# Comprehending Behavioral Statistics

**Author(s):**
Russell
Hurlburt

**Edition:
**
6

**Copyright:
**
2017

** Comprehending Behavioral Statistics** is organized to capitalize on every opportunity to enhance the reader's comprehension. The

**package exploits 21st century capabilities to provide the reader with multiple ways of approaching behavioral statistics. Packaged with free access to**

*Comprehending Behavioral Statistics/Personal Trainer**Personal Trainer*, a website that creates a multiple-learning methods approach.

** Comprehending Behavioral Statistics** features:

**Eyeball-estimation:**Your students will look at a data set and be able to say “The mean is about 20 and the standard deviation is about 4.” Or look at a scatterplot and say “The correlation is about .8. and the regression line slope is about 25 minutes per mile.” Eyeball estimation makes computation more pedagogically effective: students know approximately what the result should be and why.**Cumulative Review:**An important statistical skill is determining when a particular test is appropriate, but most textbooks do not teach this skill. Instead, students learn that “If this is chapter 11 it must be an independent-samples*t*test.”*Comprehending Behavioral Statistics*solves this problem with innovative cumulative review problems that gradually teach students how to make these important discriminations.**Numerous Figures**: Effective pedagogy emphasizes the importance of visual learning, so this textbook is heavily illustrated. There are more than 400 annotated figures, perhaps two or three times more than in other texts.**Efficiency Features**: Comprehending statistics requires work and practice - it is vital to be as efficient as possible. Colored edges of the statistical tables in Appendix A allow the reader to easily access the tables. Appendix C includes all formulas used within the text in one place. In addition, frequently used formulas used throughout are reprinted at the front and back of the textbook. Finally, complete answers are provided, including intermediate steps, to half the exercises.

**CHAPTER 1 Introduction **

1.1 Inductive Statements

1.2 Statistical Reasoning

1.3 Rational Decision Making

1.4 A Classic Example: Pygmalion in the Classroom

1.5 Samples from Populations

1.6 Probability

1.7 A Note to the Student

Exercises for Chapter 1 13*In Personal Trainer*

LECTLET 1A: Introduction to Statistics

LECTLET 1B: Basic Concepts

LABS: Lab for Chapter 1

ALGEBRA: Review

REVIEWMASTER 1A

RESOURCE 1A: Probability Is a Measure of Uncertainty**CHAPTER 2 Vaiables and Their Measurement **

2.1 Levels of Measurement

2.2 Continuous and Discrete Variables

Real Limits

Significant Figures

Rounding

2.3 Summation

Notation

Computations

2.4 Connections

Cumulative Review

Computers

Homework Tips

Exercises for Chapter 2*In Personal Trainer*

LECTLET 2A: Variables and Their Measurement

LABS: Lab for Chapter 2

DATAGEN: Statistical Computational Package and Data Generator Algebra: Summation

REVIEwMASTER 2A

RESOURCE 2X: Additional Exercises**CHAPTER 3 Frequency Distributions **

3.1 Distributions as Tables

3.2 Distributions as Graphs

Histogram

Frequency Polygon

3.3 Eyeball-estimation

3.4 The Shape of Distributions

Describing Distributions

The Normal Distribution

3.5 Eyeball-calibration

3.6 Bar Graphs of Nominal and Ordinal Variables

3.7 Connections

Cumulative Review

Computers

Homework Tips

Exercises for Chapter 3*In Personal Trainer*

LECTLET 3A: Frequency Distributions as Tables

LECTLET 3B: Frequency Distributions as Graphs

LABS: Lab for Chapter 3

REVIEwMASTER 3A

RESOURCE 3A: Stem and Leaf Displays

RESOURCE 3X: Additional Exercises**CHAPTER 4 Measures of Central **

4.1 Mode

Eyeball-estimating the Mode

Determining the Mode

4.2 Median

Eyeball-estimating the Median

Computing the Median

4.3 Mean

Eyeball-estimating the Mean

Eyeball Calibration

Computing the Sample Mean

4.4 Comparing the Mode, Median, and Mean

4.5 Computing the Population Mean

4.6 Connections

Cumulative Review

Journals

Computers

Homework Tips

Exercises for Chapter 4*In Personal Trainer*

LECTLET 4A: Measures of Central Tendency

LECTLET 4B: Computing and Eyeball-estimating the Mean

LABS: Lab for Chapter 4

ESTAT MEANEST: Eyeball-estimate the Mean (Balancing-point Method)

ESTAT MEANNUM: Eyeball-estimate the Mean (Range Method)

DATAGEN: Statistical Computational Package and Data Generator

REVIEwMASTER 4A

RESOURCE 4A: The Linear Method for Computing the Median

RESOURCE 4B: Computing the Mean from a Frequency Distribution

RESOURCE 4X: Additional Exercises**CHAPTER 5 Measures of Variation **

5.1 Range

5.2 Variance and Standard Deviation

Formulas

Eyeball-estimating the Standard Deviation

Inflection Point Method

Range Method

Computing the Standard Deviation of a Sample

5.3 Eyeball-calibration for Distributions

5.4 Connections

Cumulative Review

Journals

Computers

Homework Tips

Exercises for Chapter 5*In Personal Trainer*

LECTLET 5A: Measures of Variation

LECTLET 5B: Computing and Eyeball-estimating the Standard Deviation

LABS: Lab for Chapter 5

ESTAT SDEST: Eyeball-estimate the Standard Deviation (Inflection-point Method)

