Statistics Alive!

List of Figures
List of Tables
Preface
Supplemental Material for Use With Statistics Alive!
Acknowledgments
About the Authors
PART I. PRELIMINARY INFORMATION: "FIRST THINGS FIRST"
Module 1. Math Review, Vocabulary, and Symbols
Getting Started
Common Terms and Symbols in Statistics
Fundamental Rules and Procedures for Statistics
More Rules and Procedures
Module 2. Measurement Scales
What Is Measurement?
Scales of Measurement
Continuous Versus Discrete Variables
Real Limits
PART II. TABLES AND GRAPHS: "ON DISPLAY"
Module 3. Frequency and Percentile Tables
Why Use Tables?
Frequency Tables
Relative Frequency or Percentage Tables
Grouped Frequency Tables
Percentile and Percentile Rank Tables
SPSS Connection
Module 4. Graphs and Plots
Why Use Graphs?
Graphing Continuous Data
Symmetry, Skew, and Kurtosis
Graphing Discrete Data
SPSS Connection
PART III. CENTRAL TENDENCY: "BULL'S-EYE"
Module 5. Mode, Median, and Mean
What Is Central Tendency?
Mode
Median
Mean
Skew and Central Tendency
SPSS Connection
PART IV. DISPERSION: "FROM HERE TO ETERNITY"
Module 6. Range, Variance, and Standard Deviation
What Is Dispersion?
Range
Variance
Standard Deviation
Mean Absolute Deviation
Controversy: N Versus n - 1
SPSS Connection
PART V. THE NORMAL CURVE AND STANDARD SCORES: "WHAT'S THE SCORE?"
Module 7. Percent Area and the Normal Curve
What Is a Normal Curve?
History of the Normal Curve
Uses of the Normal Curve
Looking Ahead
Module 8. z Scores
What Is a Standard Score?
Benefits of Standard Scores
Calculating z Scores
Comparing Scores Across Different Tests
SPSS Connection
Module 9. Score Transformations and Their Effects
Why Transform Scores?
Effects on Central Tendency
Effects on Dispersion
A Graphic Look at Transformations
Summary of Transformation Effects
Some Common Transformed Scores
Looking Ahead
PART VI. PROBABILITY: "ODDS ARE"
Module 10. Probability Definitions and Theorems
Why Study Probability?
Probability as a Proportion
Equally Likely Model
Mutually Exclusive Outcomes
Addition Theorem
Independent Outcomes
Multiplication Theorem
A Brief Review
Probability and Inference
Module 11. The Binomial Distribution
What Are Dichotomous Events?
Finding Probabilities by Listing and Counting
Finding Probabilities by the Binomial Formula
Finding Probabilities by the Binomial Table
Probability and Experimentation
Looking Ahead
Nonnormal Data
PART VII. INFERENTIAL THEORY: "OF TRUTH AND RELATIVITY"
Module 12. Sampling, Variables, and Hypotheses
From Description to Inference
Sampling
Variables
Hypotheses
Module 13. Errors and Significance
Random Sampling Revisited
Sampling Error
Significant Difference
The Decision Table
Type I Error
Type II Error
Module 14. The z Score as a Hypothesis Test
Inferential Logic and the z Score
Constructing a Hypothesis Test for a z Score
Looking Ahead
PART VIII. THE ONE-SAMPLE TEST: "ARE THEY FROM OUR PART OF TOWN?"
Module 15. Standard Error of the Mean
Central Limit Theorem
Sampling Distribution of the Mean
Calculating the Standard Error of the Mean
Sample Size and the Standard Error of the Mean
Looking Ahead
Module 16. Normal Deviate Z Test
Prototype Logic and the Z Test
Calculating a Normal Deviate Z Test
Examples of Normal Deviate Z Tests
Decision Making With a Normal Deviate Z Test
Looking Ahead
Module 17. One-Sample t Test
Z Test Versus t Test
Comparison of Z-Test and t-Test Formulas
Degrees of Freedom
Biased and Unbiased Estimates
When Do We Reject the Null Hypothesis?
One-Tailed Versus Two-Tailed Tests
The t Distribution Versus the Normal Distribution
The t Table Versus the Normal Curve Table
Calculating a One-Sample t Test
Interpreting a One-Sample t Test
Looking Ahead
SPSS Connection
Module 18. Interpreting and Reporting One-Sample t: Error, Confidence, and Parameter Estimates
What It Means to Reject the Null
Refining Error
Decision Making With a One-Sample t Test
Dichotomous Decisions Versus Reports of Actual p
Parameter Estimation: Point and Interval
SPSS Connection
PART IX. THE TWO-SAMPLE TEST: "OURS IS BETTER THAN YOURS"
Module 19. Standard Error of the Difference Between the Means
One-Sample Versus Two-Sample Studies
Sampling Distribution of the Difference Between the Means
Calculating the Standard Error of the Difference Between the Means
Importance of the Size of the Standard Error of the Difference Between the Means
Looking Ahead
Module 20. t Test With Independent Samples and Equal Sample Sizes
A Two-Sample Study
Inferential Logic and the Two-Sample t Test
Calculating a Two-Sample t Test
Interpreting a Two-Sample t Test
Looking Ahead
SPSS Connection
Module 21. t Test With Unequal Sample Sizes
What Makes Sample Sizes Unequal?
Comparison of Special-Case and Generalized Formulas
Calculating a t Test With Unequal Sample Sizes
Interpreting a t Test With Unequal Sample Sizes
SPSS Connection
Module 22. t Test With Related Samples
What Makes Samples Related?
Comparison of Special-Case and Related-Samples Formulas
Advantage and Disadvantage of Related Samples
Direct-Difference Formula
Calculating a t Test With Related Samples
Interpreting a t Test With Related Samples
SPSS Connection
Module 23. Interpreting and Reporting Two-Sample t: Error, Confidence, and Parameter Estimates
What Is Confidence?
