Statistical analysis with excel for dummies, 3rd edition

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Statistical Analysis
with Excel®

3RD

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EDITION


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Statistical Analysis
with Excel®

3RD

EDITION

by Joseph Schmuller, PhD

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Statistical Analysis with Excel® For Dummies®, 3rd Edition
Published by
John Wiley & Sons, Inc.
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Hoboken, NJ 07030-5774
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About the Author
Joseph Schmuller, PhD is a veteran of over 25 years in Information
Technology. He is the author of several books on computing, including the
three editions of Teach Yourself UML in 24 Hours (SAMS), and the two editions
of Statistical Analysis with Excel For Dummies. He has written numerous
articles on advanced technology. From 1991 through 1997, he was
Editor-in-Chief of PC AI magazine.

He is a former member of the American Statistical Association, and he has
taught statistics at the undergraduate and graduate levels. He holds a B.S.
from Brooklyn College, an M.A. from the University of Missouri-Kansas City,
and a Ph.D. from the University of Wisconsin, all in psychology. He and his
family live in Jacksonville, Florida, where he is on the faculty at the University
of North Florida.

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Dedication
In loving memory of my wonderful mother, Sara Riba Schmuller, who first
showed me how to work with numbers, and taught me the skills to write
about them.

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Author’s Acknowledgments
As I said in the first two editions, writing a For Dummies book is an incredible
amount of fun. You get to air out your ideas in a friendly, conversational way,
and you get a chance to throw in some humor, too. To write one more edition
is a wonderful trifecta. I worked again with a terrific team. Acquisitions
Editor Stephanie McComb and Project Editor Beth Taylor of Wiley have been

encouraging, cooperative, and above all, patient. Dennis Short is unsurpassed
as a Technical Editor. His students at Purdue are lucky to have him. Any
errors that remain are under the sole proprietorship of the author. My
deepest thanks to Stephanie and Beth. My thanks to Waterside Productions
for representing me in this effort.
Again I thank mentors in college and graduate school who helped shape my
statistical knowledge: Mitch Grossberg (Brooklyn College); Mort Goldman, Al
Hillix, Larry Simkins, and Jerry Sheridan (University of Missouri-Kansas City);
and Cliff Gillman and John Theios (University of Wisconsin-Madison). A long
time ago at the University of Missouri-Kansas City, Mort Goldman exempted
me from a graduate statistics final on one condition — that I learn the last
course topic, Analysis of Covariance, on my own. I hope he’s happy with
Appendix B.
I thank Kathryn as always for so much more than I can say. Finally, again a
special note of thanks to my friend Brad, who suggested this whole thing in
the first place!

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Publisher’s Acknowledgments
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Publishing and Editorial for Technology Dummies
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Composition Services
Debbie Stailey, Director of Composition Services

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Contents at a Glance
Introduction................................................................. 1
Part I: Getting Started with Statistical
Analysis with Excel....................................................... 7
Chapter 1: Evaluating Data in the Real World................................................................. 9
Chapter 2: Understanding Excel’s Statistical Capabilities........................................... 31

Part II: Describing Data.............................................. 63
Chapter 3: Show and Tell: Graphing Data...................................................................... 65
Chapter 4: Finding Your Center...................................................................................... 97
Chapter 5: Deviating from the Average........................................................................ 113
Chapter 6: Meeting Standards and Standings............................................................. 131
Chapter 7: Summarizing It All........................................................................................ 147
Chapter 8: What’s Normal?............................................................................................ 173

Part III: Drawing Conclusions from Data.................... 185
Chapter 9: The Confidence Game: Estimation............................................................ 187
Chapter 10: One-Sample Hypothesis Testing.............................................................. 203
Chapter 11: Two-Sample Hypothesis Testing............................................................. 219
Chapter 12: Testing More Than Two Samples............................................................ 251
Chapter 13: Slightly More Complicated Testing......................................................... 279
Chapter 14: Regression: Linear and Multiple.............................................................. 293
Chapter 15: Correlation: The Rise and Fall of Relationships.................................... 331

