendix G. Selecting the Right Statistical Test Glossary Answers to Quiz Time! Index About the Author Extended Contents Introduction: You Do Not Need to Be a Statistician to Understand Statistics! A Little Background Many Students Do Not Know What They’re Getting Into A Few Simple Steps Step 1: Identify the Problem Step 2: State a Hypothesis Step 3: Identify the Independent Variable Step 4: Identify and Describe the Dependent Variable Step 5: Choose the Right Statistical Test Step 6: Use Data Analysis Software to Test the Hypothesis So, What’s New in This Edition? Summary Do You Understand These Key Words and Phrases? 1. Identifying a Research Problem and Stating Hypotheses Introduction Step 1: Identify the Problem Characteristics of a Good Problem Statement Finding a Good Research Problem The Problem Is Interesting to the Researcher The Scope of the Problem Is Manageable by the Researcher The Researcher Has the Knowledge, Time, and Resources Needed to Investigate the Problem The Problem Can Be Researched through the Collection and Analysis of Numeric Data Investigating the Problem Has Theoretical or Practical Significance It Is Ethical to Investigate the Problem Writing the Problem Statement Problem Statements Must Be Clear and Concise The Problem Statement Must Include All Variables to Be Considered The Problem Statement Should Not Interject the Researcher’s Bias Summary of Step 1: Identify the Problem Step 2: State a Hypothesis An Example of Stating Our Hypothesis A Little More Detail The Direction of Hypotheses Using Directional Hypotheses to Test a “Greater Than” Relationship Using Directional Hypotheses to Test a “Less Than” Relationship Nondirectional Hypotheses Hypotheses Must Be Testable via the Collection and Analysis of Data Research versus Null Hypotheses Stating Null Hypotheses for Directional Hypotheses Issues Underlying the Null Hypothesis for Directional Research Hypotheses Stating Null Hypotheses for Nondirectional Hypotheses A Preview of Testing the Null Hypothesis Where Does That Leave Us? Statistical Words of Wisdom Summary of Step 2: State a Hypothesis Do You Understand These Key Words and Phrases? Quiz Time! Problem Statements Case Studies The Case of Distance Therapy The Case of the New Teacher The Case of Being Exactly Right The Case of “Does It Really Work?” The Case of Advertising The Case of Learning to Speak The Case of Kids on Cruises 2. Identifying the Independent and Dependent Variables in a Hypothesis Introduction Step 3: Identify the Independent Variable Nonmanipulated Independent Variables Another Way of Thinking about Nonmanipulated Independent Variables Manipulated or Experimental Independent Variables Levels of the Independent Variable Summary of Step 3: Identify the Independent Variable Step 4: Identify and Describe the Dependent Variable Identifying Your Dependent Variable What Type of Data Are We Collecting? Interval Data Data Types—What Is the Good News? Summary of the Dependent Variable and Data Types Measures of Central Tendency The Mean, Median, and Mode—Measures of Central Tendency The Mode Using Statistical Software to Analyze Our Data Summary of the First Part of Step 4: Identify and Describe the Dependent Variable Do You Understand These Key Words and Phrases? Do You Understand These Formulas? Quiz Time! 3. Measures of Dispersion and Measures of Relative Standing Introduction Measures of Dispersion The Range The Standard Deviation The Variance Measures of Relative Standing Percentiles Computing and Interpreting T-Scores Stanines Putting It All Together Using SPSS for T-Scores and Stanines—Not So Fast! Summary Do You Understand These Key Words and Phrases? Do You Understand These Formulas? Quiz Time! 4. Graphically Describing the Dependent Variable Introduction Graphical Descriptive Statistics Graphically Describing Nominal Data Pie Charts Bar Charts Graphically Describing Quantitative Data Scatterplots Histograms Don’t Let a Picture Tell You the Wrong Story! Summary of Graphical Descriptive Statistics The Normal Distribution Things That Can Affect the Shape of a Distribution of Quantitative Data Summary of the Normal Distribution Do You Understand These Key Words and Phrases? Quiz Time! 5. Choosing the Right