DETAILED CONTENTS PART I INTRODUCTION AND DESCRIPTIVE STATISTICS. 1. Introduction to Statistics

Transcription

1 DETAILED CONTENTS About the Author Preface to the Instructor To the Student How to Use SPSS With This Book PART I INTRODUCTION AND DESCRIPTIVE STATISTICS 1. Introduction to Statistics 1.1 Descriptive and Inferential Statistics Descriptive Statistics Inferential Statistics MAKING SENSE Populations and Samples 1.2 Statistics in Research Experimental Method Quasi-Experimental Method Correlational Method 1.3 Scales of Measurement Nominal Scales Ordinal Scales Interval Scales Ratio Scales 1.4 Types of Data Continuous and Discrete Variables Quantitative and Qualitative Variables 1.5 Research in Focus: Types of Data and Scales of Measurement 1.6 SPSS in Focus: Entering and Defining Variables v

2 vi STATISTICS FOR THE BEHAVIORAL SCIENCES 2. Summarizing Data: Tables, Graphs, and Distributions 2.1 Why Summarize Data? 2.2 Frequency Distributions for Grouped Data Simple Frequency Distributions Cumulative Frequency Relative Frequency Relative Percent Cumulative Relative Frequency and Cumulative Percent 2.3 SPSS in Focus: Frequency Distributions for Quantitative Data 2.4 Frequency Distributions for Ungrouped Data 2.5 Research in Focus: Summarizing Demographic Information 2.6 SPSS in Focus: Frequency Distributions for Categorical Data 2.7 Pictorial Frequency Distributions 2.8 Graphing Distributions: Continuous Data Histograms Frequency Polygons Ogives Stem-and-Leaf Displays 2.9 Graphing Distributions: Discrete and Categorical Data Bar Charts Pie Charts Scatter Grams 2.10 Research in Focus: Frequencies and Percents 2.11 SPSS in Focus: Histograms, Bar Charts, and Pie Charts 3. Summarizing Data: Central Tendency 3.1 Introduction to Central Tendency 3.2 Measures of Central Tendency The Mean The Weighted Mean MAKING SENSE Making the Grade The Median The Mode

3 Detailed Contents vii 3.3 Characteristics of the Mean Changing an Existing Score Adding a New Score or Removing an Existing Score Adding, Subtracting, Multiplying, or Dividing Each Score by a Constant Summing the Differences of Scores From Their Mean Summing the Squared Differences of Scores From Their Mean 3.4 Choosing an Appropriate Measure of Central Tendency Using the Mean to Describe Data Using the Median to Describe Data Using the Mode to Describe Data 3.5 Research in Focus: Describing Central Tendency 3.6 SPSS in Focus: Mean, Median, and Mode 4. Summarizing Data: Variability 4.1 Measuring Variability 4.2 Range and Midrange 4.3 Research in Focus: Reporting the Range 4.4 Measures of Variability: Quartiles and Interquartiles 4.5 Research in Focus: The Midrange of Behavior 4.6 The Variance Population Variance Sample Variance 4.7 Explaining Variance for Populations and Samples The Numerator: Why Square Deviations From the Mean? The Denominator: Sample Variance as an Unbiased Estimator The Denominator: Degrees of Freedom 4.8 The Computational Formula for Variance 4.9 The Standard Deviation 4.10 What Does the Standard Deviation Tell Us? MAKING SENSE Standard Deviation and Nonnormal Distributions 4.11 Characteristics of the Standard Deviation

4 viii STATISTICS FOR THE BEHAVIORAL SCIENCES 4.12 SPSS in Focus: Range, Variance, and Standard Deviation PART II PROBABILITY AND THE FOUNDATIONS OF INFERENTIAL STATISTICS 5. Probability 5.1 Introduction to Probability 5.2 Calculating Probability 5.3 Probability and Relative Frequency 5.4 The Relationship Between Multiple Outcomes Mutually Exclusive Outcomes Independent Outcomes Complementary Outcomes Conditional Outcomes 5.5 Conditional Probabilities and Bayes Theorem 5.6 SPSS in Focus: Probability Tables Construct a Probability Table Construct a Conditional Probability Table 5.7 Probability Distributions 5.8 The Mean of a Probability Distribution and Expected Value MAKING SENSE Expected Values and the Long-Term Mean 5.9 Research in Focus: When Are Risks Worth Taking? 5.10 The Variance and Standard Deviation of a Probability Distribution 5.11 Expected Value and the Binomial Distribution The Mean of a Binomial Distribution The Variance and Standard Deviation of a Binomial Distribution 5.12 A Final Thought on the Likelihood of Random Behavioral Outcomes