Part IV: Probability.................................................. 353
Chapter 16: Introducing Probability............................................................................. 355
Chapter 17: More on Probability.................................................................................. 379

Chapter 18: A Career in Modeling................................................................................. 393

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Part V: The Part of Tens............................................ 413
Chapter 19: Ten Statistical and Graphical Tips and Traps........................................ 415
Chapter 20: Ten Things (Thirteen, Actually)
That Just Didn’t Fit in Any Other Chapter................................................................ 421

Appendix A: When Your Worksheet Is a Database....... 451
Appendix B: The Analysis of Covariance..................... 467
Index....................................................................... 481
Bonus Appendix 1: When Your Data Live Elsewhere
Bonus Appendix 2: Tips for Teachers (And Learners)

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Table of Contents
Introduction.................................................................. 1
About This Book............................................................................................... 2
What You Can Safely Skip................................................................................ 2
Foolish Assumptions........................................................................................ 2
How This Book Is Organized........................................................................... 3
Part I: Getting Started with Statistical Analysis with Excel............... 3
Part II: Describing Data.......................................................................... 3
Part III: Drawing Conclusions from Data.............................................. 3
Part IV: Probability................................................................................. 4
Part V: The Part of Tens......................................................................... 4

Appendix A: When Your Worksheet is a Database............................. 4
Appendix B: The Analysis of Covariance............................................. 4
Bonus Appendix 1: When Your Data Live Elsewhere......................... 5
Bonus Appendix 2: Tips for Teachers (And Learners)...................... 5
Icons Used in This Book.................................................................................. 5
Where to Go from Here.................................................................................... 6

Part I: Getting Started with Statistical
Analysis with Excel........................................................ 7
Chapter 1: Evaluating Data in the Real World . . . . . . . . . . . . . . . . . . . . . 9
The Statistical (And Related) Notions You Just Have to Know.................. 9
Samples and populations..................................................................... 10
Variables: Dependent and independent............................................ 11
Types of data......................................................................................... 12
A little probability................................................................................. 13
Inferential Statistics: Testing Hypotheses................................................... 14
Null and alternative hypotheses......................................................... 15
Two types of error................................................................................ 16
What’s New in Excel 2013?............................................................................ 18
What’s Old in Excel 2013?.............................................................................. 22
Knowing the Fundamentals........................................................................... 24
Autofilling cells...................................................................................... 24
Referencing cells................................................................................... 26
What’s New in This Edition?......................................................................... 28

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Statistical Analysis with Excel For Dummies, 3rd Edition
Chapter 2: Understanding Excel’s Statistical Capabilities . . . . . . . . . 31
Getting Started................................................................................................ 31
Setting Up for Statistics................................................................................. 34
Worksheet functions in Excel 2013..................................................... 34
Quickly accessing statistical functions.............................................. 37
Array functions..................................................................................... 38
What’s in a name? An array of possibilities...................................... 42
Creating your own array formulas...................................................... 50
Using data analysis tools..................................................................... 51
Accessing Commonly Used Functions......................................................... 55
For Mac Users................................................................................................. 56
The Ribbon............................................................................................ 57
Data analysis tools................................................................................ 58

Part II: Describing Data............................................... 63
Chapter 3: Show and Tell: Graphing Data . . . . . . . . . . . . . . . . . . . . . . . . 65
Why Use Graphs?............................................................................................ 65
Some Fundamentals....................................................................................... 67
Excel’s Graphics (Chartics?) Capabilities................................................... 67
Inserting a chart.................................................................................... 68
Becoming a Columnist................................................................................... 69
Stacking the columns........................................................................... 73
One more thing..................................................................................... 74
Slicing the Pie.................................................................................................. 75
A word from the wise........................................................................... 77
Drawing the Line............................................................................................. 77
Adding a Spark................................................................................................ 81
Passing the Bar............................................................................................... 83
The Plot Thickens........................................................................................... 85

Finding Another Use for the Scatter Chart.................................................. 89
Power View!..................................................................................................... 90
For Mac Users................................................................................................. 93

