Comprehending Behavioral Statistics
Edition: 6
Copyright: 2017
Edition: 6
Copyright: 2017
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Comprehending Behavioral Statistics is organized to capitalize on every opportunity to enhance the reader's comprehension. The Comprehending Behavioral Statistics/Personal Trainer package exploits 21st century capabilities to provide the reader with multiple ways of approaching behavioral statistics. Packaged with free access to 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 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 Comprehending Behavioral Statistics/Personal Trainer package exploits 21st century capabilities to provide the reader with multiple ways of approaching behavioral statistics. Packaged with free access to 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 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.