ESTAT SDNUM: Eyeball-estimate the Standard Deviation (Range Method)

DATAGEN: Statistical Computational Package and Data Generator

REVIEwMASTER 5A

RESOURCE 5A: The Mean Deviation and the Average Absolute Deviation

RESOURCE 5B: Computational Formulas for the Standard Deviation and Variance

RESOURCE 5C: Computing the Standard Deviation from a Frequency Distribution

RESOURCE 5X: Additional Exercises**CHAPTER 6 Using Frequency Distributions **

6.1 Points in Distributions

Percentiles and Percentile Rank

Standard Scores (z Scores)

6.2 Areas Under Distributions

Using Areas Under Distributions

6.3 Areas Under Normal Distributions

Eyeball-estimation

Eyeball-calibration

Calculating Areas

6.4 Other Standardized Distributions Based on z Scores

6.5 Relative Frequencies of Real-world Normal Variables

6.6 Percentiles and Percentile Rank in Normal Distributions

6.7 Connections

Cumulative Review

Computers

Homework Tips

Exercises for Chapter 6*In Personal Trainer*

LECTLET 6A: Areas Under Distributions

LECTLET 6B: Areas Under Normal Distributions

LABS: Lab for Chapter 6

ESTAT NORMAL: Eyeball-estimate the Area Under a Normal Distribution

DATAGEN: Statistical Computational Package and Data Generator

REVIEwMASTER 6A

RESOURCE 6A: Interpolation

RESOURCE 6B: Equation of the Normal Distribution

RESOURCE 6X: Additional Exercises

CHAPTER 7 Samples and the Sampling Distribution of the Means

7.1 Random Samples

Simple Random Sampling

Samples from Populations

7.2 The Sampling Distribution of the Means

The Central Limit Theorem

Factors That Affect the Magnitude of s X : n and s

Using the Sampling Distribution of the Means

7.3 Connections

Cumulative Review

Computers

Homework Tips

Exercises for Chapter 7*In Personal Trainer*

LECTLET 7A: Samples from Populations and the Distribution of Means

LECTLET 7B: The Central Limit Theorem

LECTLET 7C: The Standard Error of the Mean

LABS: Lab for Chapter 7

ESTAT MDIST: Explore the Distribution of Means

DATAGEN: Statistical Computational Package and Data Generator

REVIEWMASTER 7A

RESOURCE 7X: Additional Exercises**CHAPTER 8 Parameter Estimation **

8.1 Where’s X? The Critical Value of z

8.2 Where's µ? Point-estimation

8.3 Where’s µ? Confidence Intervals

when s Is Known

Changing the Level of Confidence

When s Is Unknown

Opinion Polls

Four Factors That Affect the Width of a Confidence Interval

8.4 Connections

Cumulative Review

Journals

Computers

Homework Tips

Exercises for Chapter 8*In Personal Trainer*

LECTLET 8A: Confidence Intervals

LECTLET 8B: Computing Confidence Intervals

LECTLET 8C: Confidence Intervals II

LABS: Lab for Chapter 8

ESTAT CONFIDE: Eyeball-estimate the Confidence Interval

DATAGEN: Statistical Computational Package and Data Generator

REVIEwMASTER 8A

RESOURCE 8A: Unbiased Estimators and the Denominator of the Standard Deviation

RESOURCE 8B: Degrees of Freedom in the Computation of a Standard Deviation or Variance

RESOURCE 8C: Opinion Polls: Using the Confidence Interval for a Proportion

RESOURCE 8X: Additional Exercises**CHAPTER 9 Evaluating Hypotheses **

9.1 Descriptive Versus Inferential Statistics

Descriptive Statistics

Inferential Statistics

9.2 Evaluating Hypotheses

Null and Alternative Hypotheses

Directional (One-tailed) and Nondirectional (Two-tailed) Hypotheses

Type I and Type II Errors

Level of Significance (a)

Statistical Power

The Courtroom Analogy

Practical Significance

9.3 The Procedure for Evaluating Hypotheses

9.4 Connections

Cumulative Review

Computers

Journals

Homework Tips

Exercises for Chapter 9*In Personal Trainer*

LECTLET 9A: Inferential Statistics

LECTLET 9B: The Procedure for Evaluating Hypotheses

LABS: Lab for Chapter 9

REVIEwMASTER 9A

RESOURCE 9A: why Statistical Significance Testing Alone Is Not Enough**CHAPTER 10 Inferences About Means of Single Samples **

10.1 Evaluating Hypotheses About Means

When s Is Known

A Directional (One-tailed) Example

Practical Significance: Effect Size

When s Is Unknown

10.2 The Relationship Between Hypothesis Testing and Confidence Intervals

10.3 Statistical Significance Is Not Necessarily Practical Significance

10.4 One-sample t Test Eyeball-calibration

10.5 Connections

Cumulative Review

Journals

Computers

Homework Tips

Exercises for Chapter 10*In Personal Trainer*

LECTLET 10A: Inferences About Means of Single Samples: Illustrating the Null Hypothesis

LECTLET 10B: Inferences About Means of Single Samples: Completing the Evaluation

LECTLET 10C: Inferences About Means of Single Samples: when the Test Is Directional or s Is Unknown

