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CliffsQuickReview™
Statistics
By David H. Voelker, MA,
Peter Z. Orton, Ed M,
and Scott V. Adams
An International Data Group Company
New York, NY • Cleveland, OH • Indianapolis, IN
6388-2 FM.F 4/27/01 12:18 PM Page i
CliffsQuickReviewTM Statistics
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About the Authors
David Voelker is a respected educator and author
from the San Francisco Bay area.
Peter Orton is Program Director of Global Cur-
riculum Technology for IBM, designing leader-
ship development Web sites, videos, and online
simulators for IBMers globally. Orton lives in
North Carolina with his wife and 10-year-old
daughter.
Scott Adams is earning his PhD in physics at
Vanderbilt University. His main interest is in
molecular biophysics, especially electrophysiology.
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6388-2 FM.F 4/27/01 12:18 PM Page ii
Table of Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
Why You Need This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
How to Use This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
Visit Our Web Site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2
Chapter 1: Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
Types of Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
Numerical statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
Pictorial statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
Method of Statistical Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
Steps in the Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
Making Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
Comparing Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
Common Statistics Mistakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
Chapter 2: Graphic Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8
Bar Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
Dot Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
Pie Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
Ogive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11
Frequency Histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
Relative Frequency Histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
Frequency Polygon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14
Frequency Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
Stem-and-Leaf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17
Box Plot (Box-and-Whiskers) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
Scatter Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20
Chapter 3: Numerical Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
Measures of Central Tendency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24
Median . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24
Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25
Notation and formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25
Mean for grouped data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25
Median for grouped data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26
Symmetric distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28
Skewed curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28
Measures of Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29
Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30
Deviation and variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30
Standard deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31
Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31
6388-2 FM.F 4/27/01 12:18 PM Page iii
Empirical rule: The normal curve . . . . . . . . . . . . . . . . . . . . . . . . .31
Shortcut formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32
Percentile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33
Quartiles and interquartile range . . . . . . . . . . . . . . . . . . . . . . . . . .33
Measurement Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34
Chapter 4: Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37
Classic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37
Relative Frequency Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38
Probability of Simple Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38
Independent Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39
Dependent Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39
Probability of Joint Occurrences . . . . . . . . . . . . . . . . . . . . . . . . . . . .40
Multiplication rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40
Addition rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41
Non-Mutually Exclusive Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . .42
Double Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42
Conditional Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44
Probability Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44
Discrete vs. continuous variables . . . . . . . . . . . . . . . . . . . . . . . . . .45
Total of probabilities of discrete variables . . . . . . . . . . . . . . . . . . .46
The Binomial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46
Binomial experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46
Binomial table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47
Mean and standard deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . .47
Chapter 5: Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50
Populations, Samples, Parameters, and Statistics . . . . . . . . . . . . . . . .50
Sampling Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52
Random and Systematic Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53
Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54
Properties of the Normal Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54
Normal Approximation to the Binomial . . . . . . . . . . . . . . . . . . . . . .58
Chapter 6: Principles of Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62
Stating Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62
The Test Statistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63
One- and Two-tailed Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66
Type I and II Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68
Significance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69
Point Estimates and Confidence Intervals . . . . . . . . . . . . . . . . . . . . .71
Estimating a Difference Score . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72
Univariate Tests: An Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73
iv CliffsQuickReview Statistics
6388-2 FM.F 4/27/01 12:18 PM Page iv
Table of Contents v
Chapter 7: Univariate Inferential Tests . . . . . . . . . . . . . . . . . . . . . . . . . .76
One-sample z-test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76
Confidence interval for population mean using z . . . . . . . . . . . . .78
Choosing a sample size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .79
One-sample t-test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .79
Confidence interval for population mean using t . . . . . . . . . . . . . .82
Two-sample z-test for Comparing Two Means . . . . . . . . . . . . . . . . . .83
Two-sample t-test for Comparing Two Means . . . . . . . . . . . . . . . . . .84
Confidence interval for comparing two means . . . . . . . . . . . . . . .85
Pooled variance method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .86
Paired Difference t-test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .88
Test for a Single Population Proportion . . . . . . . . . . . . . . . . . . . . . . .89
Confidence interval for a single population proportion . . . . . . . . .90
Choosing a sample size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .90
Test for Comparing Two Proportions . . . . . . . . . . . . . . . . . . . . . . . . .91
Confidence interval for comparing two proportions . . . . . . . . . . .93
Chapter 8: Bivariate Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . .96
Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .96
Finding the significance of r . . . . . . . . . . . . . . . . . . . . . . . . . . . .100
The coefficient of determination . . . . . . . . . . . . . . . . . . . . . . . . .102
Simple Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102
Confidence interval for the slope . . . . . . . . . . . . . . . . . . . . . . . . .105
Confidence interval for prediction . . . . . . . . . . . . . . . . . . . . . . . .107
Assumptions and cautions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108
Chi-Square (χ2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .110
Appendix A: Common Mistakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .114
Appendix B: Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .117
CQR Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .136
CQR Resource Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .142
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .145
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .151
6388-2 FM.F 4/27/01 12:18 PM Page v
6388-2 FM.F 4/27/01 12:18 PM Page vi
INTRODUCTION
Statistics are a powerful tool for finding patterns in data and inferring
important connections between events in the real world. We are accus-
tomed to seeing statistics every day — in the news, for example. However,
many people find statistics confusing and intimidating. Often statistics are
considered to make an argument irrefutable. On the other hand, some
people perceive statistics as a trick, used to support outrageous claims.
This book is intended to clarify some of the elements of statistical reason-
ing and analysis. The format is simple, and there are many examples to
help translate abstract ideas into concrete applications.
Why You Need This Book
Can you answer yes to any of these questions?
■Do you need to review the fundamentals of statistics fast?
■Do you need a course supplement to statistics?
■Do you need a concise, comprehensive reference for statistics?
■Do you need to prepare for a statistics exam?
If so, then CliffsQuickReview Statistics is for you!
How to Use This Book
You’re in charge here. You get to decide how to use this book. You can read
it cover to cover or just look up the information you need right now. Here
are some recommended ways to search for topics.
■Use the Pocket Guide to find essential information, such as basic
statistics formulas and abbreviations.
■Flip through the book looking for subject areas at the top of each
page.
■Get a glimpse of what you’ll gain from a chapter by reading through
the “Chapter Check-In” at the beginning of each chapter.
6388-2 Intro.F 4/27/01 9:12 AM Page 1
■Use the “Chapter Checkout” at the end of each chapter to gauge your
grasp of the important information you need to know.
■Test your knowledge more completely in the CQR Review and look
for additional sources of information in the CQR Resource Center.
■Use the glossary to find key terms fast. This book defines new terms
and concepts where they first appear in the chapter. If a word is bold-
faced, you can find a more complete definition in the book’s glossary.
■Or flip through the book until you find what you’re looking for—we
organized this book to gradually build on key concepts.
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2CliffsQuickReview Statistics
6388-2 Intro.F 4/27/01 9:12 AM Page 2
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StatisticsStatisticsTheessentialsfromtheexpertsatBookmarkusatcliffsnotes.comMasterthebasics—fastCompletecoverageofcoreconceptsAccessible,topic-by-topicorganizationFreepocketguideforeasyreferenceWetakegreatnotes—andmakelearningasnapWhenitcomestopinpointingthestuffyoureallyneedtoknow,nobodydoesitbette...

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