# Elementary Statistics

**Author(s):**
Henry R
Gibson
,
Bernard L
Dillard

**Edition:
**
4

**Copyright:
**
2016

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** Elementary Statistics **is written for students with minimal preparation in mathematics while providing instructors a text that is both informative and yet firmly rooted in real-world application, addressing important contemporary issues in sociology, psychology, marketing, finance, medicine, health, factory production, education, biology, anthropology, and so on.

** Elementary Statistics **by Henry Gibson and Bernard Dillard:

- infuses energetic, up–to–date images within the text to make statistical ideas a bit more bearable.
- presents a more in–depth discussion on regression, chi square, and ANOVA.
- includes a new chapter discussing time series.
- features access to datasets through a separate and distinct website.

*Preface *

**Chapter One: Introduction **

1.1 Overview of Course (Basic Concepts)

Population

Sample

Random Sample

Internal and External Validity

1.2 Why We Sample

Sampling to Determine µ

Sampling to Determine p

Excel Excitement

Summary

Exercises

**Chapter Two: Organizing and Analyzing Data **

2.1 Graphical Representations

Histogram

Population Histograms

Frequency Polygon

Circle Graph

2.2 Measures of Central Tendency (Ungrouped Data)

Arithmetic Mean

Median

Mode

Comparison of the Mean, Median, and Mode

2.3 Measures of Dispersion or Spread (Ungrouped Data)

Range

Standard Deviation

2.4 Estimating Population Characteristics

2.5 Measures of Central Tendency and Dispersion/Spread (Grouped Data)

Mean

Standard Deviation

Modal Class

2.6 z Scores and the Use of the Standard Deviation

Two Important Findings

2.7 Additional Descriptive Topics

Pictogram

Stem-and-Leaf Display

Box-and-Whisker Plot

Quartiles

Percentiles

2.8 Writing Research Reports

Background Statement

Design and Procedures of the Study

Results

Analysis and Discussion

Conclusions and Recommendations

Excel Excitement

Summary

Exercises

Research Reports

Endnotes

**Chapter Three: Probability **

3.1 Probability Deﬁned: Empirically

Subjective Probability

3.2 Probability Deﬁned: Classically

Two Fundamental Properties

AND and OR Statements

Practice Exercises

Use of Mathematical Formulas in Simple Experiments

3.3 More Complex Experiments: Tree Diagram

3.4 More Complex Experiments: Multiplication Rules

Dependent and Independent Events

Counting Principle

3.5 Early Gambling Experiments Leading to Discovery of the Normal Curve

3.6 Additional Probability Topics

Mean and Standard Deviation of a Discrete Probability Distribution

Expected Value

Permutations and Combinations

Summary

Exercises

**Chapter Four: Normal Distribution **

4.0 Origins of the Concept

4.1 Idealized Normal Curve

Characteristics of the Normal Curve

Use of the Normal Curve Table

4.2 Applications: Idealized Normal Curve

4.3 Working Backward with the Normal Curve Table

Applications

4.4 Binomial Distribution: An Introduction to Sampling

Sampling from a Two-Category Population

Terminology

4.5 Binomial Sampling Distribution: Applications

Excel Excitement

Summary

Exercises

Endnotes

**Chapter Five: Central Limit Theorem **

5.1 Central Limit Theorem

5.2 Applying the Central Limit Theorem

Random Selection

5.3 How n and σ Aﬀect σx

