 # Elementary Statistics

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

Edition: 4

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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.

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
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
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
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

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

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

Henry R. Gibson is Professor of Mathematics at Fashion Institute of Technology, where he teaches a number of courses, including Statistical Analysis and Quantitative Methods. He received his formal training at New York University and Columbia University. Prior to teaching, he worked on the Apollo missions, during which time all of his flights were successful. Gibson also had a brief career as a Manhattan advertising executive.

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.

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