5 Detailed Contents ix 6. Probability and Normal Distributions 6.1 The Normal Distribution in Behavioral Science 6.2 Characteristics of the Normal Distribution 6.3 Research in Focus: The Statistical Norm 6.4 The Standard Normal Distribution 6.5 The Unit Normal Table: A Brief Introduction 6.6 Locating Proportions Locating Proportions Above the Mean Locating Proportions Below the Mean Locating Proportions Between Two Values 6.7 Locating Scores 6.8 SPSS in Focus: Converting Raw Scores to Standard z-scores MAKING SENSE Standard Deviation and the Normal Distribution 6.9 Going From Binomial to Normal 6.10 The Normal Approximation to the Binomial Distribution 7. Probability and Sampling Distributions 7.1 Selecting Samples From Populations Inferential Statistics and Sampling Distributions Sampling and Conditional Probabilities 7.2 Selecting a Sample: Who s in and Who s out? Sampling Strategy: The Basis for Statistical Theory Sampling Strategy: Most Used in Behavioral Research 7.3 Sampling Distributions: The Mean Unbiased Estimator

6 x STATISTICS FOR THE BEHAVIORAL SCIENCES Central Limit Theorem Minimum Variance Overview of the Sample Mean 7.4 Sampling Distributions: The Variance Unbiased Estimator Skewed Distribution Rule No Minimum Variance MAKING SENSE Minimum Variance Versus Unbiased Estimator Overview of the Sample Variance 7.5 The Standard Error of the Mean 7.6 Factors that Decrease Standard Error 7.7 SPSS in Focus: Estimating the Standard Error of the Mean 7.8 APA in Focus: Reporting the Standard Error 7.9 Standard Normal Transformations With Sampling Distributions PART III MAKING INFERENCES ABOUT ONE OR TWO MEANS 8. Introduction to Hypothesis Testing 8.1 Inferential Statistics and Hypothesis Testing 8.2 Four Steps to Hypothesis Testing MAKING SENSE Testing the Null Hypothesis 8.3 Hypothesis Testing and Sampling Distributions 8.4 Making a Decision: Types of Error Decision: Retain the Null Decision: Reject the Null 8.5 Testing a Research Hypothesis: Examples Using the z Test Nondirectional, Two-Tailed, Hypothesis Tests Directional, Upper-Tail Critical, Hypothesis Tests Directional, Lower-Tail Critical, Hypothesis Tests 8.6 Research in Focus: Directional Versus Nondirectional Tests 8.7 Measuring the Size of an Effect: Cohen s d

7 Detailed Contents xi 8.8 Effect Size, Power, and Sample Size The Relationship Between Effect Size and Power The Relationship Between Sample Size and Power 8.9 Additional Factors That Increase Power Increasing Power: Increase Effect Size, Sample Size, and Alpha Increase power: Decrease Beta, Standard Deviation (s), and Standard Error 8.10 SPSS in Focus: A Preview for Chapters 9 to APA in Focus: Reporting the Test Statistic and Effect Size 9. Testing Means: Independent Sample t Tests 9.1 Going From z to t 9.2 The Degrees of Freedom 9.3 Reading the t Table 9.4 One Independent Sample t Test 9.5 Effect Size for the One Independent Sample t Test Estimated Cohen s d Proportion of Variance 9.6 SPSS in Focus: One Independent Sample t Test 9.7 Two Independent Sample t Test MAKING SENSE The Pooled Sample Variance 9.8 Effect Size for the Two Independent Sample t Test Estimated Cohen s d Proportion of Variance 9.9 SPSS in Focus: Two Independent Sample t Test 9.10 APA in Focus: Reporting the t Statistic and Effect Size