How σ Aﬀects σx ¯

How n Aﬀects σx ¯

5.4 Central Limit Theorem Applied to Nonnormal Populations

Excel Excitement

Summary

Exercises

Endnotes

**Chapter Six: Introduction to Hypothesis Testing **

6.1 Basic Concepts of Hypothesis Testing

Accept/Reject Decision Making

Type I Error

Type II Error

Power

6.2 Applications

6.3 Controlling Error

Excel Excitement

Summary

Exercises

**Chapter Seven: Hypothesis Testing **

7.1 Two-Tailed Hypothesis Tests ( Large Sample, n ≥ 30)

Method One: The P-Value Method

Methods Two and Three: The Classical Methods

Control Charts

7.2 One-Tailed Hypothesis Tests (Large Sample, n ≥ 30)

Applications

Method One: The P-Value Method

Methods Two and Three: The Classical Methods

Control Charts

7.3 Small-Sample Hypothesis Tests (n < 30)

Applications

Method One: The P-Value Method

Methods Two and Three: The Classical Methods

Starting from Raw Data

Method One: The P-Value Method

Methods Two and Three: The Classical Methods

Excel Excitement

Summary

Exercises

Endnotes

**Chapter Eight: Conﬁdence Intervals **

8.1 Conﬁdence Interval for µ

8.2 Applications

8.3 Selecting Sample Size

8.4 Conﬁdence Intervals Using Small Samples (n , 30)

Assurance of Normal or Near Normal Population

t Score Compensation When s Is Used to Estimate s

Starting from Raw Data

Excel Excitement

Summary

Exercises

Endnotes

**Chapter Nine: Regression and Correlation **

9.0 Origins of the Concept

Galton’s Parent-Oﬀ spring Height Experiment

Application to Statistics

Least-Squares Analysis

Yule’s Application to Social Issues

Correlation Does Not Prove Cause and Eﬀect

9.1 Graphing: A Brief Review

9.2 Simple Linear Regression: Organizing and Analyzing Bivariate Data

Overview

Simple Linear Regression

9.3 Simple Linear Regression: Correlation and Related Topics

r, The Linear Correlation Coeﬃcient

Test of Signiﬁcance for r

r 2, A Measure of Explained Variation

Summary and Discussion

9.4 Using Samples to Estimate Population Characteristics

9.5 Multiple Linear Regression: Organizing and Analyzing Multivariate Data

Simple Linear Regression (Brief Summary)

Multiple Regression

Predicting the Dependent Variable

Interpreting the y-Intercept and Slopes

r 2 in Multiple Regression

Geometric Visualization of Multiple Regression

Adjusted r2

Making Inferences with the Population Regression Coeﬃcients

Excel Excitement

Summary

Exercises

Endnotes

**Chapter Ten: Chi-Square **

10.1 Chi-Square: Test of Independence

Setting up the Hypotheses

Calculating the Test Statistic

Locating the Cutoﬀ and Making a Decision

The Marascuilo Procedure

10.2 Chi-Square: Test of Homogeneity

10.3 Chi-Square: Test of Goodness-of-Fit

Excel Excitement

Summary

Exercises

Endnotes

**Chapter Eleven: Analysis of Variance **

11.1 Measurement Population Sampling: The Idea Behind ANOVA

Diﬀerence of Two Population Means (Independent Case)

Diﬀerence of Two Population Means (Dependent Case)

11.2 One-Way Analysis of Variance (ANOVA) for Equal Sample Sizes

Overview of ANOVA Test

Logic of ANOVA

Sum-of-Squared Distances

11.3 One-Way Analysis of Variance (ANOVA) for Unequal Sample Sizes

11.4 Tukey’s Multiple Comparisons Method for One-Way ANOVA

Rejecting H0: Taking a Closer Look

Tukey Deﬁned

Tukey Applied

11.5 Two-Way Analysis of Variance (ANOVA)

One-Way ANOVA (Brief Summary)