Statistical Test Introduction The Very Basics The Central Limit Theorem The Sampling Distribution of the Means Summary of the Central Limit Theorem and the Sampling Distribution of the Means How Are We Doing So Far? Estimating Population Parameters Using Confidence Intervals The Alpha Value Type I and Type II Errors Predicting a Population Parameter Based on a Sample Statistic Using Confidence Intervals Pay Close Attention Here Confidence Intervals for Alpha = .01 and Alpha = .10 Another Way to Think about z Scores in Confidence Intervals Tying This All Together Be Careful When Changing Your Alpha Values Do We Understand Everything We Need to Know about Confidence Intervals? Testing Hypotheses about a Population Parameter Based on a Sample Statistic Making a Decision about the Certification Examination Scores We Are Finally Going to Test Our Hypothesis! Testing a One-Tailed Hypothesis Testing a One-Tailed “Less Than” Hypothesis Summarizing What We Just Said Be Careful When Changing Your Alpha Values The Heart of Inferential Statistics Probability Values A Few More Examples Great News—We Will Always Use Software to Compute Our p Value Step 5: Choose the Right Statistical Test You Already Know a Few Things A Couple of Notes about the Table Summary of Step 5: Choose the Right Statistical Test Do You Understand These Key Words and Phrases? Do You Understand These Formulas and Symbols? Quiz Time! 6. The One-Sample t-Test Introduction Welcome to the Guinness Breweries The t Distribution Putting This Together Determining the Critical Value of t Degrees of Freedom Be Careful Computing Degrees of Freedom Let’s Get Back to Our Anxiety Hypothesis Plotting Our Critical Value of t The Statistical Effect Size of Our Example Let’s Look at a Directional Hypothesis Using the p Value Check Your Mean Scores! One More Time Important Note about Software Packages Let’s Use the Six-Step Model! The Case of Slow Response Time The Case of Stopping Sneezing The Case of Growing Tomatoes Summary Do You Understand These Key Words and Phrases? Do You Know These Formulas? Quiz Time! 7. The Independent-Sample t-Test Introduction If We Have Samples from Two Independent Populations, How Do We Know If They Are Significantly Different from One Another? The Sampling Distribution of Mean Differences Calculating the t Value for the Independent-Sample t-Test Pay Attention Here Testing Our Hypothesis The p Value Note on Variance and the t-Test The Statistical Effect Size of Our Example Let’s Try Another Example Remember the Effect Size How Does This Work for a Directional Hypothesis? Reminder—Always Pay Attention to the Direction of the Means! The Case of the Cavernous Lab The Case of the Report Cards The Case of the Anxious Athletes Putting the Independent-Sample t-Test to Work Summary Do You Understand These Key Words and Phrases? Do You Understand These Formulas? Quiz Time! The Case of the Homesick Blues The Case of the Cold Call The Case of the Prima Donnas The Case of the Wrong Side of the Road The Case of Workplace Satisfaction The Case of the Flower Show 8. The Dependent-Sample t-Test Introduction That’s Great, but How Do We Test Our Hypotheses? Independence versus Dependence Computing the t Value for a Dependent-Sample t-Test Testing a One-Tailed “Greater Than” Hypothesis The Effect Size for a Dependent-Sample t-Test Testing a One-Tailed “Less Than” Hypothesis Testing a Two-Tailed Hypothesis Let’s Move Forward and Use Our Six-Step Model Step 1: Identify the Problem Step 2: State a Hypothesis Step 3: Identify the Independent Variable Step 4: Identify and Describe the Dependent Variable Step 5: Choose the Right Statistical Test Step 6: Use Data Analysis Software to Test the Hypothesis The Case of the Unexcused Students Step 1: Identify the Problem Step 2: State a Hypothesis Step 3: Identify the Independent Variable Step 4: Identify and Describe the Dependent Variable Step 5: Choose the Right Statistical Test Step 6: Use Data Analysis Software to Test the Hypothesis The Case of Never Saying Never Step 1: Identify the Problem Step 2: State a Hypothesis Step 3: Identify the Independent Variable Step 4: Identify and Describe the Dependent Variable Step 5: Choose the Right Statistical Test Step 