SOLUTION: Campbellsville University Statistics Normal Distribution Discussion

12th Edition
Exploring Statistics
Tales of Distributions
Chris Spatz
Outcrop Publishers
Conway, Arkansas
Exploring Statistics: Tales of Distributions
12th Edition
Chris Spatz
Cover design: Grace Oxley
Answer Key: Jill Schmidlkofer
Webmaster & Ebook: Fingertek Web Design, Tina Haggard
Managers: Justin Murdock, Kevin Spatz
Online study guide available at
http://exploringstatistics.com/studyguide.php
Copyright © 2019 by Outcrop Publishers, LLC
All rights reserved. No part of this publication may be reproduced, distributed, or transmitted in any form or by any
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write to the publisher at the address below.
Outcrop Publishers
615 Davis Street
Conway, AR 72034
Email: info@outcroppublishers.com
Website: outcroppublishers.com
Library of Congress Control Number: [Applied for]
ISBN-13 (hardcover): 978-0-9963392-2-3
ISBN-13 (ebook): 978-0-9963392-3-0
ISBN-13 (study guide): 978-0-9963392-4-7
Examination copies are provided to academics and professionals to consider for adoption as a course textbook.
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Photo Credits – Chapter 1
Karl Pearson – Courtesy of Wellcomeimages.org
Ronald A. Fisher – R.A. Fisher portrait, 0006973, Special Collections Research Center, North Carolina State
University Libraries, Raleigh, North Carolina
Jerzy Neyman – Paul R. Halmos Photograph Collection, e_ph 0223_01, Dolph Briscoe Center for American History,
The University of Texas at Austin
Jacob Cohen – New York University Archives, Records of the NYU Photo Bureau
Printed in the United States of America by Walsworth ®
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About The Author
About The Author
Chris Spatz is at Hendrix College where he twice served as chair of
the Psychology Department. Dr. Spatz’s undergraduate education
was at Hendrix, and his PhD in experimental psychology is from
Tulane University in New Orleans. He subsequently completed
postdoctoral fellowships in animal behavior at the University of
California, Berkeley, and the University of Michigan. Before
returning to Hendrix to teach, Spatz held positions at The University
of the South and the University of Arkansas at Monticello.
Spatz served as a reviewer for the journal Teaching of Psychology
for more than 20 years. He co-authored a research methods textbook,
wrote several chapters for edited books, and was a section editor for the
Encyclopedia of Statistics in Behavioral Science.
In addition to writing and publishing, Dr. Spatz enjoys the outdoors,
especially canoeing, camping, and gardening. He swims several times
a week (mode = 3). Spatz has been an opponent of high textbook prices for years, and he is
happy to be part of a new wave of authors who provide high-quality textbooks to students at
affordable prices.
v
vi
Dedication
With love and affection,
this textbook is dedicated to
Thea Siria Spatz, Ed.D., CHES
Brief Contents
Brief Contents
Preface xiv
1 Introduction 1
2 Exploring Data: Frequency Distributions and Graphs 29
3 Exploring Data: Central Tendency 45
4 Exploring Data: Variability 59
5 Other Descriptive Statistics 77
6 Correlation and Regression 94
7 Theoretical Distributions Including the Normal Distribution 127
8 Samples, Sampling Distributions, and Confidence Intervals 150
9 Effect Size and NHST: One-Sample Designs 175
10 Effect Size, Confidence Intervals, and NHST:
Two-Sample Designs 200
11 Analysis of Variance: Independent Samples 231
12 Analysis of Variance: Repeated Measures 259
13 Analysis of Variance: Factorial Design 271
14 Chi Square Tests 303
15 More Nonparametric Tests 328
16 Choosing Tests and Writing Interpretations 356
Appendixes
A Getting Started 371
B Grouped Frequency Distributions and Central Tendency 376
C Tables 380
D Glossary of Words 401
E Glossary of Symbols 405
F Glossary of Formulas 407
G Answers to Problems 414
References 466
Index 472
vii
viii
Contents
Contents
Preface
xiv
chapter 1 Introduction 1
Disciplines That Use Quantitative Data 5
What Do You Mean, “Statistics”? 6
Statistics: A Dynamic Discipline 8
Some Terminology 9
Problems and Answers 12
Scales of Measurement 13
Statistics and Experimental Design 16
Experimental Design Variables 17
Statistics and Philosophy 20
Statistics: Then and Now 21
How to Analyze a Data Set 22
Helpful Features of This Book 22
Computers, Calculators, and Pencils 24
Concluding Thoughts 25
Key Terms 27
Transition Passage to Descriptive Statistics 28
chapter 2 Exploring Data: Frequency Distributions
and Graphs 29
Simple Frequency Distributions 31
Grouped Frequency Distributions 33
Graphs of Frequency Distributions 35
Describing Distributions 39
Contents
The Line Graph 41
More on Graphics 42
A Moment to Reflect 43
Key Terms 44
chapter 3 Exploring Data: Central Tendency
45
Measures of Central Tendency 46
Finding Central Tendency of Simple Frequency Distributions 49
When to Use the Mean, Median, and Mode 52
Determining Skewness From the Mean and Median 54
The Weighted Mean 55
Estimating Answers 56
Key Terms 58
chapter 4 Exploring Data: Variability
59
Range 61
Interquartile Range 61
Standard Deviation 63
Standard Deviation as a Descriptive Index of Variability
ŝ as an Estimate of σ 69
Variance 73
Statistical Software Programs 74
Key Terms 76
chapter 5 Other Descriptive Statistics
Describing Individual Scores 78
Boxplots 82
Effect Size Index 86
The Descriptive Statistics Report 89
Key Terms 92
77
Transition Passage to Bivariate Statistics
chapter 6 Correlation and Regression
Bivariate Distributions 96
Positive Correlation 96
Negative Correlation 99
Zero Correlation 101
Correlation Coefficient 102
Scatterplots 106
64
94
93
ix
x
Contents
Interpretations of r 106
Uses of r 110
Strong Relationships but Low Correlation Coefficients
Other Kinds of Correlation Coefficients 115
Linear Regression 116
The Regression Equation 117
Key Terms 124
What Would You Recommend? Chapters 2-6 125
112
Transition Passage to Inferential Statistics
126
chapter 7 Theoretical Distributions Including the
Normal Distribution 127
Probability 128
A Rectangular Distribution 129
A Binomial Distribution 130
Comparison of Theoretical and Empirical Distributions 131
The Normal Distribution 132
Comparison of Theoretical and Empirical Answers 146
Other Theoretical Distributions 146
Key Terms 147
Transition Passage to the Analysis of Data From
Experiments 149
chapter 8 Samples, Sampling Distributions, and
Confidence Intervals 150
Random Samples 152
Biased Samples 155
Research Samples 156
Sampling Distributions 157
Sampling Distribution of the Mean 157
Central Limit Theorem 159
Constructing a Sampling Distribution When σ Is Not Available
The t Distribution 165
Confidence Interval About a Population Mean 168
Categories of Inferential Statistics 172
Key Terms 173
164
Contents
Transition Passage to Null Hypothesis Significance
Testing 174
chapter 9 Effect Size and NHST: One-Sample Designs
175
Effect Size Index 176
The Logic of Null Hypothesis Significance Testing (NHST) 179
Using the t Distribution for Null Hypothesis Significance Testing 182
A Problem and the Accepted Solution 184
The One-Sample t Test 186
An Analysis of Possible Mistakes 188
The Meaning of p in p
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