Chapter 4: Finding Your Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Means: The Lore of Averages........................................................................ 97
Calculating the mean............................................................................ 98
AVERAGE and AVERAGEA................................................................... 99
AVERAGEIF and AVERAGEIFS............................................................ 101
TRIMMEAN........................................................................................... 104
Other means to an end....................................................................... 106
Medians: Caught in the Middle................................................................... 108
Finding the median............................................................................. 108
MEDIAN................................................................................................ 109

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Table of Contents
Statistics À La Mode..................................................................................... 110
Finding the mode................................................................................ 110
MODE.SNGL and MODE.MULT.......................................................... 110

Chapter 5: Deviating from the Average . . . . . . . . . . . . . . . . . . . . . . . . . 113
Measuring Variation..................................................................................... 114
Averaging squared deviations: Variance and how to calculate it......114
VAR.P and VARPA............................................................................... 117
Sample variance.................................................................................. 119
VAR.S and VARA................................................................................. 119
Back to the Roots: Standard Deviation...................................................... 120

Population standard deviation......................................................... 121
STDEV.P and STDEVPA...................................................................... 121
Sample standard deviation................................................................ 122
STDEV.S and STDEVA......................................................................... 122
The missing functions: STDEVIF and STDEVIFS.............................. 123
Related Functions......................................................................................... 127
DEVSQ.................................................................................................. 127
Average deviation............................................................................... 128
AVEDEV................................................................................................ 129

Chapter 6: Meeting Standards and Standings . . . . . . . . . . . . . . . . . . . 131
Catching Some Zs......................................................................................... 131
Characteristics of z-scores................................................................ 132
Bonds versus the Bambino................................................................ 132
Exam scores......................................................................................... 133
STANDARDIZE..................................................................................... 134
Where Do You Stand?.................................................................................. 136
RANK.EQ and RANK.AVG................................................................... 136
LARGE and SMALL.............................................................................. 138
PERCENTILE.INC and PERCENTILE.EXC ......................................... 139
PERCENTRANK.INC and PERCENTRANK.EXC................................. 141
Data analysis tool: Rank and Percentile........................................... 143
For Mac Users............................................................................................... 145

Chapter 7: Summarizing It All . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Counting Out................................................................................................. 147
COUNT, COUNTA, COUNTBLANK, COUNTIF, COUNTIFS.............. 147
The Long and Short of It.............................................................................. 150
MAX, MAXA, MIN, and MINA ............................................................ 150
Getting Esoteric............................................................................................ 152

SKEW and SKEW.P.............................................................................. 152
KURT..................................................................................................... 154
Tuning In the Frequency.............................................................................. 156
FREQUENCY......................................................................................... 156
Data analysis tool: Histogram........................................................... 158

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Can You Give Me a Description?................................................................. 160
Data analysis tool: Descriptive Statistics......................................... 160
Be Quick About It!......................................................................................... 162
Instant Statistics........................................................................................... 165
For Mac Users............................................................................................... 167
Descriptive statistics.......................................................................... 167
Histogram............................................................................................ 169
Instant statistics.................................................................................. 170

Chapter 8: What’s Normal? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
Hitting the Curve.......................................................................................... 173
Digging deeper.................................................................................... 174
Parameters of a normal distribution................................................ 175
NORM.DIST.......................................................................................... 177
NORM.INV............................................................................................ 178
A Distinguished Member of the Family...................................................... 179

NORM.S.DIST....................................................................................... 181
NORM.S.INV......................................................................................... 181
PHI and GAUSS.................................................................................... 182

Part III: Drawing Conclusions from Data..................... 185
Chapter 9: The Confidence Game: Estimation . . . . . . . . . . . . . . . . . . . 187
Understanding Sampling Distribution....................................................... 187
An EXTREMELY Important Idea: The Central Limit Theorem................ 189
Simulating the Central Limit Theorem............................................. 190
The Limits of Confidence............................................................................. 195
Finding confidence limits for a mean............................................... 195
CONFIDENCE.NORM........................................................................... 198
Fit to a t.......................................................................................................... 199
CONFIDENCE.T.................................................................................... 201