6: Use Data Analysis Software to Test the Hypothesis Just in Case—A Nonparametric Alternative Summary Do You Understand These Key Words and Phrases? Do You Understand These Formulas? Quiz Time! The Case of Technology and Achievement The Case of Worrying about Our Neighbors The Case of SPAM The Case of “We Can’t Get No Satisfaction” The Case of “Winning at the Lottery” 9. Analysis of Variance and Multivariate Analysis of Variance Introduction Understanding the ANOVA The Different Types of ANOVAs One-Way ANOVA Factorial ANOVA Multivariate ANOVA (MANOVA) Assumptions of the ANOVA Random Samples Independence of Scores Normal Distribution of Data Homogeneity of Variance Calculating the ANOVA Descriptive Statistics The Total Variance The Total Sum of Squares The Between Sum of Squares The Within Sum of Squares Computing the Degrees of Freedom Computing the Mean Square Computing the F Value The F Distribution Determining the Area under the Curve for F Distributions The p Value for an ANOVA Effect Size for the ANOVA Testing a Hypothesis Using the ANOVA The Case of Multiple Means of Math Mastery The Post-Hoc Comparisons Multiple-Comparison Tests Always Observe the Means! The Case of Seniors Skipping School The Case of Quality Time The Case of Regional Discrepancies The Factorial ANOVA The Case of Age Affecting Ability Interpreting the Interaction p Value The Case of the Coach The Multivariate ANOVA (MANOVA) Assumptions of the MANOVA Using the MANOVA The Case of Balancing Time Summary Do You Understand These Key Words and Phrases? Do You Understand These Formulas? Quiz Time! The Case of Degree Completion The Case of Seasonal Depression The Case of Driving Away The Case of Climbing The Case of Employee Productivity 10. The Chi-Square Tests Introduction The One-Way Chi-Square Test The Factorial Chi-Square Test (the Chi-Square Test of Independence) Computing the Chi-Square Statistic The Chi-Square Distribution What about the Post-Hoc Test? Working with an Even Number of Expected Values The Case of the Belligerent Bus Drivers The Case of the Irate Parents The Chi-Square Test of Independence Computing Chi-Square for the Test of Independence Computing Expected Values for the Test of Independence Computing the Chi-Square Value for the Test of Independence Determining the Degrees of Freedom for the Test of Independence We Are Finally Going to Test Our Hypothesis Using SPSS to Check What We Just Computed The Case of Corporal Punishment Post-Hoc Tests Following the Chi-Square The Case of Type of Instruction and Learning Style Summary Do You Understand These Key Words and Phrases? Do You Understand These Formulas? Quiz Time! The Case of Prerequisites and Performance The Case of Getting What You Asked For The Case of Money Meaning Nothing The Case of Equal Opportunity 11. The Correlational Procedures Introduction Understanding the Idea of Correlations Interpreting Pearson’s r A Word of Caution An Even More Important Word of Caution! A Nonparametric Correlational Procedure The p Value of a Correlation The Case of the Absent Students Another Example: The Case against Sleep The Case of Height versus Weight The Case of Different Tastes Once We Have a Linear Relationship, What Can We Do with It? Linear Regression The Regression Equation Computing the Slope Computing the Intercept Why Wasn’t It Exactly Right? Using the Six-Step Model: The Case of Age and Driving Summary Do You Understand These Key Words and Phrases? Do You Understand These Formulas? Quiz Time! The Case of “Like Father, Like Son” The Case of “Can’t We All Just Get Along?” The Case of More Is Better The Case of More Is Better Still Conclusion: Have We Accomplished What We Set Out to Do? Statistics in a New Light A Limited Set of Statistical Techniques The Use of Statistical Software Packages A Straightforward Approach At Long Last Appendix A. Area under the Normal Curve Table (Critical Values of z) Appendix B. Critical Values of t Appendix C. Critical Values of F When Alpha = .01 Appendix D. Critical Values of F When Alpha = .05 Appendix E. Critical Values of F When Alpha = .10 Appendix F. Critical Values of Chi-Square Appendix G. Selecting the Right Statistical Test Glossary Answers to Quiz Time! Index About the Author