Two-Way ANOVA

The Mathematics Behind Variation Sources

Analyzing Sources of Variation

11.6 Tukey’s Multiple Comparisons Methods for Two-Way ANOVA

The Factor A and Factor B Eﬀects: Tukey and Interaction

Tukey and Factor A

Tukey and Factor B

Excel Excitement

Summary

Exercises

Endnotes

**Chapter Twelve: Time Series **

12.1 The World According to Time Series

Time Series Deﬁned

The Classic Multiplicative Model and Its Four Components

12.2 Smoothing a Time Series

The Cyclical Component Revisited

Simple Moving Averages

Weighted Moving Averages

Exponentially Weighted Moving Averages

12.3 Forecasting Techniques

EWMA Revisited

Regression Revisited

Practice Exercises

12.4 Decomposing the Time Series

Removing the Trend Component

Identifying the Seasonal-Random Eﬀect

Eliminating the Random Eﬀect

Linear Forecasting with Deseasonalized Data

One Final Modiﬁcation

Excel Excitement

Summary

Exercises

Endnotes

**Chapter Thirteen: Additional Topics**

13.1 Two-Category Population Sampling

Small-n Binomial Tests

Use of Binomial Tables

Test of a Single Proportion, Two-Tailed (Large Sample, np and n(1 2 p) Each $ 5)

Test of a Single Proportion, One-Tailed (Large Sample)

Conﬁdence Interval Estimate of p (Large Sample)

Test of a Single Proportion (Small n)

Diﬀerence between Two Proportions

13.2 Nonparametric Tests

Sign Test (For Two Dependent Samples)

Wilcoxon Rank-Sum Test (For Two Independent Samples, Each n1, n2 $ 10)

Spearman’s Rank Correlation Coeﬃcient, rs

Excel Excitement

Summary

Exercises

Endnotes

*Answer Key *

*Statistical Tables
Normal Curve (z) Table
t Table
F Table (α = 0.05)
F Table (α = 0.01)
Q Table (α = 0.05)
Q Table (α = 0.01)
Spearman’s rs Table
Binomial Tables
Chi-Square Table
r Table
Random Numbers Table *

*Index *

**Henry R Gibson**

**Bernard L Dillard**

**Bernard L. Dillard** is an associate professor of mathematics at Fashion Institute of Technology in New York City. He enjoys teaching a variety of courses, including Statistical Analysis, Data Analysis for Business Applications, and The Mathematics of Personal Finance. He is the coauthor of *Elementary Statistics (4th edition)*, also published by Kendall Hunt. Away from mathematics, Bernard enjoys acting, modeling, traveling, and watching independent films.

** Elementary Statistics **is written for students with minimal preparation in mathematics while providing instructors a text that is both informative and yet firmly rooted in real-world application, addressing important contemporary issues in sociology, psychology, marketing, finance, medicine, health, factory production, education, biology, anthropology, and so on.

** Elementary Statistics **by Henry Gibson and Bernard Dillard:

- infuses energetic, up–to–date images within the text to make statistical ideas a bit more bearable.
- presents a more in–depth discussion on regression, chi square, and ANOVA.
- includes a new chapter discussing time series.
- features access to datasets through a separate and distinct website.

