Introduction to Real World Statistics

Edward T. Vieira, Jr. is an Associate Professor, Research Director, and member of the Institutional Review Board at Simmons College, Boston, Massachusetts, USA. He earned his M.B.A from Bryant University and Ph.D. from the University of Connecticut. Currently, Dr. Vieira serves on the editorial boards of seven peer-reviewed journals providing statistical and methodological expertise. He has over 30 years of management, research, and consulting experience in areas such as marketing research, community outreach focus groups, organizational research, and education evaluation research.

This book serves students being introduced to quantitative research as well as research professionals seeking to add to their statistical analysis and quantitative reasoning skills. Its emphasis on providing the reasons and prerequisites for using a statistical procedure make it valuable as a book-shelf reference as well as a textbook. Integration of relevant exercises to be carried out with SPSS enhances understanding of general statistical concepts with a body of hands-on experience, and that combination results in a very valuable skill set that will serve the reader well for years.James H. Watt, Professor Emeritus, University of ConnecticutProfessor Vieira combines a straightforward approach to applied statistics with the most accessible statistical package, SPSS. His non-technical, clear, and concise writing style makes Introduction to Real World Statistics a valuable handbook and reference for students and practitioners as well as an effective text for introductory statistics courses.John Lowe, Associate Dean for Undergraduate Programs, Simmons CollegeThis is a textbook that attempts to bridge areas of content that are traditionally addressed independently: a the conceptual knowledge of technical information; b. the real world application of such technical knowledge and c. a leading software tool that assists a researcher in applying the conceptual knowledge of technical information to a real world context. Vieira seems to have used the feedback he received from his students over several decades to successfully build a bridge across these three content areas. This textbook and its approach are a welcome addition for making the process of learning statistics in the social sciences a lot smoother and a lot more relevant to students. Michael G. Elasmar, Ph.D., Associate Professor and Director of the Marketing Communication Research graduate program, Boston UniversityDr. Vieira’s book is comprehensive, clear, and has great examples to illustrate the concepts. I particularly liked the section on Sampling. I envision that this book would be suitable for a variety of audiences and levels.Clayton W. Barrows, University of New Hampshire

• PrefaceWhy Read This Book?Notable FeaturesAssumes No Prior Knowledge of StatisticsShort Digestible Chapters That Build and Integrate Real World Statistical SkillsAn Alternative to the Traditional Hypothesis Testing ApproachInterdisciplinary ApplicationsSPSS Step-by-Step Detailed Instructions with ScreenshotsChapter PowerPoints and Test BankA Systematic Approach to Teaching StatisticsBook OrganizationAcknowledgmentsPART I: GETTING STARTED1 Introduction to Real World Statistics Learning Objectives 1.1 What Is Statistics?Sample Data vs. Census Data 1.2 Reification 1.3 Naïve Science: The Deception of Common Sense Real World Snapshot 1.4 Importance of Statistics Statistical Assumptions Summary of Key Concepts Introductory Applied Exercises 2 Statistics: Descriptive, Correlation, and Inferential Learning Objectives 2.1 Introduction to Descriptive, Correlation, and Inferential Statistics 2.2 Descriptive Statistics Measures of Variation 2.3 Correlation Statistics 2.4 Inferential StatisticsReal World Snapshot 2.5 