25,99 €
Mehr erfahren.
- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
- Veröffentlichungsjahr: 2022
The odds-on best way to master stats. Statistics All-in-One For Dummies is packed with lessons, examples, and practice problems to help you slay your stats course. Develop confidence and understanding in statistics with easy-to-understand (even fun) explanations of key concepts. Plus, you'll get access to online chapter quizzes and other resources that will turn you into a stats master. This book teaches you how to interpret graphs, determine probability, critique data, and so much more. Written by an expert author and serious statistics nerd, Statistics AIO For Dummies explains everything in terms anyone can understand. * Get a grasp of basic statistics concepts required in every statistics course * Clear up the process of interpreting graphs, understanding polls, and analyzing data * Master correlation, regression, and other data analysis tools * Score higher on stats tests and get a better grade in your high school or college class Statistics All-in-One For Dummies follows the curriculum of intro college statistics courses (including AP Stats!) so you can learn everything you need to know to get the grade you need--the Dummies way.
Sie lesen das E-Book in den Legimi-Apps auf:
Seitenzahl: 1034
Ähnliche
Statistics All-in-One For Dummies®
Published by: John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, www.wiley.com
Copyright © 2023 by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the Publisher. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permissions.
Trademarks: Wiley, For Dummies, the Dummies Man logo, Dummies.com, Making Everything Easier, and related trade dress are trademarks or registered trademarks of John Wiley & Sons, Inc., and may not be used without written permission. All other trademarks are the property of their respective owners. John Wiley & Sons, Inc., is not associated with any product or vendor mentioned in this book.
LIMIT OF LIABILITY/DISCLAIMER OF WARRANTY: WHILE THE PUBLISHER AND AUTHORS HAVE USED THEIR BEST EFFORTS IN PREPARING THIS WORK, THEY MAKE NO REPRESENTATIONS OR WARRANTIES WITH RESPECT TO THE ACCURACY OR COMPLETENESS OF THE CONTENTS OF THIS WORK AND SPECIFICALLY DISCLAIM ALL WARRANTIES, INCLUDING WITHOUT LIMITATION ANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. NO WARRANTY MAY BE CREATED OR EXTENDED BY SALES REPRESENTATIVES, WRITTEN SALES MATERIALS OR PROMOTIONAL STATEMENTS FOR THIS WORK. THE FACT THAT AN ORGANIZATION, WEBSITE, OR PRODUCT IS REFERRED TO IN THIS WORK AS A CITATION AND/OR POTENTIAL SOURCE OF FURTHER INFORMATION DOES NOT MEAN THAT THE PUBLISHER AND AUTHORS ENDORSE THE INFORMATION OR SERVICES THE ORGANIZATION, WEBSITE, OR PRODUCT MAY PROVIDE OR RECOMMENDATIONS IT MAY MAKE. THIS WORK IS SOLD WITH THE UNDERSTANDING THAT THE PUBLISHER IS NOT ENGAGED IN RENDERING PROFESSIONAL SERVICES. THE ADVICE AND STRATEGIES CONTAINED HEREIN MAY NOT BE SUITABLE FOR YOUR SITUATION. YOU SHOULD CONSULT WITH A SPECIALIST WHERE APPROPRIATE. FURTHER, READERS SHOULD BE AWARE THAT WEBSITES LISTED IN THIS WORK MAY HAVE CHANGED OR DISAPPEARED BETWEEN WHEN THIS WORK WAS WRITTEN AND WHEN IT IS READ. NEITHER THE PUBLISHER NOR AUTHORS SHALL BE LIABLE FOR ANY LOSS OF PROFIT OR ANY OTHER COMMERCIAL DAMAGES, INCLUDING BUT NOT LIMITED TO SPECIAL, INCIDENTAL, CONSEQUENTIAL, OR OTHER DAMAGES.
For general information on our other products and services, please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993, or fax 317-572-4002. For technical support, please visit https://hub.wiley.com/community/support/dummies.
Wiley publishes in a variety of print and electronic formats and by print-on-demand. Some material included with standard print versions of this book may not be included in e-books or in print-on-demand. If this book refers to media such as a CD or DVD that is not included in the version you purchased, you may download this material at http://booksupport.wiley.com. For more information about Wiley products, visit www.wiley.com.