LABS: Lab for Chapter 10

ESTAT TTEST1 : Eyeball-calibrate One-sample t Tests

DATAGEN: Statistical Computational Package and Data Generator

REVIEwMASTER 10A

RESOURCE 10A: Eyeball-estimating One-sample t Tests

RESOURCE 10X: Additional Exercises**CHAPTER 11 Inferences About Means of Two Independent Samples **

11.1 Hypotheses with Two Independent Samples

Dependent and Independent Variables

The Null Hypothesis

Experimental Outcomes

11.2 The Test Statistic

11.3 Standard Error of the Difference Between Two Means

Pooled Variance 272 • Interpreting the Standard Error of the Difference Between Two Means

11.4 Evaluating Hypotheses About Means of Two Independent Samples

Procedure

A Directional (One-tailed) Example

11.5 Practical Significance Versus Statistical Significance Revisited

11.6 Two-sample t Test Eyeball-calibration

11.7 Connections

Cumulative Review

Journals

Computers

Homework Tips

Exercises for Chapter 11*In Personal Trainer*

LECTLET 11A: Hypothesis Evaluation with Two Independent Samples: The Test Statistic

LECTLET 11B: Hypothesis Evaluation with Two Independent Samples: The Standard Error of the Difference Between Two Means

LECTLET 11C: Hypothesis Evaluation with Two Independent Samples: Completing the Analysis

LABS: Lab for Chapter 11

ESTAT DIFFM: Explore the Distribution of the Differences between Two Means

ESTAT TTEST2: Eyeball-calibrate Two-independent-samples t Tests

DATAGEN: Statistical Computational Package and Data Generator

REVIEwMASTER 11A

RESOURCE 11A: Eyeball-estimating Two-independent-samples t Tests

RESOURCE 11X: Additional Exercises**CHAPTER 12 Inferences About Means of Two Dependent Samples **

12.1 Dependent-samples Tests

12.2 Evaluating Hypotheses About Means of Two Dependent Samples

An Example

Null Hypothesis

Test Statistic

Evaluating the Hypothesis

12.3 Comparing Dependent- and Independent-samples t Tests

12.4 Dependent-samples t Test Eyeball-calibration

12.5 Connections

Cumulative Review

Journals

Computers

Homework Tips

Exercises for Chapter 12*In Personal Trainer*

LECTLET 12A: Inferences About Two Dependent Samples

LABS: Lab for Chapter 12

DATAGEN: Statistical Computational Package and Data Generator

REVIEwMASTER 12A

RESOURCE 12A: Eyeball-estimating Dependent-samples t Tests

RESOURCE 12X: Additional Exercises**CHAPTER 13 Statistical Power **

13.1 Statistical Power

An Example

Illustrating Power

13.2 Factors That Increase Power

Increasing the Sample Size Increases Power

Increasing the Raw Effect Size Increases Power

Decreasing s Increases Power

Increasing a Increases Power

Changing from a Nondirectional to a Directional Test Increases Power

13.3 Using Power to Determine Sample Size

An Example

13.4 Connections

Cumulative Review

Journals

Homework Tips

Exercises for Chapter 13*In Personal Trainer*

LECTLET 13A: Statistical Power

LECTLET 13B: Consequences of Statistical Power

LABS: Lab for Chapter 13

ESTAT POwER: Exploring Four Influences on Statistical Power

REVIEwMASTER 13A

RESOURCE 13X: Additional Exercises**CHAPTER 14 Inferences About Two or More Means: Analysis of Variance **

14.1 why Multiple t Tests Are Not Appropriate

14.2 Hypotheses with Three or More Samples

Null Hypothesis

Alternative Hypothesis

14.3 Logic of Analysis of Variance

MS: Between-group Point-estimate of s2

MS: Within-group Point-estimate of s2

F Ratio

ANOVA Is Nondirectional

14.4 Partitioning the Sum of Squares

14.5 Review of the Procedure

14.6 Another Example

14.7 ANOVA Eyeball-calibration

14.8 Number of Subjects Required for Adequate Power

14.9 Connections

Cumulative Review

Journals

Computers

Homework Tips

Exercises for Chapter 14*In Personal Trainer*

LECTLET 14A: Hypotheses with Three or More Groups

LECTLET 14B: Logic of the Analysis of Variance

LECTLET 14C: Computing the Analysis of Variance

LECTLET 14D: Interpreting the Analysis of Variance

LABS: Lab for Chapter 14

ESTAT ANOVA-ST: Explore the ANOVA Summary Table

ESTAT ANOVA-F: Explore the F-ratio

DATAGEN: Statistical Computational Package and Data Generator

REVIEwMASTER 14A

RESOURCE 14A: Computational Formulas for ANOVA

RESOURCE 14B: Eyeball-estimating the Analysis of Variance

RESOURCE 14X: Additional Exercises**CHAPTER 15 Post Hoc Tests, A Priori Tests, Repeated-Measures ANOVA, and Two-way ANOVA **