Descriptive, Correlation, and Inferential Statistics Summary of Key Concepts Descriptive, Correlation, and Inferential Statistics Applied Exercises 3 Data and Types of Variables Learning Objectives 3.1 Introduction to Variables 3.2 Kinds of Variables 3.3 Variables by Type of Data Categorical Data Binary-Level Data (Variable) Nominal-Level Data (Variable) Ordinal-Level Data (Variable) Numeric Data Ratio-Level Data (Variable) Interval-Level Data (Variable) Scale Response Formatted Variables: A Special Case Appropriate Analysis for Variable (Data) Type Real World Snapshot 3.4 Variables by Influence Independent Variables (Predictors) Dependent Variables (Outcomes) Control Variables Interaction Variables Summary of Key Concepts Variables Applied Exercises 4 SPSS Statistics Data Management Basics: Preparing Data for Analysis Learning Objectives 4.1 Introduction to SPSS and Data, Output, and Syntax Files4.2 Setting up the Data File 4.3 Key SPSS Data Management Tools 4.4 Opening SPSS 4.5 Formatting the Variables’ Data Name Type Width Decimals Label Values MissingColumnAlign Measure Role 4.6 The SPSS Data File Data Access Manual Entry Opening an Existing SPSS Data File Opening Other Formatted Spreadsheet Data Files Text Files Cut and Paste Saving the Data File Saving Data in SPSS Saving Data in Other Spreadsheet Formats 4.7 The SPSS Output File Creating a New SPSS Output File Opening an Existing SPSS Output File Displaying the Full P-Value in the Output File Saving an SPSS Output File Saving Output for the SPSS Output Viewer Saving SPSS Output in Another Format 4.8 A Brief Review of the Syntax File 4.9 Creating a Codebook Creating a Codebook from Scratch Real World Snapshot The SPSS Codebook Summary of Key Concepts Data Management Applied Exercises PART II: SAMPLING CONSIDERATIONS5 Sampling Strategies Learning Objectives 5.1 Introduction to the Sampling Process 5.2 Probability Sampling Random vs. Representative Sampling Random Sampling and the Shape of Data Distribution Simple Random Sampling Systematic Random Sampling Cluster (Random) Sampling Stratified Random Sampling Real World Snapshot 5.3 Nonprobability Sampling Convenience Sampling Expert Sampling Quota Sampling Snowball Sampling Summary of Key Concepts Sampling Applied Exercises 6 Sample Size Learning Objectives 6.1 Introduction to Sample Size Numeric Data Central Limit Theorem Categorical Data Other Considerations 6.2 Power Analysis and Sample Size Finite Population Correction Informed Power Analysis Real World Snapshot Comparison of Unequal Sample Sizes Data Assumptions 6.3 Examples Using SPSS: Step-by-Step Instructions Example 6.1: Means: One-sample t-test that mean = specific value Interpretation Example 6.2: Means: Paired t-test that mean = 0 Interpretation Example 6.3: Proportions: One-sample test that proportion = ".50" Interpretation Example 6.4: Proportions: 2 × 2 for independent samples (chi-square or Fisher’s exact test) Interpretation Example 6.5: Correlations: One-sample test that correlation = 0 Interpretation Example 6.6: ANOVA: One-way analysis of variance Interpretation Example 6.7: Regression: One set of predictors Interpretation Example 6.8: Clustering Interpretation Summary of Key Concepts Sample Size Applied Exercises 7 Sources and Types of Statistical Error Learning Objectives 7.1 Introduction to Sources of Statistical Error Real World Snapshot 7.2 Sampling Error Sampling Random Error Sampling Systematic Error 7.3 Nonsampling Error Nonsampling Random Error Nonsampling Systematic Error Summary of Key Concepts Statistical Error Applied Exercises 8 Missing Data Learning Objectives 8.1 Introduction to Missing Data 8.2 Missing Value (Data) Analysis Real World Snapshot 8.3 Methods for Replacing Missing Values Listwise (Casewise) Pairwise Series Mean Mean of Nearby Points Median of Nearby