Applied Statistics I - International Student Edition

1. Evaluating Numeric 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 Non-experimental Research Design Quasi- Experimental 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 2 A: More About Levels of Measurement Appendix 2 B: Justification for 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 3 A: Getting Started in IBM SPSS (R) version 25 Appendix 3 B: Missing Values in Frequency Tables Appendix 3 C: 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: 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 4 A Order of Arithmetic Operations Appendix 4 B Rounding 5. Graphs: Bar Charts, Histograms, and Box Plots 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 Box Plot (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 Original Units of X Understanding Values of z Qualitative Description of Normal Distribution Shape More Precise Description of Normal Distribution Shape 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 Reporting Information About Distribution Shape, Missing Values, Outliers, and Descriptive Statistics for Quantitative Variables Summary Appendix 6 A: The Mathematics of the Normal Distribution Appendix 6 B: How to Select and Remove Outliers in SPSS Appendix 6 C: Quantitative Assessments of Departure from Normality Appendix 6 D: Why Are Some Real-World Variables Approximately Normally Distributed? 7. Sampling Error and Confidence Intervals Descriptive Versus Inferential Uses of Statistics Notations 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 Effect of N on Value of the Population Standard Error Describing the Location of a Single Outcome for M Relative to a Population Sampling Distribution (Setting Up a z Ratio) What We Do When ?? 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 CIs 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 (?) Level Specifying Reject Regions Based on ?, 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 Example: Mean Driving Speed (Nondirectional Test) SPSS Analysis: One Sample t Test for Mean Driving Speed "Exact" p Values Reporting Results for a Two-tailed One-Sample t Test The Driving Speed Data Reconsidered Using a One-Tailed Test Reporting Results for a One-tailed One-Sample t Test: Advantages/ 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 of Type I Error From Multiple Tests Interpretation of Null Outcomes 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 9 A Further Explanation of Statistical Power 10. Bivariate Pearson Correlation Research Situations Where Pearson r Is Used Correlation and Causal Inference How Sign and Magnitude of r Describe an X, Y Relationship Setting Up Scatter Plots With Examples of Perfect Linearity Most Associations Are Not Perfect Different Situations In Which r = 0 Assumptions for Use of Pearson r Preliminary Data Screening for Pearson r Effect of Extreme Bivariate Outliers Research Example Data Screening for Research Example Computation of Pearson r How Computation for Correlation Is Related to Pattern of Data Points in the Scatter Plot Testing the Hypothesis That ?0 = 0 Reporting Many Correlations and Inflated Risk of Type I Error Obtaining CIs for Correlations Pearson's r and r2 as Effect-Size Indexes and Partition of Variance Statistical Power and Sample Size for Correlation Studies Interpretation of Outcomes for Pearson's r SPSS Example Results Sections for One and Several Pearson r Values Reasons to Be Skeptical of Correlations Summary Appendix 10 A: Nonparametric Alternatives to Pearson r Appendix 10 B: Setting Up a 95% CI for Pearson r Appendix 10 C: Testing Significance of Differences Between Correlations Appendix 10 D: Factors That Artifactually Influence the Magnitude of Pearson's r Appendix 10 E: Analysis of Non Linear Relationships 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 Plotting the Regression Line: Salary Data Results Section: Salary Data Using Regression Equation to Predict Score for Individual: Joe's Hr Data Partition of SS in Bivariate Regression: Joe's Hr Data Issues in Planning a Bivariate Regression Study Plotting Residuals Standard Error of the Estimate, sy.x Summary Appendix 11 A OLS Derivation of Equation for Regression Coefficients Appendix 11 B Fully Worked Example for SS values: Joe's HR Data 12. The Independent Samples t Test Research Situations Where the Independent Samples t Test is Used Hypothetical Research Example Assumptions for Use of the 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 12 A: A Nonparametric Alternative to the Independent Samples t Test 13. One-Way Between-S Analysis of Variance Research Situations Where Between-S 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 (CIs) 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 Procedure 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 A ANOVA Model and Division of Scores Into Components Appendix B Expected Value of F When H0 is True Appendix C Comparison of ANOVA to t Test Appendix D Nonparametric Alternative to One Way Between S ANOVA 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 of Results For Independent Samples t and Paired Samples t Tests Effect Size and Power Some Design Problems in Repeated Measures Designs Results for Paired Samples t-Test: Stress and HR Further Evaluation of Assumptions for Larger Dataset Summary Appendix A Nonparametric Alternative to Paired Samples t: Wilcoxon Signed Rank Test 15. One Way Repeated Measures ANOVA 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 for 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 15 A Test for Person by Treatment Interaction 16. Factorial Analysis of Variance (Between - S) 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, df, and MS in Two Way Factorial 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 16 A: Unequal Cell ns in Factorial ANOVA Appendix 16 B: Weighted Versus Unweighted Means Appendix 16 C: Model for Factorial ANOVA Appendix 16 D: Fixed Versus Random Factors 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 True Computation of Chi Squared Significance Test Evaluation of Statistical Significance of ?2. 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 17 A: Margin of Error For Percentages in Surveys Appendix 17 B: Contingency Tables With Repeated Measures: McNemar Test Appendix 17 C: Fisher Exact Test Appendix 17 D: How Marginal Distributions for X and Y Constrain Maximum Value of ?? Appendix 17 E: Other Uses of ?2 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 Degrees of Belief