15.1 Interpreting ANOVA: Post Hoc Tests

15.2 Instead of ANOVA: A Priori Tests

A Priori Tests when There Are Two Groups

Comparisons

15.3 Repeated-Measures Analysis of Variance

15.4 Two-way Analysis of Variance

15.5 Displaying the Outcome of a Two-way Design

15.6 Main Effects

15.7 Interaction

Kinds of Interaction

Null Hypothesis for Interaction

15.8 Interpreting Two-way ANOVA

15.9 Connections

Cumulative Review

Journals

Computers

Homework Tips

Exercises for Chapter 15*In Personal Trainer*

LECTLET 15A: Post Hoc Tests and A Priori Tests

LECTLET 15B: Repeated-measures Analysis of Variance

LECTLET 15C: Two-way Analysis of Variance

LABS: Lab for Chapter 15

REVIEwMASTER 15A

RESOURCE 15A: Comprehending and Computing Post Hoc Tests

RESOURCE 15B: Comprehending and Computing A Priori Tests

RESOURCE 15C: Comprehending and Computing Repeated-measures ANOVA

RESOURCE 15D: Comprehending and Computing Two-way ANOVA

RESOURCE 15X: Additional Exercises**CHAPTER 16 Measures of the Relationship Between Two Variables: Correlation **

16.1 Correlation Coefficient

Scoffer Diagrams

Values of r

16.2 Pearson’s r

z Score Formulas

How It works

Factors That Affect the Size of r

Correlation Does Not Imply Causation

Testing Hypotheses About r

Power

16.3 Spearman’s rs

Ranking

Testing Hypotheses About rs

16.4 Connections

Cumulative Review

Journals

Computers

Homework Tips

Exercises for Chapter 16*In Personal Trainer*

LECTLET 16A: Correlation

LECTLET 16B: Computing the Correlation Coefficient

LABS: Lab for Chapter 16

ESTAT SCATTER: Eyeball-estimate the Correlation Coefficient

DATAGEN: Statistical Computational Package and Data Generator

REVIEwMASTER 16A

RESOURCE 16A: Computational Formulas for the Pearson Correlation Coefficient

RESOURCE 16B: The Significance Test for r Is Derived from the Test Statistic t

RESOURCE 16X: Additional Exercises**CHAPTER 17 Prediction: Linear Regression **

17.1 Regression Lines

Notation

The Equation

The Equation for a Straight Line

Eyeball-estimating the Constants

Computing the Constants

Interpreting the Constants

17.2 The Best (Least Squares) Regression Line

Error of Prediction

The Best Line

17.3 Standard Error of Estimate

Coefficient of Determination

Predicted Distribution

17.4 Regression Line in Standard Form

Regression to the Mean

17.5 Interpreting Correlation and Regression

IQ

Personality

17.6 Hypothesis Testing in Regression

17.7 Connections

Cumulative Review

Journals

Computers

Homework Tips

Exercises for Chapter 17*In Personal Trainer*

LECTLET 17A: Linear Regression

LECTLET 17B: Computing the Regression Equation

LECTLET 17C: The Standard Error of Estimate

LABS: Lab for Chapter 17

ESTAT REGTRy: Eyeball-estimate the Regression Line and its Constants

ESTAT COREST: The Implications of Correlated Data

DATAGEN: Statistical Computational Package and Data Generator

REVIEwMASTER 17A

RESOURCE 17A: Computational Formula for the Regression Line Slope

RESOURCE 17B: what Causes Regression to the Mean?

RESOURCE 17C: Partitioning the Regression Sum of Squares

RESOURCE 17D: A Small Correlation Can Have Dramatic Impact

RESOURCE 17X: Additional Exercises**CHAPTER 18 Some Nonparametric Statistical Tests **

18.1 Testing with a Nonnormal Distribution

18.2 Nonparametric Statistical Tests

18.3 Tests for Data Measured at the Nominal Level

One Sample: The ?2 Goodness of Fit Test

Two Independent Samples: The ?2 Test of Independence

Two Dependent Samples: The McNemar Test for Significance of Change

18.4 Tests for Data Measured at the Ordinal Level

Two Independent Samples: The Mann-whitney U Test

Two Dependent Samples: The wilcoxon Matched-pairs Signed-rank Test

k Independent Samples: The Kruskal-wallis H Test

18.5 Choosing Between Parametric and Nonparametric Tests

18.6 Connections

Cumulative Review

Journals

Computers

Homework Tips

Exercises for Chapter 18*In Personal Trainer*

LECTLET 18A: Nonparametric Statistics: Chi-square

LECTLET 18B: Nonparametric Statistics Based on Order

LABS: Lab for Chapter 18

REVIEwMASTER 18A

RESOURCE 18X: Additional Exercises**References
APPENDIX A Statistical Tables
APPENDIX B Review of Basic Arithmetic
APPENDIX C Summary of Statistical Formulas Used in This Text
APPENDIX D Answers to Selected Exercises
List of Symbols and Glossary
Index**

**Russell Hurlburt**

Russell T. Hurlburt, Ph.D., is professor of Psychology at the University of Nevada, Las Vegas. He received his Ph.D. in clinical psychology from the University of South Dakota after a BS in aeronautical engineering from Princeton and an MS in mechanical engineering from the University of New Mexico. His clinical psychology and engineering backgrounds make him ideally situated to write about introductory statistics with accuracy and sensitivity.

Dr. Hurlburt has been writing computer demonstrations of statistical concepts for students since 1979 (for historical reference, the first Macintosh was built in 1984). He developed the “eyeball estimation” techniques for comprehending the concepts of statistics that are incorporated in his textbooks *Comprehending Behavioral Statistics* and *Personal Trainer* beginning in the early 1980s. All those materials have been revised and refined in constant collaboration with students in well over 100 statistics classes.