Points Linear Interpolation Linear Trend at Point 8.4 New Data Replacement Methods Expectation Maximization Multiple Imputation 8.5 Examples Using SPSS: Step-by-Step Instructions Example 8.1: The MCAR Case Interpretation Write-Up Example 8.2: The NMAR Case Interpretation Write-Up Summary of Key Concepts Missing Data Applied Exercises PART III: DATA SCREENING, DESCRIBING, AND PROBABILITIES9 Describing Categorical Variables Learning Objectives 9.1 Introduction to Describing Categorical Variables Real World Snapshot 9.2 Charting Categorical Variables Pie Chart Dichotomous (Two-Category) Pie Chart Example 9.1: A Pie Chart with Two Categories Describing and Reporting Multiple Category Pie Chart Example 9.2: A Pie Chart with More Than Two Categories Describing and Reporting Bar Chart Example 9.3: A Bar Chart with More Than Two Categories Describing and Reporting 9.3 Categorical Variable Tables Single Variable Tables Example 9.4: A Single Categorical Variable with Two Categories Table Describing and Reporting Example 9.5: A Single Categorical Variable with More Than Two Categories Table Describing and Reporting Multiple Variable Tables Two Variables Example 9.6: Two Categorical Variables Each with Two or More Categories Table Describing and Reporting Three Variables Example 9.7: Three Categorical Variables Each with Two or More Categories Table Describing and Reporting Summary of Concepts Describing Categorical Variables Applied Exercises 10 Basic Probabilities for Categorical Variables Learning Objectives 10.1 Introduction to Basic Probability 10.2 Assumptions Real World Snapshot 10.3 Simple (Marginal) Probability 10.4 Joint Probability 10.5 Conditional Probability 10.6 Tables 10.7 Multiplication Rule in Probability 10.8 Addition Rule in Probability Summary of Key Concepts Categorical Data Probability Applied Exercises 11 The Concepts of Data Distribution, Probability Values, and Significance Testing Learning Objectives 11.1 Introduction to Data Distribution and Probability 11.2 Numerical Data Distribution Standard Deviation and the Normal Distribution Real World Snapshot Z-Distribution and Z-Scores T-Distribution Probability Based on the Normal Distribution Probability Value (P-Values) Level of Significance (Alpha) and Significance Testing 11.3 Categorical Data Distribution The Chi-Square Significance Test Degrees of Freedom Two Types of Expected Observations Probability (P-Values) Based on the Chi-Square Distribution 11.4 Confidence Intervals 11.5 Conclusion Summary of Key Concepts Distribution and Significance Testing Applied Exercises 12 Numeric Variables: Data Screening and Removing Outliers Learning Objectives 12.1 Introduction to Numeric Data Screening and Removing Outliers Real World Snapshot 12.2 Measuring Central Tendency Mean Median Mode Coefficient of Skewness 12.3 Measuring Dispersion Range Variance Standard Deviation Coefficient of Variation Coefficient of Kurtosis 12.4 Screening Data: Identifying and Removing Outliers Outliers Visual Assessment Statistical Measures Methods for Identifying and Removing Outliers Simple Outlier Removal Standard Deviation Rule Trimming or Truncating Winsorizing Outlier Labeling Rule Data Removal and Analysis Data Screening and the Removal of Outliers Assumptions 12.5 Examples Using SPSS: Step-by-Step Instructions Example 12.1: Simple Outlier Removal SPSS Output Interpretation Example 12.2: Outlier Labeling Rule Removal SPSS Output Interpretation 12.6 Other Remedies for Non-Normal Data Distribution Summary of Key Concepts Numeric Data Screening and Removing Outliers Applied Exercises PART IV: STATISTICAL ANALYSISCategorical Variables13 Chi-Square Goodness of Fit Test: Comparing Counts in a Single Variable with Two or More Categories Learning Objectives 13.1 Introduction to the Chi-Square Goodness of Fit Test 13.2 