Chapter 10: One-Sample Hypothesis Testing . . . . . . . . . . . . . . . . . . . . 203
Hypotheses, Tests, and Errors................................................................... 203
Hypothesis tests and sampling distributions................................. 204
Catching Some Z’s Again............................................................................. 207
ZTEST................................................................................................... 209
t for One......................................................................................................... 211
T.DIST, T.DIST.RT, and T.DIST.2T .................................................... 212
T.INV and T.INV.2T............................................................................. 213
Testing a Variance........................................................................................ 214
CHISQ.DIST and CHISQ.DIST.RT........................................................ 216
CHISQ.INV and CHISQ.INV.RT........................................................... 217

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Table of Contents
Chapter 11: Two-Sample Hypothesis Testing . . . . . . . . . . . . . . . . . . . 219
Hypotheses Built for Two............................................................................ 219
Sampling Distributions Revisited............................................................... 220
Applying the Central Limit Theorem................................................ 221
Z’s once more...................................................................................... 223
Data analysis tool: z-Test: Two Sample for Means......................... 224
t for Two........................................................................................................ 227
Like peas in a pod: Equal variances................................................. 227
Like p’s and q’s: Unequal variances................................................. 229
T.TEST.................................................................................................. 229
Data Analysis Tool: t-Test: Two Sample .......................................... 230
A Matched Set: Hypothesis Testing for Paired Samples.......................... 234
T.TEST for matched samples............................................................ 235
Data analysis tool: t-test: Paired Two Sample for Means .............. 237
Testing Two Variances................................................................................ 239
Using F in conjunction with t............................................................. 241
F.TEST.................................................................................................. 242
F.DIST and F.DIST.RT.......................................................................... 244
F.INV and F.INV.RT.............................................................................. 245
Data Analysis Tool: F-test Two Sample for Variances.................... 246
For Mac Users............................................................................................... 248

Chapter 12: Testing More Than Two Samples . . . . . . . . . . . . . . . . . . . 251
Testing More Than Two............................................................................... 251
A thorny problem............................................................................... 252
A solution............................................................................................. 253
Meaningful relationships................................................................... 257
After the F-test..................................................................................... 258
Data analysis tool: Anova: Single Factor.......................................... 262

Comparing the means........................................................................ 263
Another Kind of Hypothesis, Another Kind of Test................................. 265
Working with repeated measures ANOVA....................................... 266
Getting trendy..................................................................................... 268
Data analysis tool: Anova: Two Factor Without Replication......... 271
Analyzing trend................................................................................... 273
For Mac Users............................................................................................... 275
Single Factor Analysis of Variance................................................... 275
Repeated Measures............................................................................ 276

Chapter 13: Slightly More Complicated Testing . . . . . . . . . . . . . . . . . 279
Cracking the Combinations......................................................................... 279
Breaking down the variances............................................................ 280
Data analysis tool: Anova: Two-Factor Without Replication......... 281

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Statistical Analysis with Excel For Dummies, 3rd Edition
Cracking the Combinations Again.............................................................. 284
Rows and columns.............................................................................. 284
Interactions.......................................................................................... 285
The analysis......................................................................................... 285
Data analysis tool: Anova: Two-Factor With Replication.............. 287
For Mac Users............................................................................................... 290

Chapter 14: Regression: Linear and Multiple . . . . . . . . . . . . . . . . . . . . 293
The Plot of Scatter........................................................................................ 293
Graphing Lines.............................................................................................. 295
Regression: What a Line!.............................................................................. 297
Using regression for forecasting....................................................... 299
Variation around the regression line............................................... 299
Testing hypotheses about regression.............................................. 301
Worksheet Functions for Regression......................................................... 307
SLOPE, INTERCEPT, STEYX............................................................... 307
FORECAST............................................................................................ 309
Array function: TREND....................................................................... 309
Array function: LINEST....................................................................... 313
Data Analysis Tool: Regression ................................................................. 315
Tabled output...................................................................................... 317
Graphic output.................................................................................... 319
Juggling Many Relationships at Once: Multiple Regression................... 320
Excel Tools for Multiple Regression.......................................................... 321
TREND revisited.................................................................................. 321
LINEST revisited.................................................................................. 322
Regression data analysis tool revisited........................................... 325
For Mac Users............................................................................................... 327