Dr. Hurlburt is also one of the pioneers of “thought sampling,” the use of beepers to trigger the random sampling of thoughts and feelings in participants’ own natural environments. He is the originator of the “descriptive experience sampling method,” which provides qualitative, idiographic descriptions of inner experience.

** Comprehending Behavioral Statistics** is organized to capitalize on every opportunity to enhance the reader's comprehension. The

**package exploits 21st century capabilities to provide the reader with multiple ways of approaching behavioral statistics. Packaged with free access to**

*Comprehending Behavioral Statistics/Personal Trainer**Personal Trainer*, a website that creates a multiple-learning methods approach.

** Comprehending Behavioral Statistics** features:

**Eyeball-estimation:**Your students will look at a data set and be able to say “The mean is about 20 and the standard deviation is about 4.” Or look at a scatterplot and say “The correlation is about .8. and the regression line slope is about 25 minutes per mile.” Eyeball estimation makes computation more pedagogically effective: students know approximately what the result should be and why.**Cumulative Review:**An important statistical skill is determining when a particular test is appropriate, but most textbooks do not teach this skill. Instead, students learn that “If this is chapter 11 it must be an independent-samples*t*test.”*Comprehending Behavioral Statistics*solves this problem with innovative cumulative review problems that gradually teach students how to make these important discriminations.**Numerous Figures**: Effective pedagogy emphasizes the importance of visual learning, so this textbook is heavily illustrated. There are more than 400 annotated figures, perhaps two or three times more than in other texts.**Efficiency Features**: Comprehending statistics requires work and practice - it is vital to be as efficient as possible. Colored edges of the statistical tables in Appendix A allow the reader to easily access the tables. Appendix C includes all formulas used within the text in one place. In addition, frequently used formulas used throughout are reprinted at the front and back of the textbook. Finally, complete answers are provided, including intermediate steps, to half the exercises.

**CHAPTER 1 Introduction **

1.1 Inductive Statements

1.2 Statistical Reasoning

1.3 Rational Decision Making

1.4 A Classic Example: Pygmalion in the Classroom

1.5 Samples from Populations

1.6 Probability

1.7 A Note to the Student

Exercises for Chapter 1 13*In Personal Trainer*

LECTLET 1A: Introduction to Statistics

LECTLET 1B: Basic Concepts

LABS: Lab for Chapter 1

ALGEBRA: Review

REVIEWMASTER 1A

RESOURCE 1A: Probability Is a Measure of Uncertainty**CHAPTER 2 Vaiables and Their Measurement **

2.1 Levels of Measurement

2.2 Continuous and Discrete Variables

Real Limits

Significant Figures

Rounding

2.3 Summation

Notation

Computations

2.4 Connections

Cumulative Review

Computers

Homework Tips

Exercises for Chapter 2*In Personal Trainer*

LECTLET 2A: Variables and Their Measurement

LABS: Lab for Chapter 2

DATAGEN: Statistical Computational Package and Data Generator Algebra: Summation

REVIEwMASTER 2A

RESOURCE 2X: Additional Exercises**CHAPTER 3 Frequency Distributions **

3.1 Distributions as Tables

3.2 Distributions as Graphs

Histogram

Frequency Polygon

3.3 Eyeball-estimation

3.4 The Shape of Distributions

Describing Distributions

The Normal Distribution

3.5 Eyeball-calibration

3.6 Bar Graphs of Nominal and Ordinal Variables

3.7 Connections

Cumulative Review

Computers

Homework Tips

Exercises for Chapter 3*In Personal Trainer*

LECTLET 3A: Frequency Distributions as Tables

LECTLET 3B: Frequency Distributions as Graphs

LABS: Lab for Chapter 3

REVIEwMASTER 3A

RESOURCE 3A: Stem and Leaf Displays

RESOURCE 3X: Additional Exercises**CHAPTER 4 Measures of Central **

4.1 Mode

Eyeball-estimating the Mode

Determining the Mode

4.2 Median

Eyeball-estimating the Median

Computing the Median

4.3 Mean

Eyeball-estimating the Mean

Eyeball Calibration

Computing the Sample Mean

4.4 Comparing the Mode, Median, and Mean

4.5 Computing the Population Mean

4.6 Connections

Cumulative Review

Journals

Computers

Homework Tips

Exercises for Chapter 4*In Personal Trainer*

LECTLET 4A: Measures of Central Tendency

LECTLET 4B: Computing and Eyeball-estimating the Mean

LABS: Lab for Chapter 4

ESTAT MEANEST: Eyeball-estimate the Mean (Balancing-point Method)

ESTAT MEANNUM: Eyeball-estimate the Mean (Range Method)

DATAGEN: Statistical Computational Package and Data Generator

REVIEwMASTER 4A

RESOURCE 4A: The Linear Method for Computing the Median

RESOURCE 4B: Computing the Mean from a Frequency Distribution

RESOURCE 4X: Additional Exercises**CHAPTER 5 Measures of Variation **

5.1 Range

5.2 Variance and Standard Deviation

Formulas

Eyeball-estimating the Standard Deviation

Inflection Point Method

Range Method

Computing the Standard Deviation of a Sample

5.3 Eyeball-calibration for Distributions

5.4 Connections

Cumulative Review

Journals

Computers

Homework Tips

Exercises for Chapter 5*In Personal Trainer*

LECTLET 5A: Measures of Variation

LECTLET 5B: Computing and Eyeball-estimating the Standard Deviation

LABS: Lab for Chapter 5

ESTAT SDEST: Eyeball-estimate the Standard Deviation (Inflection-point Method)