Library of Congress Control Number: 2022945239
ISBN 978-1-119-90256-0 (pbk); ISBN 978-1-119-90257-7 (ebk); ISBN 978-1-119-90258-4 (ebk)
Statistics All-in-One For Dummies®
To view this book's Cheat Sheet, simply go to www.dummies.com and search for “Statistics All-in-One For Dummies Cheat Sheet” in the Search box.
Table of Contents
Cover
Title Page
Copyright
Introduction
About This Book
Foolish Assumptions
Icons Used in This Book
Beyond the Book
Where to Go from Here
Unit 1: Getting Started with Statistics
Chapter 1: The Statistics of Everyday Life
Statistics and the Media: More Questions than Answers?
Using Statistics at Work
Chapter 2: Taking Control: So Many Numbers, So Little Time
Detecting Errors, Exaggerations, and Just Plain Lies
Feeling the Impact of Misleading Statistics
Chapter 3: Tools of the Trade
Thriving in a Statistical World
Statistics: More than Just Numbers
Designing Appropriate Studies
Collecting Quality Data
Grabbing Some Basic Statistical Jargon
Drawing Credible Conclusions
Becoming a Sleuth, Not a Skeptic
Unit 2: Number-Crunching Basics
Chapter 4: Crunching Categorical Data
Summing Up Data with Descriptive Statistics
Crunching Categorical Data: Tables and Percents
Practice Questions Answers and Explanations
Whaddya Know? Chapter 4 Quiz
Answers to Chapter 4 Quiz
Chapter 5: Means, Medians, and More
Measuring the Center with Mean and Median
Accounting for Variation
Examining the Empirical Rule (68-95-99.7)
Measuring Relative Standing with Percentiles
Practice Questions Answers and Explanations
Whaddya Know? Chapter 5 Quiz
Answers to Chapter 5 Quiz
Chapter 6: Getting the Picture: Graphing Categorical Data
Take Another Little Piece of My Pie Chart
Raising the Bar on Bar Graphs
Practice Questions Answers and Explanations
Whaddya Know? Chapter 6 Quiz
Answers to Chapter 6 Quiz
Chapter 7: Going by the Numbers: Graphing Numerical Data
Handling Histograms
Examining Boxplots
Tackling Time Charts
Practice Questions Answers and Explanations
Whaddya Know? Chapter 7 Quiz
Answers to Chapter 7 Quiz
Unit 3: Distributions and the Central Limit Theorem
Chapter 8: Coming to Terms with Probability
A Set Notation Overview
Probabilities of Events Involving A and/or B
Understanding and Applying the Rules of Probability
Recognizing Independence in Multiple Events
Including Mutually Exclusive Events
Distinguishing Independent from Mutually Exclusive Events
Avoiding Probability Misconceptions
Predictions Using Probability
Practice Questions Answers and Explanations
Whaddya Know? Chapter 8 Quiz
Answers to Chapter 8 Quiz
Chapter 9: Random Variables and the Binomial Distribution
Defining a Random Variable
Identifying a Binomial
Finding Binomial Probabilities Using a Formula
Finding Probabilities Using the Binomial Table
Checking Out the Mean and Standard Deviation of the Binomial
Practice Questions Answers and Explanations
Whaddya Know? Chapter 9 Quiz
Answers to Chapter 9 Quiz
Chapter 10: The Normal Distribution
Exploring the Basics of the Normal Distribution
Meeting the Standard Normal (
Z
-) Distribution
Finding Probabilities for a Normal Distribution
Knowing Where You Stand with Percentiles
Finding X When You Know the Percent
Normal Approximation to the Binomial
Practice Questions Answers and Explanations
Whaddya Know? Chapter 10 Quiz
Answers to Chapter 10 Quiz
Chapter 11: The t-Distribution
Basics of the
t
-Distribution
Using the
t
-Table
Studying Behavior Using the
t
-Table
Practice Questions Answers and Explanations
Whaddya Know? Chapter 11 Quiz
Answers to Chapter 11 Quiz
Chapter 12: Sampling Distributions and the Central Limit Theorem
Defining a Sampling Distribution
The Mean of a Sampling Distribution
Measuring Standard Error
Looking at the Shape of a Sampling Distribution
Finding Probabilities for the Sample Mean
The Sampling Distribution of the Sample Proportion
Finding Probabilities for the Sample Proportion
Practice Questions Answers and Explanations