Calculating and Understanding the Chi-Square Statistic Real World Snapshot 13.3 Data Assumptions 13.4 Examples Using SPSS: Step-by-Step Instructions Example 13.1: Equal Expected Counts: The Significant Case SPSS Output Interpretation Data Screening Chi-Square Goodness of Fit Test Analysis Reporting Results Write-Up Example 13.2: Equal Expected Counts: The Nonsignificant Case SPSS Output Interpretation Data Screening Chi-Square Goodness of Fit Test Analysis Reporting Results Write-Up Example 13.3: Specified Expected Counts: Both Cases SPSS Output Interpretation Data Screening Chi-Square Goodness of Fit Analysis Reporting Significant Results Write-Up Reporting Nonsignificant Results Write-Up Summary of Key Concepts Chi-Square Goodness of Fit Test Applied Exercises 14 Chi-Square Test of Independence: Comparing Counts between Two Variables Each with Two or More Categories Learning Objectives 14.1 Introduction to the Chi-Square Test of Independence 14.2 Calculating and Understanding the Chi-Square Test of Independence 14.3 Data Assumptions Real World Snapshot 14.4 Examples Using SPSS: Step-by-Step Instructions Example 14.1: A 2 × 2 Chi-Square Test of Independence: The Significant Case SPSS Output Interpretation Data Screening Chi-Square Test of Independence Analysis Reporting Results Write-Up Example 14.2: A 2 × 2 Chi-Square Test of Independence: The Nonsignificant Case SPSS Output Interpretation Data Screening Chi-Square Test of Independence Analysis Reporting Results Write-Up Example 14.3: A 3 × 5 Chi-Square Test of Independence: Both Cases SPSS Output Interpretation Data Screening Chi-Square Test of Independence Analysis Reporting Significant Results Write-Up Reporting Nonsignificant Results Write-Up Summary of Key Concepts Chi-Square Test of Independence Applied Exercises 15 Chi-Square Test of the Same Sample: Comparing Counts of the Same Sample Measured Twice Using a Categorical Variable Learning Objectives 15.1 Introduction to the Same Sample Measured Twice Using a Categorical Variable 15.2 Data Assumptions Real World Snapshot 15.3 Examples Using SPSS: Step-by-Step Instructions Example 15.1: A Crosstabs 2 × 2 Repeated Measures McNemar Test: The Significant Case SPSS Output Interpretation Data ScreeningChi-Square Test for Repeated Counts Analysis Reporting Results Write-Up Example 15.2: A Crosstabs 2 × 2 Repeated Measures McNemar Test: The Nonsignificant Case SPSS Output Interpretation Data Screening Chi-Square Test for Repeated Counts Analysis Reporting Results Write-Up Example 15.3: A Crosstabs 4 × 2 Repeated Measures McNemar-Bowker Test: Both Cases SPSS Output Interpretation Data Screening Chi-Square Test for Repeated Counts Analysis Reporting Significant Results Write-Up Reporting Nonsignificant Results Write-Up Summary of Key Concepts Chi-Square Test of Two Related Samples Measured Twice Applied Exercises Numeric Variables16 T-Test: Comparing a Single Sample Mean to a Specific Value Learning Objectives 16.1 Introduction to the Single Sample T-Test 16.2 Confidence Interval for a Single Sample T-Test Real World Snapshot 16.3 Data Assumptions 16.4 Examples Using SPSS: Step-by-Step Instructions Example 16.1: Single Sample T-Tests: The Significant Case SPSS Output Interpretation Data Screening Single Sample T-Test Analysis Reporting Results Write-Up Example 16.2: Single Sample T-Tests: The Nonsignificant Case SPSS Output Interpretation Data Screening Single Sample T-Test Analysis Reporting Results Write-Up Summary of Key Concepts 16.5 Single Sample T-Test Applied Exercises 17 T-Test: Comparing Two Independent Samples’ Variable Means Learning Objectives 17.1 Introduction to the Two Independent Samples T-Test 17.2 Equality of Variance Real World Snapshot Pooled or Separate Two Independent Samples T-Test 17.3 Data Assumptions 17.4 Examples Using SPSS: Step-by-Step