Refining Error and Confidence
Decision Making With a Two-Sample t Test
Dichotomous Decisions Versus Reports of Actual p
Parameter Estimation: Point and Interval
SPSS Connection
PART X. THE MULTISAMPLE TEST: "OURS IS BETTER THAN YOURS OR THEIRS"
Module 24. ANOVA Logic: Sums of Squares, Partitioning, and Mean Squares
When Do We Use ANOVA?
ANOVA Assumptions
Partitioning of Deviation Scores
From Deviation Scores to Variances
From Variances to Mean Squares
From Mean Squares to F
Looking Ahead
Module 25. One-Way ANOVA: Independent Samples and Equal Sample Sizes
What Is a One-Way ANOVA?
Inferential Logic and ANOVA
Deviation Score Method
Raw Score Method
Remaining Steps for Both Methods: Mean Squares and F
Interpreting a One-Way ANOVA
The ANOVA Summary Table
SPSS Connection
PART XI. POST HOC TESTS: "SO WHO'S RESPONSIBLE?"
Module 26. Tukey HSD Test
Why Do We Need a Post Hoc Test?
Calculating the Tukey HSD
Interpreting the Tukey HSD
SPSS Connection
Module 27. Scheffe Test
Why Do We Need a Post Hoc Test?
Calculating the Scheffe
Interpreting the Scheffe
SPSS Connection
PART XII. MORE THAN ONE INDEPENDENT VARIABLE: "DOUBLE DUTCH JUMP ROPE"
Module 28. Main Effects and Interaction Effects
What Is a Factorial ANOVA?
Factorial ANOVA Designs
Number and Type of Hypotheses
Main Effects
Interaction Effects
Looking Ahead
Module 29. Factorial ANOVA
Review of Factorial ANOVA Designs
Data Setup and Preliminary Expectations
Sums of Squares Formulas
Calculating Factorial ANOVA Sums of Squares: Raw Score Method
Factorial Mean Squares and Fs
Interpreting a Factorial F Test
The Factorial ANOVA Summary Table
SPSS Connection
PART XIII. NONPARAMETRIC STATISTICS: "WITHOUT FORM OR VOID"
Module 30. One-Variable Chi-Square: Goodness of Fit
What Is a Nonparametric Test?
Chi-Square as a Goodness-of-Fit Test
Formula for Chi-Square
Inferential Logic and Chi-Square
Calculating a Chi-Square Goodness of Fit
Interpreting a Chi-Square Goodness of Fit
Looking Ahead
SPSS Connection
Module 31. Two-Variable Chi-Square: Test of Independence
Chi-Square as a Test of Independence
Prerequisites for a Chi-Square Test of Independence
Formula for a Chi-Square
Finding Expected Frequencies
Calculating a Chi-Square Test of Independence
Interpreting a Chi-Square Test of Independence
SPSS Connection
PART XIV. EFFECT SIZE AND POWER: "HOW MUCH IS ENOUGH?"
Module 32. Measures of Effect Size
What Is Effect Size?
For Two-Sample t Tests
For ANOVA F Tests
For Chi-Square Tests
Module 33. Power and the Factors Affecting It
What Is Power?
Factors Affecting Power
Putting It Together: Alpha, Power, Effect Size, and Sample Size
Looking Ahead
PART XV. CORRELATION: "WHITHER THOU GOEST, I WILL GO"
Module 34. Relationship Strength and Direction
Experimental Versus Correlational Studies
Plotting Correlation Data
Relationship Strength
Relationship Direction
Linear and Nonlinear Relationships
Outliers and Their Effects
Looking Ahead
SPSS Connection
Module 35. Pearson r
What Is a Correlation Coefficient?
Calculation of a Pearson r
Formulas for Pearson r
z-Score Scatterplots and r
Calculating Pearson r: Deviation Score Method
Interpreting a Pearson r Coefficient
Looking Ahead
SPSS Connection
Module 36. Correlation Pitfalls
Effect of Sample Size on Statistical Significance
Statistical Significance Versus Practical Importance
Effect of Restriction in Range
Effect of Sample Heterogeneity or Homogeneity
Effect of Unreliability in the Measurement Instrument
Correlation Versus Causation
PART XVI. LINEAR PREDICTION: "YOU'RE SO PREDICTABLE"
Module 37. Linear Prediction
Correlation Permits Prediction
Logic of a Prediction Line
Equation for the Best-Fitting Line
Using a Prediction Equation to Predict Scores on Y
Another Calculation Example
SPSS Connection
Module 38. Standard Error of Prediction
What Is a Confidence Interval?
Correlation and Prediction Error
Distribution of Prediction Error
Calculating the Standard Error of Prediction
Using the Standard Error of Prediction to Calculate Confidence Intervals
Factors Influencing the Standard Error of Prediction
Another Calculation Example
Module 39. Introduction to Multiple Regression
What Is Regression?
Prediction Error, Revisited
Why Multiple Regression?
The Multiple Regression Equation
Multiple Regression and Predicted Variance
Hypothesis Testing in Multiple Regression
An Example
The General Linear Model
SPSS Connection
PART XVII. REVIEW: "SAY IT AGAIN, SAM"
Module 40. Selecting the Appropriate Analysis
Review of Descriptive Methods
Review of Inferential Methods
Appendix A: Normal Curve Table
Appendix B: Binomial Table
Appendix C: t Table
Appendix D: F Table (ANOVA)
Appendix E: Studentized Range Statistic (for Tukey HSD)
Appendix F: Chi-Square Table
Appendix G: Correlation Table
Appendix H: Odd Solutions to Textbook Exercises
References
Index