Chapter 15: Correlation: The Rise and Fall of Relationships . . . . . . . 331
Scatterplots Again........................................................................................ 331
Understanding Correlation.......................................................................... 332
Correlation and Regression......................................................................... 334
Testing Hypotheses About Correlation..................................................... 338
Is a correlation coefficient greater than zero?................................ 338
Do two correlation coefficients differ?............................................. 339
Worksheet Functions for Correlation........................................................ 340

CORREL and PEARSON...................................................................... 341
RSQ....................................................................................................... 342
COVARIANCE.P and COVARIANCE.S................................................ 343
Data Analysis Tool: Correlation.................................................................. 343
Tabled output...................................................................................... 345
Data Analysis Tool: Covariance.................................................................. 348
Testing Hypotheses About Correlation..................................................... 349
Worksheet Functions: FISHER, FISHERINV...................................... 349
For Mac Users............................................................................................... 350

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Table of Contents

Part IV: Probability................................................... 353
Chapter 16: Introducing Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
What Is Probability?..................................................................................... 355
Experiments, trials, events, and sample spaces............................. 356
Sample spaces and probability......................................................... 356
Compound Events........................................................................................ 357
Union and intersection....................................................................... 357
Intersection again............................................................................... 358
Conditional Probability................................................................................ 359
Working with the probabilities......................................................... 360
The foundation of hypothesis testing.............................................. 360
Large Sample Spaces.................................................................................... 361
Permutations....................................................................................... 362
Combinations...................................................................................... 362
Worksheet Functions................................................................................... 363

FACT..................................................................................................... 363
PERMUT and PERMUTIONA.............................................................. 364
COMBIN and COMBINA...................................................................... 365
Random Variables: Discrete and Continuous........................................... 365
Probability Distributions and Density Functions..................................... 366
The Binomial Distribution........................................................................... 368
Worksheet Functions................................................................................... 369
BINOM.DIST and BINOM.DIST.RANGE............................................. 370
NEGBINOM.DIST.................................................................................. 372
Hypothesis Testing with the Binomial Distribution................................. 373
BINOM.INV........................................................................................... 374
More on hypothesis testing............................................................... 375
The Hypergeometric Distribution.............................................................. 376
HYPGEOM.DIST................................................................................... 377

Chapter 17: More on Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
Discovering Beta........................................................................................... 379
BETA.DIST............................................................................................ 381
BETA.INV.............................................................................................. 383
Poisson........................................................................................................... 384
POISSON.DIST...................................................................................... 385
Working with Gamma................................................................................... 387
The Gamma function and GAMMA................................................... 387
The Gamma Distribution and GAMMA.DIST.................................... 388
GAMMA.INV......................................................................................... 390
Exponential.................................................................................................... 391
EXPON.DIST......................................................................................... 391

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Chapter 18: A Career in Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
Modeling a Distribution............................................................................... 393
Plunging into the Poisson distribution............................................ 394
Using POISSON.DIST........................................................................... 396
Testing the model’s fit........................................................................ 396
A word about CHISQ.TEST................................................................. 399
Playing ball with a model................................................................... 400
A Simulating Discussion.............................................................................. 402
Taking a chance: The Monte Carlo method.................................... 403
Loading the dice.................................................................................. 403
Simulating the Central Limit Theorem............................................. 407
For Mac Users............................................................................................... 410

Part V: The Part of Tens............................................. 413
Chapter 19: Ten Statistical and Graphical Tips and Traps . . . . . . . . 415
Significant Doesn’t Always Mean Important............................................. 415
Trying to Not Reject a Null Hypothesis
Has a Number of Implications................................................................. 416
Regression Isn’t Always Linear................................................................... 416
Extrapolating Beyond a Sample Scatterplot Is a Bad Idea...................... 417
Examine the Variability Around a Regression Line.................................. 417
A Sample Can Be Too Large........................................................................ 417
Consumers: Know Your Axes...................................................................... 418
Graphing a Categorical Variable as Though It’s a