Whaddya Know? Chapter 12 Quiz
Answers to Chapter 12 Quiz
Unit 4: Guesstimating and Hypothesizing with Confidence
Chapter 13: Leaving Room for a Margin of Error
Seeing the Importance of that Plus or Minus
Finding the Margin of Error: A General Formula
Determining the Impact of Sample Size
Practice Questions Answers and Explanations
Whaddya Know? Chapter 13 Quiz
Answers to Chapter 13 Quiz
Chapter 14: Confidence Intervals: Making Your Best Guesstimate
Not All Estimates Are Created Equal
Linking a Statistic to a Parameter
Getting with the Jargon
Interpreting Results with Confidence
Zooming In on Width
Choosing a Confidence Level
Factoring In the Sample Size
Counting On Population Variability
Calculating a Confidence Interval for a Population Mean
Figuring Out What Sample Size You Need
Determining the Confidence Interval for One Population Proportion
Creating a Confidence Interval for the Difference of Two Means
Estimating the Difference of Two Proportions
Spotting Misleading Confidence Intervals
Practice Questions Answers and Explanations
Whaddya Know? Chapter 14 Quiz
Answers to Chapter 14 Quiz
Chapter 15: Claims, Tests, and Conclusions
Setting Up the Hypotheses
Gathering Good Evidence (Data)
Compiling the Evidence: The Test Statistic
Weighing the Evidence and Making Decisions: p-Values
Making Conclusions
Assessing the Chance of a Wrong Decision
Practice Questions Answers and Explanations
Whaddya Know? Chapter 15 Quiz
Answers to Chapter 15 Quiz
Chapter 16: Commonly Used Hypothesis Tests: Formulas and Examples
Testing One Population Mean
Handling Small Samples and Unknown Standard Deviations: The
t
-Test
Testing One Population Proportion
Comparing Two (Independent) Population Averages
Testing for an Average Difference (The Paired
t
-Test)
Comparing Two Population Proportions
Practice Questions Answers and Explanations
Whaddya Know? Chapter 16 Quiz
Answers to Chapter 16 Quiz
Unit 5: Statistical Studies and the Hunt for a Meaningful Relationship
Chapter 17: Polls, Polls, and More Polls
Recognizing the Impact of Polls
Behind the Scenes: The Ins and Outs of Surveys
Practice Questions Answers and Explanations
Whaddya Know? Chapter 17 Quiz
Answers to Chapter 17 Quiz
Chapter 18: Experiments and Observational Studies: Medical Breakthroughs or Misleading Results?
Boiling Down the Basics of Studies
Designing a Good Experiment
Interpreting Experiment Results
Practice Questions Answers and Explanations
Whaddya Know? Chapter 18 Quiz
Answers to Chapter 18 Quiz
Chapter 19: Looking for Links: Correlation and Regression
Picturing a Relationship with a Scatterplot
Quantifying Linear Relationships Using the Correlation
Working with Linear Regression
Making Proper Predictions
Regression Analysis: Understanding the Output
Residing with Residuals
Explaining the Relationship: Correlation versus Cause and Effect
Practice Questions Answers and Explanations
Whaddya Know? Chapter 19 Quiz
Answers to Chapter 19 Quiz
Chapter 20: Two-Way Tables and Independence
Interpreting Two-Way Tables
Checking Independence and Describing Dependence
Cautiously Interpreting Results
Practice Questions Answers and Explanations
Whaddya Know? Chapter 20 Quiz
Answers to Chapter 20 Quiz
Appendix : Tables for Reference
The
Z
-Table
The
t
-Table
The Binomial Table
Index
About the Author
Advertisement Page
Connect with Dummies
End User License Agreement
List of Illustrations
Chapter 2
FIGURE 2-1: Bar charts showing a) number of times each number was drawn; and b)...
Chapter 3
FIGURE 3-1: A standard normal (
Z
-) distribution has a bell-shaped curve with me...
Chapter 5
FIGURE 5-1: A) Data skewed right; B) data skewed left; and C) symmetric data.
FIGURE 5-2: The Empirical Rule (68 percent, 95 percent, and 99.7 percent).
Chapter 6
FIGURE 6-1: Pie chart showing how people in the U.S. spend their money.
FIGURE 6-2: Pie chart breaking down a state’s lottery revenue.
FIGURE 6-3: Pie chart for takeout food survey results.