*Preface *

**Chapter One: Introduction **

1.1 Overview of Course (Basic Concepts)

Population

Sample

Random Sample

Internal and External Validity

1.2 Why We Sample

Sampling to Determine µ

Sampling to Determine p

Excel Excitement

Summary

Exercises

**Chapter Two: Organizing and Analyzing Data **

2.1 Graphical Representations

Histogram

Population Histograms

Frequency Polygon

Circle Graph

2.2 Measures of Central Tendency (Ungrouped Data)

Arithmetic Mean

Median

Mode

Comparison of the Mean, Median, and Mode

2.3 Measures of Dispersion or Spread (Ungrouped Data)

Range

Standard Deviation

2.4 Estimating Population Characteristics

2.5 Measures of Central Tendency and Dispersion/Spread (Grouped Data)

Mean

Standard Deviation

Modal Class

2.6 z Scores and the Use of the Standard Deviation

Two Important Findings

2.7 Additional Descriptive Topics

Pictogram

Stem-and-Leaf Display

Box-and-Whisker Plot

Quartiles

Percentiles

2.8 Writing Research Reports

Background Statement

Design and Procedures of the Study

Results

Analysis and Discussion

Conclusions and Recommendations

Excel Excitement

Summary

Exercises

Research Reports

Endnotes

**Chapter Three: Probability **

3.1 Probability Deﬁned: Empirically

Subjective Probability

3.2 Probability Deﬁned: Classically

Two Fundamental Properties

AND and OR Statements

Practice Exercises

Use of Mathematical Formulas in Simple Experiments

3.3 More Complex Experiments: Tree Diagram

3.4 More Complex Experiments: Multiplication Rules

Dependent and Independent Events

Counting Principle

3.5 Early Gambling Experiments Leading to Discovery of the Normal Curve

3.6 Additional Probability Topics

Mean and Standard Deviation of a Discrete Probability Distribution

Expected Value

Permutations and Combinations

Summary

Exercises

**Chapter Four: Normal Distribution **

4.0 Origins of the Concept

4.1 Idealized Normal Curve

Characteristics of the Normal Curve

Use of the Normal Curve Table

4.2 Applications: Idealized Normal Curve

4.3 Working Backward with the Normal Curve Table

Applications

4.4 Binomial Distribution: An Introduction to Sampling

Sampling from a Two-Category Population

Terminology

4.5 Binomial Sampling Distribution: Applications

Excel Excitement

Summary

Exercises

Endnotes

**Chapter Five: Central Limit Theorem **

5.1 Central Limit Theorem

5.2 Applying the Central Limit Theorem

Random Selection

5.3 How n and σ Aﬀect σx

How σ Aﬀects σx ¯

How n Aﬀects σx ¯

5.4 Central Limit Theorem Applied to Nonnormal Populations

Excel Excitement

Summary

Exercises

Endnotes

**Chapter Six: Introduction to Hypothesis Testing **

6.1 Basic Concepts of Hypothesis Testing

Accept/Reject Decision Making

Type I Error

Type II Error

Power

6.2 Applications

6.3 Controlling Error

Excel Excitement

Summary

Exercises

**Chapter Seven: Hypothesis Testing **

7.1 Two-Tailed Hypothesis Tests ( Large Sample, n ≥ 30)

Method One: The P-Value Method

Methods Two and Three: The Classical Methods

Control Charts

7.2 One-Tailed Hypothesis Tests (Large Sample, n ≥ 30)

Applications

Method One: The P-Value Method

Methods Two and Three: The Classical Methods

Control Charts

7.3 Small-Sample Hypothesis Tests (n < 30)

Applications

Method One: The P-Value Method

Methods Two and Three: The Classical Methods

Starting from Raw Data

Method One: The P-Value Method

Methods Two and Three: The Classical Methods

Excel Excitement

Summary

Exercises

Endnotes

**Chapter Eight: Conﬁdence Intervals **

8.1 Conﬁdence Interval for µ

8.2 Applications

8.3 Selecting Sample Size

8.4 Conﬁdence Intervals Using Small Samples (n , 30)

Assurance of Normal or Near Normal Population

t Score Compensation When s Is Used to Estimate s

Starting from Raw Data

Excel Excitement

Summary

Exercises

Endnotes

**Chapter Nine: Regression and Correlation **

9.0 Origins of the Concept

Galton’s Parent-Oﬀ spring Height Experiment

Application to Statistics

Least-Squares Analysis

Yule’s Application to Social Issues

Correlation Does Not Prove Cause and Eﬀect

9.1 Graphing: A Brief Review

9.2 Simple Linear Regression: Organizing and Analyzing Bivariate Data

Overview

Simple Linear Regression

9.3 Simple Linear Regression: Correlation and Related Topics

r, The Linear Correlation Coeﬃcient

Test of Signiﬁcance for r

r 2, A Measure of Explained Variation

Summary and Discussion

9.4 Using Samples to Estimate Population Characteristics

9.5 Multiple Linear Regression: Organizing and Analyzing Multivariate Data

Simple Linear Regression (Brief Summary)