Instructions Example 17.1: Two Independent Samples T-Tests: The Significant Case SPSS Output Interpretation Data Screening Two Independent Samples T-Test Analysis Reporting Results Write-Up Example 17.2: Two Independent Samples T-Tests: The Nonsignificant Case SPSS Output Interpretation Data Screening Two Independent Samples T-Test Analysis Reporting Results Write-Up Summary of Key Concepts Two Independent Samples T-Test Applied Exercises 18 Analysis of Variance (ANOVA): Comparing More Than Two Independent Samples’ Means to Test for Differences among Them by One Type of Classification Learning Objectives 18.1 Introduction to One-Way ANOVA 18.2 Variance Real World Snapshot 18.3 Data Assumptions 18.4 Strategies for Addressing Violations of Assumptions 18.5 Examples Using SPSS: Step-by-Step Instructions Example 18.1: ANOVA F-Test: The Significant Case SPSS Output Interpretation Data Screening ANOVA (Analysis) Reporting Results Write-Up Example 18.2: ANOVA F-Test: The Nonsignificant Case SPSS Output Interpretation Data Screening ANOVA (Analysis) Reporting Results Write-Up Summary of Key Concepts One-Way ANOVA F-Test Applied Exercises 19 Paired T-Test: Comparing the Means of the Same Sample Measured Twice Using a Numeric Variable Learning Objectives 19.1 Introduction to the Paired-Sample T-Test 19.2 Paired T-Test Calculations Real World Snapshot 19.3 Data Assumptions 19.4 Examples Using SPSS: Step-by-Step Instructions Example 19.1: Paired-Sample T-Tests: The Significant Case SPSS Output Interpretation Data Screening Paired-Sample T-Test Analysis Reporting Results Write-Up Example 19.2: Single Sample T-Tests: The Nonsignificant Case SPSS Output Interpretation Data Screening Paired-Sample T-Test Analysis Reporting Results Write-Up Summary of Key Concepts Paired-Samples T-Test Applied Exercises 20 General Linear Model Repeated Measures: Comparing Means of the Same Sample Measured More Than Twice Using a Numeric Variable Learning Objectives 20.1 Introduction to General Linear Model Repeated Measures Real World Snapshot 20.2 Data Assumptions 20.3 Strategies for Addressing Violations of Assumptions 20.4 Examples Using SPSS: Step-by-Step Instructions Example 20.1: General Linear Model Repeated Measures: The Significant Case SPSS Output Interpretation Data Screening General Linear Model Repeated Measures Analysis Reporting Results Write-Up Example 20.2: General Linear Model Repeated Measures: The Nonsignificant Case SPSS Output Interpretation Data Screening General Linear Model Repeated Measures Analysis Reporting Results Write-Up Summary of Key Concepts General Linear Model Repeated Measures Applied Exercises 21 Correlation Analysis: Looking for an Association between Two Variables Learning Objectives 21.1 Introduction to Pearson, Spearman, and Partial Bivariate Correlations Explained Variance (r2) 21.2 Strength and Directionality of Correlations Correlation Strength Correlation Directionality Linear Correlation Strength and Directionality Together 21.3 Calculating a Correlation for Numeric Data Real World Snapshot 21.4 Types of Correlations 21.5 General Data Assumptions 21.6 Examples Using SPSS: Step-by-Step Instructions Example 21.1: Pearson Correlation: The Significant Case SPSS Output Interpretation Data Screening Pearson Correlation Analysis Reporting Results Write-Up Example 21.2: Pearson Correlation: The Nonsignificant Case SPSS Output Interpretation Data Screening Pearson Correlation Analysis Reporting Results Write-Up Example 21.3: Spearman Correlation: Both Cases SPSS Output Interpretation Data Screening Spearman Correlation Analysis Reporting Significant Results Write-Up Reporting Nonsignificant Results Write-Up Example 21.4: Partial Correlation: Both Cases SPSS Output Interpretation Data Screening Partial Correlation Analysis Reporting Nonsignificant