ESTAT SDNUM: Eyeball-estimate the Standard Deviation (Range Method)

DATAGEN: Statistical Computational Package and Data Generator

REVIEwMASTER 5A

RESOURCE 5A: The Mean Deviation and the Average Absolute Deviation

RESOURCE 5B: Computational Formulas for the Standard Deviation and Variance

RESOURCE 5C: Computing the Standard Deviation from a Frequency Distribution

RESOURCE 5X: Additional Exercises**CHAPTER 6 Using Frequency Distributions **

6.1 Points in Distributions

Percentiles and Percentile Rank

Standard Scores (z Scores)

6.2 Areas Under Distributions

Using Areas Under Distributions

6.3 Areas Under Normal Distributions

Eyeball-estimation

Eyeball-calibration

Calculating Areas

6.4 Other Standardized Distributions Based on z Scores

6.5 Relative Frequencies of Real-world Normal Variables

6.6 Percentiles and Percentile Rank in Normal Distributions

6.7 Connections

Cumulative Review

Computers

Homework Tips

Exercises for Chapter 6*In Personal Trainer*

LECTLET 6A: Areas Under Distributions

LECTLET 6B: Areas Under Normal Distributions

LABS: Lab for Chapter 6

ESTAT NORMAL: Eyeball-estimate the Area Under a Normal Distribution

DATAGEN: Statistical Computational Package and Data Generator

REVIEwMASTER 6A

RESOURCE 6A: Interpolation

RESOURCE 6B: Equation of the Normal Distribution

RESOURCE 6X: Additional Exercises

CHAPTER 7 Samples and the Sampling Distribution of the Means

7.1 Random Samples

Simple Random Sampling

Samples from Populations

7.2 The Sampling Distribution of the Means

The Central Limit Theorem

Factors That Affect the Magnitude of s X : n and s

Using the Sampling Distribution of the Means

7.3 Connections

Cumulative Review

Computers

Homework Tips

Exercises for Chapter 7*In Personal Trainer*

LECTLET 7A: Samples from Populations and the Distribution of Means

LECTLET 7B: The Central Limit Theorem

LECTLET 7C: The Standard Error of the Mean

LABS: Lab for Chapter 7

ESTAT MDIST: Explore the Distribution of Means

DATAGEN: Statistical Computational Package and Data Generator

REVIEWMASTER 7A

RESOURCE 7X: Additional Exercises**CHAPTER 8 Parameter Estimation **

8.1 Where’s X? The Critical Value of z

8.2 Where's µ? Point-estimation

8.3 Where’s µ? Confidence Intervals

when s Is Known

Changing the Level of Confidence

When s Is Unknown

Opinion Polls

Four Factors That Affect the Width of a Confidence Interval

8.4 Connections

Cumulative Review

Journals

Computers

Homework Tips

Exercises for Chapter 8*In Personal Trainer*

LECTLET 8A: Confidence Intervals

LECTLET 8B: Computing Confidence Intervals

LECTLET 8C: Confidence Intervals II

LABS: Lab for Chapter 8

ESTAT CONFIDE: Eyeball-estimate the Confidence Interval

DATAGEN: Statistical Computational Package and Data Generator

REVIEwMASTER 8A

RESOURCE 8A: Unbiased Estimators and the Denominator of the Standard Deviation

RESOURCE 8B: Degrees of Freedom in the Computation of a Standard Deviation or Variance

RESOURCE 8C: Opinion Polls: Using the Confidence Interval for a Proportion

RESOURCE 8X: Additional Exercises**CHAPTER 9 Evaluating Hypotheses **

9.1 Descriptive Versus Inferential Statistics

Descriptive Statistics

Inferential Statistics

9.2 Evaluating Hypotheses

Null and Alternative Hypotheses

Directional (One-tailed) and Nondirectional (Two-tailed) Hypotheses

Type I and Type II Errors

Level of Significance (a)

Statistical Power

The Courtroom Analogy

Practical Significance

9.3 The Procedure for Evaluating Hypotheses

9.4 Connections

Cumulative Review

Computers

Journals

Homework Tips

Exercises for Chapter 9*In Personal Trainer*

LECTLET 9A: Inferential Statistics

LECTLET 9B: The Procedure for Evaluating Hypotheses

LABS: Lab for Chapter 9

REVIEwMASTER 9A

RESOURCE 9A: why Statistical Significance Testing Alone Is Not Enough**CHAPTER 10 Inferences About Means of Single Samples **

10.1 Evaluating Hypotheses About Means

When s Is Known

A Directional (One-tailed) Example

Practical Significance: Effect Size

When s Is Unknown

10.2 The Relationship Between Hypothesis Testing and Confidence Intervals

10.3 Statistical Significance Is Not Necessarily Practical Significance

10.4 One-sample t Test Eyeball-calibration

10.5 Connections

Cumulative Review

Journals

Computers

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Exercises for Chapter 10*In Personal Trainer*

LECTLET 10A: Inferences About Means of Single Samples: Illustrating the Null Hypothesis

LECTLET 10B: Inferences About Means of Single Samples: Completing the Evaluation

LECTLET 10C: Inferences About Means of Single Samples: when the Test Is Directional or s Is Unknown

