Statistics II for Dummies (For Dummies (Math & Science))

413 Pages·2009·6.07 MB·English

by  Deborah Rumsey

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Statistics II
FOR
DUMmIES
‰
by Deborah Rumsey, PhD
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Statistics II For Dummies®
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Dedication
To my husband Eric: My sun rises and sets with you. To my son Clint: I love
you up to the moon and back.
About the Author
Deborah Rumsey has a PhD in Statistics from The Ohio State University
(1993), where she’s a Statistics Education Specialist/Auxiliary Faculty
Member for the Department of Statistics. Dr. Rumsey has been given the dis-
tinction of being named a Fellow of the American Statistical Association. She
has also won the Presidential Teaching Award from Kansas State University.
She’s the author of Statistics For Dummies, Statistics Workbook For Dummies,
and Probability For Dummies and has published numerous papers and given
many professional presentations on the subject of statistics education. Her
passions include being with her family, bird watching, getting more seat time
on her Kubota tractor, and cheering the Ohio State Buckeyes on to another
National Championship.
Author’s Acknowledgments
Thanks again to Lindsay Lefevere and Kathy Cox for giving me the opportu-
nity to write this book; to Natalie Harris and Chrissy Guthrie for their unwav-
ering support and perfect chiseling and molding of my words and ideas;
to Kim Gilbert, University of Georgia, for a thorough technical view; and to
Elizabeth Rea and Sarah Westfall for great copy-editing. Special thanks to
Elizabeth Stasny for guidance and support from day one; and to Joan Garfi eld
for constant inspiration and encouragement.
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Contents at a Glance
Introduction ................................................................ 1
Part I: Tackling Data Analysis and
Model-Building Basics ................................................. 7
Chapter 1: Beyond Number Crunching: The Art and Science of Data Analysis ........9
Chapter 2: Finding the Right Analysis for the Job .......................................................21
Chapter 3: Reviewing Confi dence Intervals and Hypothesis Tests ...........................37
Part II: Using Different Types of Regression
to Make Predictions ................................................... 53
Chapter 4: Getting in Line with Simple Linear Regression .........................................55
Chapter 5: Multiple Regression with Two X Variables................................................83
Chapter 6: How Can I Miss You If You Won’t Leave?
Regression Model Selection .......................................................................................103
Chapter 7: Getting Ahead of the Learning Curve with Nonlinear Regression .......115
Chapter 8: Yes, No, Maybe So: Making Predictions by
Using Logistic Regression ..........................................................................................137
Part III: Analyzing Variance with ANOVA ................. 151
Chapter 9: Testing Lots of Means? Come On Over to ANOVA! ................................153
Chapter 10: Sorting Out the Means with Multiple Comparisons .............................173
Chapter 11: Finding Your Way through Two-Way ANOVA .......................................191
Chapter 12: Regression and ANOVA: Surprise Relatives! .........................................207
Part IV: Building Strong Connections
with Chi-Square Tests .............................................. 219
Chapter 13: Forming Associations with Two-Way Tables ........................................221
Chapter 14: Being Independent Enough for the Chi-Square Test ............................241
Chapter 15: Using Chi-Square Tests for Goodness-of-Fit
(Your Data, Not Your Jeans) ......................................................................................263
Part V: Nonparametric Statistics:
Rebels without a Distribution ................................... 273
Chapter 16: Going Nonparametric ...............................................................................275
Chapter 17: All Signs Point to the Sign Test and Signed Rank Test .........................287
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Chapter 18: Pulling Rank with the Rank Sum Test.....................................................303
Chapter 19: Do the Kruskal-Wallis and Rank the Sums with the Wilcoxon ............313
Chapter 20: Pointing Out Correlations with Spearman’s Rank ................................325
Part VI: The Part of Tens .......................................... 333
Chapter 21: Ten Common Errors in Statistical Conclusions ....................................335
Chapter 22: Ten Ways to Get Ahead by Knowing Statistics .....................................347
Chapter 23: Ten Cool Jobs That Use Statistics ..........................................................357
Appendix: Reference Tables ...................................... 367
Index ...................................................................... 379
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Table of Contents
Introduction ................................................................. 1
About This Book ..............................................................................................1
Conventions Used in This Book .....................................................................2
What You’re Not to Read ................................................................................3
Foolish Assumptions .......................................................................................3
How This Book Is Organized ..........................................................................3
Part I: Tackling Data Analysis and Model-Building Basics ................4
Part II: Using Different Types of Regression to Make Predictions ...4
Part III: Analyzing Variance with ANOVA ............................................4
Part IV: Building Strong Connections with Chi-Square Tests ...........5
Part V: Nonparametric Statistics: Rebels without a Distribution ....5
Part VI: The Part of Tens .......................................................................5
Icons Used in This Book .................................................................................5
Where to Go from Here ...................................................................................6
Part I: Tackling Data Analysis and
Model-Building Basics .................................................. 7
Chapter 1: Beyond Number Crunching:
The Art and Science of Data Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . .9
Data Analysis: Looking before You Crunch ..................................................9
Nothing (not even a straight line) lasts forever ...............................11
Data snooping isn’t cool .....................................................................11
No (data) fi shing allowed ....................................................................12
Getting the Big Picture: An Overview of Stats II ........................................13
Population parameter .........................................................................13
Sample statistic ....................................................................................14
Confi dence interval ..............................................................................14
Hypothesis test ....................................................................................15
Analysis of variance (ANOVA) ...........................................................15
Multiple comparisons..........................................................................16
Interaction effects ................................................................................16
Correlation ............................................................................................17
Linear regression .................................................................................18
Chi-square tests ...................................................................................19
Nonparametrics ...................................................................................20
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viii
Statistics II For Dummies
Chapter 2: Finding the Right Analysis for the Job . . . . . . . . . . . . . . . . .21
Categorical versus Quantitative Variables .................................................22
Statistics for Categorical Variables .............................................................23
Estimating a proportion ......................................................................23
Comparing proportions ......................................................................24
Looking for relationships between categorical variables...............25
Building models to make predictions ...............................................26
Statistics for Quantitative Variables ...........................................................27
Making estimates .................................................................................27
Making comparisons ...........................................................................28
Exploring relationships .......................................................................28
Predicting y using x .............................................................................30
Avoiding Bias .................................................................................................31
Measuring Precision with Margin of Error .................................................33
Knowing Your Limitations ............................................................................34
Chapter 3: Reviewing Confi dence Intervals
and Hypothesis Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37
Estimating Parameters by Using Confi dence Intervals .............................38
Getting the basics: The general form of a confi dence interval ......38
Finding the confi dence interval for a population mean ..................39
What changes the margin of error? ...................................................40
Interpreting a confi dence interval .....................................................43
What’s the Hype about Hypothesis Tests? ................................................44
What Ho and Ha really represent ......................................................44
Gathering your evidence into a test statistic ...................................45
Determining strength of evidence with a p-value ............................45
False alarms and missed opportunities: Type I and II errors.........46
The power of a hypothesis test .........................................................48
Part II: Using Different Types of Regression
to Make Predictions .................................................... 53
Chapter 4: Getting in Line with Simple Linear Regression. . . . . . . . . .55
Exploring Relationships with Scatterplots and Correlations ...................56
Using scatterplots to explore relationships .....................................57
Collating the information by using the correlation coeffi cient ......58
Building a Simple Linear Regression Model ...............................................60
Finding the best-fi tting line to model your data...............................60
The y-intercept of the regression line ...............................................61
The slope of the regression line.........................................................62
Making point estimates by using the regression line ......................63
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