Results Write-Up Reporting Significant Results Write-Up Summary of Key Concepts Correlation Analysis Applied Exercises 22 Single Linear Regression Learning Objectives 22.1 Introduction to Single Linear Regression Prediction vs. Cause and Effect 22.2 Prediction Model Applying the Prediction Model Standardized Regression Coefficients Real World Snapshot 22.3 Data Assumptions Testing Data Assumptions 22.4 Examples Using SPSS: Step-by-Step Instructions Example 22.1: Single Linear Regression: The Significant Case SPSS Output Interpretation Data Screening Single Linear Regression Analysis Reporting Results Write-Up Example 22.2: Single Linear Regression: The Nonsignificant Case SPSS Output Interpretation Data Screening Single Linear Regression Analysis Reporting Results Write-Up Summary of Key Concepts Single Linear Regression Applied Exercises 23 Multiple Linear Regression Learning Objectives 23.1 Introduction to Multiple Linear Regression 23.2 Prediction Model R-Square and Adjusted R-Square Real World Snapshot 23.3 Data Assumptions 23.4 Examples Using SPSS: Step-by-Step Instructions Example 23.1: Multiple Linear Regression: The Significant Case SPSS Output Interpretation Data Screening Multiple Linear Regression Analysis Reporting Results Write-Up Example 23.2: Multiple Linear Regression: The Nonsignificant Case SPSS Output Interpretation Data Screening Multiple Linear Regression Analysis Reporting Results Write-Up Summary of Key Concepts Multiple Linear Regression Applied Exercises APPENDICESAppendix A: Glossary Appendix B: Chapter Statistical Exercise Solutions B.1 Chapter 1 B.2 Chapter 2 B.3 Chapter 3 B.4 Chapter 4 B.5 Chapter 5 B.6 Chapter 6 B.7 Chapter 7 B.8 Chapter 8 B.9 Chapter 9 B.10 Chapter 10 B.11 Chapter 11 B.12 Chapter 12 B.13 Chapter 13 B.14 Chapter 14 B.15 Chapter 15 B.16 Chapter 16 B.17 Chapter 17 B.18 Chapter 18 B.19 Chapter 19 B.20 Chapter 20 B.21 Chapter 21 B.22 Chapter 22 B.23 Chapter 23 Appendix C: Case Studies and Solutions C.1 Case Study Questions Financial Attributes Gift Shop Customers Health Issues Moving Services Sample Size Matters Violent Crime Recidivism What Motivates Students to Perform Psychological Effects of the Workplace C.2 Case Study Solutions Financial Attributes Gift Shop Customers Health Issues Moving Services Sample Size Matters Violent Crime Recidivism What Motivates Students to Perform Psychological Effects of the Workplace Appendix D: Research Goal and Objectives D.1 Research Goal E.2 Research Objectives Developing and Testing Research Statements Developing and Answering Research Questions D.3 The Interconnected Parts of Research Goals and Objectives Appendix E: Types of Research Design E.1 Introduction to Research Designs E.2 Survey or Self-Report Research Design Person-to-Person Administered Survey Self-Administered Survey E.3 Experimental Research Design Cause and Effect Relationship Lab Experiment Field Experiment Manipulation Check External Influences Managing the Effects of Unaccounted for Extraneous Variables The Experimental Design Process Model E.4 Observational Research Design Personal Observation Mechanical Observation Content Analysis E.5 Other Research Designs Single Time vs. Repeated Measures Designs Cross-Sectional Design Longitudinal Design Mixed Research Designs Appendix F: Comparing Counts of the Same Sample Measured More ThanTwice Using a Categorical Variable F.1 A Categorical Variable Measured More Than Twice Using the Same Sample F.2 Data Assumptions Appendix G: More on Linear Regression G.1 Introduction to Other Tools in Regression Analysis G.2 The Influence of Outliers on Linear Regression Results G.3 Linear Regression Methods Stepwise Hierarchical G.4 Dummy Coding G.5 Interaction Terms (Variables) G.6 Residual Analysis G.7 Multicollinearity Appendix H: Statistics Flow Chart References Index