LABS: Lab for Chapter 10

ESTAT TTEST1 : Eyeball-calibrate One-sample t Tests

DATAGEN: Statistical Computational Package and Data Generator

REVIEwMASTER 10A

RESOURCE 10A: Eyeball-estimating One-sample t Tests

RESOURCE 10X: Additional Exercises**CHAPTER 11 Inferences About Means of Two Independent Samples **

11.1 Hypotheses with Two Independent Samples

Dependent and Independent Variables

The Null Hypothesis

Experimental Outcomes

11.2 The Test Statistic

11.3 Standard Error of the Difference Between Two Means

Pooled Variance 272 • Interpreting the Standard Error of the Difference Between Two Means

11.4 Evaluating Hypotheses About Means of Two Independent Samples

Procedure

A Directional (One-tailed) Example

11.5 Practical Significance Versus Statistical Significance Revisited

11.6 Two-sample t Test Eyeball-calibration

11.7 Connections

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Exercises for Chapter 11*In Personal Trainer*

LECTLET 11A: Hypothesis Evaluation with Two Independent Samples: The Test Statistic

LECTLET 11B: Hypothesis Evaluation with Two Independent Samples: The Standard Error of the Difference Between Two Means

LECTLET 11C: Hypothesis Evaluation with Two Independent Samples: Completing the Analysis

LABS: Lab for Chapter 11

ESTAT DIFFM: Explore the Distribution of the Differences between Two Means

ESTAT TTEST2: Eyeball-calibrate Two-independent-samples t Tests

DATAGEN: Statistical Computational Package and Data Generator

REVIEwMASTER 11A

RESOURCE 11A: Eyeball-estimating Two-independent-samples t Tests

RESOURCE 11X: Additional Exercises**CHAPTER 12 Inferences About Means of Two Dependent Samples **

12.1 Dependent-samples Tests

12.2 Evaluating Hypotheses About Means of Two Dependent Samples

An Example

Null Hypothesis

Test Statistic

Evaluating the Hypothesis

12.3 Comparing Dependent- and Independent-samples t Tests

12.4 Dependent-samples t Test Eyeball-calibration

12.5 Connections

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Exercises for Chapter 12*In Personal Trainer*

LECTLET 12A: Inferences About Two Dependent Samples

LABS: Lab for Chapter 12

DATAGEN: Statistical Computational Package and Data Generator

REVIEwMASTER 12A

RESOURCE 12A: Eyeball-estimating Dependent-samples t Tests

RESOURCE 12X: Additional Exercises**CHAPTER 13 Statistical Power **

13.1 Statistical Power

An Example

Illustrating Power

13.2 Factors That Increase Power

Increasing the Sample Size Increases Power

Increasing the Raw Effect Size Increases Power

Decreasing s Increases Power

Increasing a Increases Power

Changing from a Nondirectional to a Directional Test Increases Power

13.3 Using Power to Determine Sample Size

An Example

13.4 Connections

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Exercises for Chapter 13*In Personal Trainer*

LECTLET 13A: Statistical Power

LECTLET 13B: Consequences of Statistical Power

LABS: Lab for Chapter 13

ESTAT POwER: Exploring Four Influences on Statistical Power

REVIEwMASTER 13A

RESOURCE 13X: Additional Exercises**CHAPTER 14 Inferences About Two or More Means: Analysis of Variance **

14.1 why Multiple t Tests Are Not Appropriate

14.2 Hypotheses with Three or More Samples

Null Hypothesis

Alternative Hypothesis

14.3 Logic of Analysis of Variance

MS: Between-group Point-estimate of s2

MS: Within-group Point-estimate of s2

F Ratio

ANOVA Is Nondirectional

14.4 Partitioning the Sum of Squares

14.5 Review of the Procedure

14.6 Another Example

14.7 ANOVA Eyeball-calibration

14.8 Number of Subjects Required for Adequate Power

14.9 Connections

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Exercises for Chapter 14*In Personal Trainer*

LECTLET 14A: Hypotheses with Three or More Groups

LECTLET 14B: Logic of the Analysis of Variance

LECTLET 14C: Computing the Analysis of Variance

LECTLET 14D: Interpreting the Analysis of Variance

LABS: Lab for Chapter 14

ESTAT ANOVA-ST: Explore the ANOVA Summary Table

ESTAT ANOVA-F: Explore the F-ratio

DATAGEN: Statistical Computational Package and Data Generator

REVIEwMASTER 14A

RESOURCE 14A: Computational Formulas for ANOVA

RESOURCE 14B: Eyeball-estimating the Analysis of Variance

RESOURCE 14X: Additional Exercises**CHAPTER 15 Post Hoc Tests, A Priori Tests, Repeated-Measures ANOVA, and Two-way ANOVA **

15.1 Interpreting ANOVA: Post Hoc Tests

15.2 Instead of ANOVA: A Priori Tests

A Priori Tests when There Are Two Groups

Comparisons

15.3 Repeated-Measures Analysis of Variance

15.4 Two-way Analysis of Variance

15.5 Displaying the Outcome of a Two-way Design

15.6 Main Effects

15.7 Interaction

Kinds of Interaction

Null Hypothesis for Interaction

15.8 Interpreting Two-way ANOVA

15.9 Connections

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Exercises for Chapter 15*In Personal Trainer*