Quantitative Variable Is Just Wrong....................................................... 418
Whenever Appropriate, Include Variability in Your Graph.................... 419
Be Careful When Relating Statistics Textbook Concepts to Excel......... 420

Chapter 20: Ten Things (Thirteen, Actually)
That Just Didn’t Fit in Any Other Chapter . . . . . . . . . . . . . . . . . . . . . . . 421
Forecasting Techniques............................................................................... 421
A moving experience.......................................................................... 422
How to be a smoothie, exponentially............................................... 424
Graphing the Standard Error of the Mean................................................. 425
Probabilities and Distributions................................................................... 429
PROB..................................................................................................... 429
WEIBULL.DIST..................................................................................... 429
Drawing Samples.......................................................................................... 430
Testing Independence: The True Use of CHISQ.TEST.............................. 431
Logarithmica Esoterica................................................................................ 434
What is a logarithm?........................................................................... 434
What is e?............................................................................................. 436
LOGNORM.DIST................................................................................... 439
LOGNORM.INV.................................................................................... 440

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Table of Contents
Array Function: LOGEST.................................................................... 441
Array Function: GROWTH.................................................................. 445
The Logs of Gamma............................................................................ 448
Sorting Data................................................................................................... 449
For Mac Users............................................................................................... 450

Appendix A: When Your Worksheet Is a Database........ 451
Introducing Excel Databases....................................................................... 451
The Satellites database...................................................................... 452
The criteria range............................................................................... 453
The format of a database function................................................... 454
Counting and Retrieving.............................................................................. 455
DCOUNT and DCOUNTA ................................................................... 455
DGET..................................................................................................... 456
Arithmetic...................................................................................................... 457
DMAX and DMIN................................................................................. 457
DSUM.................................................................................................... 457
DPRODUCT.......................................................................................... 458
Statistics........................................................................................................ 458
DAVERAGE........................................................................................... 458
DVAR and DVARP............................................................................... 458
DSTDEV and DSTDEVP....................................................................... 459
According to Form.............................................................................. 459
Pivot Tables................................................................................................... 461

Appendix B: The Analysis of Covariance...................... 467
Covariance: A Closer Look.......................................................................... 467
Why You Analyze Covariance..................................................................... 468
How You Analyze Covariance..................................................................... 469
ANCOVA in Excel.......................................................................................... 470
Method 1: ANOVA............................................................................... 471
Method 2: Regression......................................................................... 475
After the ANCOVA............................................................................... 478
And One More Thing.................................................................................... 479

Index........................................................................ 481
Bonus Appendix 1: When Your Data Live Elsewhere
Bonus Appendix 2: Tips for Teachers (And Learners)

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Introduction

W

hat? Yet another statistics book? Well . . . this is a statistics book, all
right, but in my humble (and thoroughly biased) opinion, it’s not just
another statistics book.
What? Yet another Excel book? Same thoroughly biased opinion — it’s not
just another Excel book. What? Yet another edition of a book that’s not just
another statistics book and not just another Excel book? Well . . . yes. You got
me there.
So here’s the deal — for the previous two editions and for this one. Many
statistics books teach you the concepts but don’t give you a way to apply
them. That often leads to a lack of understanding. With Excel, you have a

ready-made package for applying statistics concepts.
Looking at it from the opposite direction, many Excel books show you Excel’s
capabilities but don’t tell you about the concepts behind them. Before I tell
you about an Excel statistical tool, I give you the statistical foundation it’s
based on. That way, you understand the tool when you use it — and you use
it more effectively.
I didn’t want to write a book that’s just “select this menu” and “click this
button.” Some of that is necessary, of course, in any book that shows you
how to use a software package. My goal was to go way beyond that.
I also didn’t want to write a statistics “cookbook”: When-faced-with-problem#310-use-statistical-procedure-#214. My goal was to go way beyond that, too.
Bottom line: This book isn’t just about statistics or just about Excel — it
sits firmly at the intersection of the two. In the course of telling you about
statistics, I cover every Excel statistical feature. (Well . . . almost. I left one
out. I left it out of the first two editions, too. It’s called “Fourier Analysis.” All
the necessary math to understand it would take a whole book, and you might
never use this tool, anyway.)

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