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# Statistics Alive!

Third Edition

- Wendy J. Steinberg
- Matthew Price - University of Vermont, USA

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**Other Titles in:**

Educational Research Methods | Psychology (General) | Quantitative/Statistical Research (General)

October 2020 | 624 pages | SAGE Publications, Inc

Statistics need not be dull and dry! Engage and inspire your students with

Students are shown the underlying logic to what they're learning, and well-crafted practice and self-check features help ensure that that new knowledge sticks. Coverage of probability theory and mathematical proofs is complemented by expanded conceptual coverage. In the

SAGE Edge offers a robust online environment featuring an impressive array of free tools and resources for review, study, and further exploration, keeping both instructors and students on the cutting edge of teaching and learning. Learn More.

Statistics Alive!,

ISBN: 978-1-0718-3088-8

**Statistics Alive!**Presenting essential content on statistical analysis in short, digestible modules, this text is written in a conversational tone with anecdotal stories and light-hearted humor; it’s an*enjoyable*read that will ensure your students are always prepared for class.Students are shown the underlying logic to what they're learning, and well-crafted practice and self-check features help ensure that that new knowledge sticks. Coverage of probability theory and mathematical proofs is complemented by expanded conceptual coverage. In the

**Third Edition,**new coauthor Matthew Price includes simplified practice problems and increased coverage of conceptual statistics, integrated discussions of effect size with hypothesis testing, and new coverage of ethical practices for conducting research.**Give your students the SAGE Edge!**SAGE Edge offers a robust online environment featuring an impressive array of free tools and resources for review, study, and further exploration, keeping both instructors and students on the cutting edge of teaching and learning. Learn More.

**Bundle and SAVE!**Statistics Alive!,

*Third Edition*+ Student Study GuideISBN: 978-1-0718-3088-8

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. Scheffé Test

Why Do We Need a Post Hoc Test?

Calculating the Scheffé

Interpreting the Scheffé

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

### Supplements

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