LECTLET 15A: Post Hoc Tests and A Priori Tests

LECTLET 15B: Repeated-measures Analysis of Variance

LECTLET 15C: Two-way Analysis of Variance

LABS: Lab for Chapter 15

REVIEwMASTER 15A

RESOURCE 15A: Comprehending and Computing Post Hoc Tests

RESOURCE 15B: Comprehending and Computing A Priori Tests

RESOURCE 15C: Comprehending and Computing Repeated-measures ANOVA

RESOURCE 15D: Comprehending and Computing Two-way ANOVA

RESOURCE 15X: Additional Exercises**CHAPTER 16 Measures of the Relationship Between Two Variables: Correlation **

16.1 Correlation Coefficient

Scoffer Diagrams

Values of r

16.2 Pearson’s r

z Score Formulas

How It works

Factors That Affect the Size of r

Correlation Does Not Imply Causation

Testing Hypotheses About r

Power

16.3 Spearman’s rs

Ranking

Testing Hypotheses About rs

16.4 Connections

Cumulative Review

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Exercises for Chapter 16*In Personal Trainer*

LECTLET 16A: Correlation

LECTLET 16B: Computing the Correlation Coefficient

LABS: Lab for Chapter 16

ESTAT SCATTER: Eyeball-estimate the Correlation Coefficient

DATAGEN: Statistical Computational Package and Data Generator

REVIEwMASTER 16A

RESOURCE 16A: Computational Formulas for the Pearson Correlation Coefficient

RESOURCE 16B: The Significance Test for r Is Derived from the Test Statistic t

RESOURCE 16X: Additional Exercises**CHAPTER 17 Prediction: Linear Regression **

17.1 Regression Lines

Notation

The Equation

The Equation for a Straight Line

Eyeball-estimating the Constants

Computing the Constants

Interpreting the Constants

17.2 The Best (Least Squares) Regression Line

Error of Prediction

The Best Line

17.3 Standard Error of Estimate

Coefficient of Determination

Predicted Distribution

17.4 Regression Line in Standard Form

Regression to the Mean

17.5 Interpreting Correlation and Regression

IQ

Personality

17.6 Hypothesis Testing in Regression

17.7 Connections

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Exercises for Chapter 17*In Personal Trainer*

LECTLET 17A: Linear Regression

LECTLET 17B: Computing the Regression Equation

LECTLET 17C: The Standard Error of Estimate

LABS: Lab for Chapter 17

ESTAT REGTRy: Eyeball-estimate the Regression Line and its Constants

ESTAT COREST: The Implications of Correlated Data

DATAGEN: Statistical Computational Package and Data Generator

REVIEwMASTER 17A

RESOURCE 17A: Computational Formula for the Regression Line Slope

RESOURCE 17B: what Causes Regression to the Mean?

RESOURCE 17C: Partitioning the Regression Sum of Squares

RESOURCE 17D: A Small Correlation Can Have Dramatic Impact

RESOURCE 17X: Additional Exercises**CHAPTER 18 Some Nonparametric Statistical Tests **

18.1 Testing with a Nonnormal Distribution

18.2 Nonparametric Statistical Tests

18.3 Tests for Data Measured at the Nominal Level

One Sample: The ?2 Goodness of Fit Test

Two Independent Samples: The ?2 Test of Independence

Two Dependent Samples: The McNemar Test for Significance of Change

18.4 Tests for Data Measured at the Ordinal Level

Two Independent Samples: The Mann-whitney U Test

Two Dependent Samples: The wilcoxon Matched-pairs Signed-rank Test

k Independent Samples: The Kruskal-wallis H Test

18.5 Choosing Between Parametric and Nonparametric Tests

18.6 Connections

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Exercises for Chapter 18*In Personal Trainer*

LECTLET 18A: Nonparametric Statistics: Chi-square

LECTLET 18B: Nonparametric Statistics Based on Order

LABS: Lab for Chapter 18

REVIEwMASTER 18A

RESOURCE 18X: Additional Exercises**References
APPENDIX A Statistical Tables
APPENDIX B Review of Basic Arithmetic
APPENDIX C Summary of Statistical Formulas Used in This Text
APPENDIX D Answers to Selected Exercises
List of Symbols and Glossary
Index**

**Russell Hurlburt**

Russell T. Hurlburt, Ph.D., is professor of Psychology at the University of Nevada, Las Vegas. He received his Ph.D. in clinical psychology from the University of South Dakota after a BS in aeronautical engineering from Princeton and an MS in mechanical engineering from the University of New Mexico. His clinical psychology and engineering backgrounds make him ideally situated to write about introductory statistics with accuracy and sensitivity.

Dr. Hurlburt has been writing computer demonstrations of statistical concepts for students since 1979 (for historical reference, the first Macintosh was built in 1984). He developed the “eyeball estimation” techniques for comprehending the concepts of statistics that are incorporated in his textbooks *Comprehending Behavioral Statistics* and *Personal Trainer* beginning in the early 1980s. All those materials have been revised and refined in constant collaboration with students in well over 100 statistics classes.

Dr. Hurlburt is also one of the pioneers of “thought sampling,” the use of beepers to trigger the random sampling of thoughts and feelings in participants’ own natural environments. He is the originator of the “descriptive experience sampling method,” which provides qualitative, idiographic descriptions of inner experience.