Multiple Regression

Predicting the Dependent Variable

Interpreting the y-Intercept and Slopes

r 2 in Multiple Regression

Geometric Visualization of Multiple Regression

Adjusted r2

Making Inferences with the Population Regression Coeﬃcients

Excel Excitement

Summary

Exercises

Endnotes

**Chapter Ten: Chi-Square **

10.1 Chi-Square: Test of Independence

Setting up the Hypotheses

Calculating the Test Statistic

Locating the Cutoﬀ and Making a Decision

The Marascuilo Procedure

10.2 Chi-Square: Test of Homogeneity

10.3 Chi-Square: Test of Goodness-of-Fit

Excel Excitement

Summary

Exercises

Endnotes

**Chapter Eleven: Analysis of Variance **

11.1 Measurement Population Sampling: The Idea Behind ANOVA

Diﬀerence of Two Population Means (Independent Case)

Diﬀerence of Two Population Means (Dependent Case)

11.2 One-Way Analysis of Variance (ANOVA) for Equal Sample Sizes

Overview of ANOVA Test

Logic of ANOVA

Sum-of-Squared Distances

11.3 One-Way Analysis of Variance (ANOVA) for Unequal Sample Sizes

11.4 Tukey’s Multiple Comparisons Method for One-Way ANOVA

Rejecting H0: Taking a Closer Look

Tukey Deﬁned

Tukey Applied

11.5 Two-Way Analysis of Variance (ANOVA)

One-Way ANOVA (Brief Summary)

Two-Way ANOVA

The Mathematics Behind Variation Sources

Analyzing Sources of Variation

11.6 Tukey’s Multiple Comparisons Methods for Two-Way ANOVA

The Factor A and Factor B Eﬀects: Tukey and Interaction

Tukey and Factor A

Tukey and Factor B

Excel Excitement

Summary

Exercises

Endnotes

**Chapter Twelve: Time Series **

12.1 The World According to Time Series

Time Series Deﬁned

The Classic Multiplicative Model and Its Four Components

12.2 Smoothing a Time Series

The Cyclical Component Revisited

Simple Moving Averages

Weighted Moving Averages

Exponentially Weighted Moving Averages

12.3 Forecasting Techniques

EWMA Revisited

Regression Revisited

Practice Exercises

12.4 Decomposing the Time Series

Removing the Trend Component

Identifying the Seasonal-Random Eﬀect

Eliminating the Random Eﬀect

Linear Forecasting with Deseasonalized Data

One Final Modiﬁcation

Excel Excitement

Summary

Exercises

Endnotes

**Chapter Thirteen: Additional Topics**

13.1 Two-Category Population Sampling

Small-n Binomial Tests

Use of Binomial Tables

Test of a Single Proportion, Two-Tailed (Large Sample, np and n(1 2 p) Each $ 5)

Test of a Single Proportion, One-Tailed (Large Sample)

Conﬁdence Interval Estimate of p (Large Sample)

Test of a Single Proportion (Small n)

Diﬀerence between Two Proportions

13.2 Nonparametric Tests

Sign Test (For Two Dependent Samples)

Wilcoxon Rank-Sum Test (For Two Independent Samples, Each n1, n2 $ 10)

Spearman’s Rank Correlation Coeﬃcient, rs

Excel Excitement

Summary

Exercises

Endnotes

*Answer Key *

*Statistical Tables
Normal Curve (z) Table
t Table
F Table (α = 0.05)
F Table (α = 0.01)
Q Table (α = 0.05)
Q Table (α = 0.01)
Spearman’s rs Table
Binomial Tables
Chi-Square Table
r Table
Random Numbers Table *

*Index *

**Henry R Gibson**

**Bernard L Dillard**

**Bernard L. Dillard** is an associate professor of mathematics at Fashion Institute of Technology in New York City. He enjoys teaching a variety of courses, including Statistical Analysis, Data Analysis for Business Applications, and The Mathematics of Personal Finance. He is the coauthor of *Elementary Statistics (4th edition)*, also published by Kendall Hunt. Away from mathematics, Bernard enjoys acting, modeling, traveling, and watching independent films.