8 xii STATISTICS FOR THE BEHAVIORAL SCIENCES 10. Testing Means: Related Samples t Test 10.1 Related and Independent Samples Repeated-Measures Design Matched-Pairs Design 10.2 Introduction to the Related Samples t Test The Test Statistic Degrees of Freedom Assumptions 10.3 Related Samples t Test: Repeated-Measures Design MAKING SENSE Increasing Power by Reducing Error 10.4 SPSS in Focus: The Related Samples t Test 10.5 Related Samples t Test: Matched-Pairs Design 10.6 Measuring Effect Size for the Related Samples t Test Estimated Cohen s d Proportion of Variance 10.7 Advantages for Selecting Related Samples 10.8 APA in Focus: Reporting the t Statistic and Effect Size for Related Samples 11. Estimation and Confidence Intervals 11.1 Point Estimation and Interval Estimation 11.2 The Process of Estimation 11.3 Estimation for the One Independent Sample z Test MAKING SENSE Estimation, Significance, and Effect Size 11.4 Estimation for the One Independent Sample t Test 11.5 SPSS in Focus: Confidence Intervals for the One Independent Sample t Test 11.6 Estimation for the Two Independent Sample t Test 11.7 SPSS in Focus: Confidence Intervals for the Two Independent Sample t Test 11.8 Estimation for the Related Samples t Test

9 Detailed Contents xiii 11.9 SPSS in Focus: Confidence Intervals for the Related Samples t Test Characteristics of Estimation: Precisions and Certainty APA in Focus: Reporting Confidence Intervals PART IV MAKING INFERENCES ABOUT THE VARIABILITY OF TWO OR MORE MEANS 12. Analysis of Variance: One-Way Between-Subjects Design 12.1 Increasing k: A Shift to Analyzing Variance 12.2 An Introduction to Analysis of Variance Identifying the Type of ANOVA Two Ways to Select Independent Samples Changes in Notation 12.3 Sources of Variation and the Test Statistic 12.4 Degrees of Freedom 12.5 The One-Way Between-Subjects ANOVA MAKING SENSE Mean Squares and Variance 12.6 What Is the Next Step? 12.7 Post Hoc Comparisons Fisher s Least Significant Difference (LSD) Test Tukey s Honestly Significant Difference (HSD) Test 12.8 SPSS in Focus: The One-Way Between-Subjects ANOVA 12.9 Measuring Effect Size Eta-Squared (η 2 or R 2 ) Omega-Squared (ω 2 ) APA in Focus: Reporting the F Statistic, Significance, and Effect Size

10 xiv STATISTICS FOR THE BEHAVIORAL SCIENCES 13. Analysis of Variance: One-Way Within-Subjects Design 13.1 Observing the Same Participants Across Groups The One-Way Within-Subjects ANOVA Selecting Related Samples: The Within-Subjects Design 13.2 Sources of Variation and the Test Statistic Between Groups Variation Error Variation MAKING SENSE Sources of Error 13.3 Degrees of Freedom 13.4 The One-Way Within-Subjects ANOVA MAKING SENSE Mean Squares and Variance 13.5 Post Hoc Comparison: Bonferroni Procedure 13.6 SPSS in Focus: The One-Way Within-Subjects ANOVA 13.7 Measuring Effect Size Partial Eta-Squared (η 2 P ) Partial Omega-Squared (ω 2 P ) 13.8 The Within-Subjects Design: Consistency and Power 13.9 APA in Focus: Reporting the F Statistic, Significance, and Effect Size 14. Analysis of Variance: Two-Way Between-Subjects Factorial Design 14.1 Observing Two Factors at the Same Time 14.2 New Terminology and Notation 14.3 Designs for the Two-Way ANOVA 2-Between or Between-Subjects Design 1-Between 1-Within or Mixed Design 2-Within or Within-Subjects Design

11 Detailed Contents xv 14.4 Describing Variability: Main Effects and Interactions Sources of Variability Testing Main Effects Testing the Interaction MAKING SENSE Graphing Interactions Outcomes and Order of Interpretation 14.5 The Two-Way Between-Subjects ANOVA 14.6 Analyzing Main Effects and Interactions Interactions: Simple Main Effect Tests Main Effects: Pairwise Comparisons 14.7 Measuring Effect Size Eta-Squared (η 2 or R 2 ) Omega-Squared (ω 2 ) 14.8 SPSS in Focus: The Two-Way Between-Subjects ANOVA 14.9 APA in Focus: Reporting Main Effects, Interactions, and Effect Size PART V MAKING INFERENCES ABOUT PATTERNS, FREQUENCIES, AND ORDINAL DATA 15. Correlation 15.1 Treating Factors as Dependent Measures 15.2 Describing a Correlation The Direction of a Correlation The Strength of a Correlation 15.3 Pearson Correlation Coefficient MAKING SENSE Understanding Covariance Effect Size: The Coefficient of Determination Hypothesis Testing: Testing for Significance 15.4 SPSS in Focus: Pearson Correlation Coefficient 15.5 Assumptions of Tests for Linear Correlations Homoscedasticity Linearity Normality

12 xvi STATISTICS FOR THE BEHAVIORAL SCIENCES 15.6 Limitations in Interpretation Causality Outliers Restriction of Range 15.7 Alternative to Pearson r: Spearman Correlation Coefficient 15.8 SPSS in Focus: Spearman Correlation Coefficient 15.9 Alternative to Pearson r: Point-Biserial Correlation Coefficient SPSS in Focus: Point-Biserial Correlation Coefficient Alternative to Pearson r: Phi Correlation Coefficient SPSS in Focus: Phi Correlation Coefficient APA in Focus: Reporting Correlations 16. Linear Regression 16.1 From Relationships to Predictions 16.2 Fundamentals of Linear Regression 16.3 What Makes the Regression Line the Best Fitting Line 16.4 The Slope and y Intercept of a Straight Line 16.5 Using the Method of Least Squares to Find the Best Fit MAKING SENSE SP, SS, and the Slope of a Regression Line 16.6 Using Analysis of Regression to Measure Significance 16.7 SPSS in Focus: Analysis of Regression 16.8 Using the Standard Error of Estimate to Measure Accuracy 16.9 Multiple Regression APA in Focus: Reporting Regression Analysis

13 Detailed Contents xvii 17. Nonparametric Tests: Chi-Square Tests 17.1 Tests for Nominal Data 17.2 The Chi-Square Goodness-of-Fit Test The Test Statistic MAKING SENSE The Relative Size of a Discrepancy The Degrees of Freedom MAKING SENSE Degrees of Freedom Hypothesis Testing for Goodness of Fit 17.3 SPSS in Focus: The Chi-Square Goodness-of-Fit Test 17.4 Interpreting the Chi-Square Goodness-of-Fit Test Interpreting a Significant Chi-Square Goodness-of-Fit Test Using the Chi-Square Goodness-of-Fit Test to Support the Null Hypothesis 17.5 Independent Observations and Expected Frequency Size 17.6 The Chi-Square Test for Independence Determining Frequencies Expected The Test Statistic The Degrees of Freedom Hypothesis Testing for Independence 17.7 The Relationship Between Chi-Square and the Phi Coefficient 17.8 Using the Phi Coefficient as a Measure for Effect Size Effect Size Using Proportion of Variance Effect Size Using the Phi Coefficient Effect Size Using Cramer s V 17.9 SPSS in Focus: The Two-Way Chi-Square Test for Independence APA in Focus: Reporting the Chi-Square Test 18. Nonparametric Tests: Tests for Ordinal Data 18.1 Tests for Ordinal Data Scales of Measurement and Variance MAKING SENSE Reducing Variability Minimizing Bias: Tied Ranks

14 xviii STATISTICS FOR THE BEHAVIORAL SCIENCES 18.2 The Sign Test One-Sample Sign Test Related Samples Sign Test The Normal Approximation for the Sign Test 18.3 SPSS in Focus: The Related Samples Sign Test The Wilcoxon Signed-Ranks T Test Interpretation of the Test Statistic T The Normal Approximation for the Wilcoxon T 18.5 SPSS in Focus: The Wilcoxon Signed-Ranks T Test 18.6 The Mann-Whitney U Test Interpretation of the Test Statistic U Computing the Test Statistic U The Normal Approximation for U 18.7 SPSS in Focus: The Mann-Whitney U Test 18.8 The Kruskal-Wallis H Test Interpretation of the Test Statistic H 18.9 SPSS in Focus: The Kruskal-Wallis H Test The Friedman Test Interpretation of the Test Statistic χ 2 R SPSS in Focus: The Friedman Test APA in Focus: Reporting Nonparametric Tests Appendix A. Mathematics in Statistics A.1 Positive and Negative Numbers A.2 Addition A.3 Subtraction A.4 Multiplication A.5 Division A.6 Fractions A.7 Decimals and Percents A.8 Exponents and Roots A.9 Order of Computation

15 Detailed Contents xix A.10 Equations: Solving for x A.11 Summation Notation Appendix B. Statistical Tables Table B.1 Unit Normal Table Table B.2 The t Table Table B.3 The F Table Table B.4 Studentized Range Statistic Table Table B.5 The Pearson Correlation Table Table B.6 The Spearman Correlation Table Table B.7 The Chi-Square Table Table B.8 Binomial Probability Distribution Table Table B.9 The Wilcoxon T Table Table B.10 The Mann-Whitney U Table Appendix C. Chapter Solutions for Even-Numbered Problems Glossary References Index