FIGURE 6-4: Side-by-side pie charts on the aging population, 2020 versus 2050 p...
FIGURE 6-5: Bar graph showing transportation expenses by household income group...
FIGURE 6-6: Bar graph of lottery sales and expenditures for a certain state.
FIGURE 6-7: Bar graph for survey data with multiple responses.
Chapter 7
FIGURE 7-1: Histogram of Best Actress Academy Award winners’ ages, 1929–2021.
FIGURE 7-2: Comparing the shape of a) a symmetric histogram and b) a skewed-lef...
FIGURE 7-3: Descriptive statistics for Best Actress ages (1929–2021).
FIGURE 7-4: Histogram #1 showing time between eruptions for Old Faithful geyser...
FIGURE 7-5: Histogram #2 showing time between eruptions for Old Faithful geyser...
FIGURE 7-6: Histogram #3 of Old Faithful geyser eruption times.
FIGURE 7-7: Boxplot of Best Actress ages (1929–2021;
awards).
FIGURE 7-8: Histograms of two symmetric data sets.
FIGURE 7-9: Boxplots of the two symmetric data sets from Figure 7-8.
FIGURE 7-10: Descriptive statistics for Old Faithful data.
FIGURE 7-11: Boxplot of eruption times for Old Faithful geyser
.
FIGURE 7-12: Time Chart #1 for ages of Best Actress Academy Award winners, 1929...
FIGURE 7-13: Time Chart #2 for ages of Best Actress Oscar Award winners, 1929–2...
FIGURE 7-14: Time chart showing intervals between eruptions for Old Faithful ge...
FIGURE 7-15: Time chart showing daily average intervals between eruptions for O...
Chapter 10
FIGURE 10-1: Three normal distributions, with means and standard deviations of ...
FIGURE 10-2: The
Z
-distribution has a mean of 0 and standard deviation of 1.
FIGURE 10-3: The distribution of fish lengths in a pond (
X
).
FIGURE 10-4: Standardizing numbers from a normal distribution (
X
) to numbers on...
FIGURE 10-5: Bottom 10 percent of fish in the pond, according to length.
Chapter 11
FIGURE 11-1: Comparing the standard normal (
Z
-) distribution to a generic
t
-dis...
FIGURE 11-2: A comparison of
t
-distributions for different sample sizes to the
Chapter 12
FIGURE 12-1: Distributions of a) individual rolls of one die; and b) average of...
FIGURE 12-2: Distributions of times for 1 worker, 10 workers, and 50 workers.
FIGURE 12-3: Distributions of fish lengths a) in pond #1; b) in pond #2.
FIGURE 12-4: Population percentages for responses to ACT math-help question.
FIGURE 12-5: Sampling distribution of proportion of students responding yes to ...
Chapter 15
FIGURE 15-1: Decisions for
: not-equal-to.
Chapter 19
FIGURE 19-1: Scatterplot of cricket chirps in relation to outdoor temperature.
FIGURE 19-2: Scatterplots with correlations of a) +1.00; b) –0.50; c) +0.85; an...
FIGURE 19-3: Scatterplot of the small data set.
FIGURE 19-4: Regression Analysis for the Small Data Set
Chapter 20
FIGURE 20-1: Pie charts showing marginal distributions for a) pet camping vari...
FIGURE 20-2: Pie chart showing the joint distribution of the pet camping and o...
FIGURE 20-3: Stacked bar graph showing the conditional distributions of opinion...
FIGURE 20-4: Bar graph showing the conditional distributions of voting pattern...
Guide
Cover
Title Page
Copyright
Table of Contents
Begin Reading
Appendix : Tables for Reference
Index
About the Author
Pages
i
v
vi
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
533
534
535
536
Introduction
You get hit with an incredible amount of statistical information on a daily basis. You know what I’m talking about: charts, graphs, tables, and headlines that talk about the results of the latest poll, survey, experiment, or other scientific study. The purpose of this book is to develop and sharpen your skills in sorting through, analyzing, and evaluating all that info, and to do so in a clear, fun, and pain-free way with tons of opportunities to practice. You also gain the ability to decipher and make important decisions about statistical results (for example, the results of the latest medical studies), while being ever aware of the ways that people can mislead you with statistics. And you see how to do it right when it’s your turn to design the study, collect the data, crunch the numbers, and/or draw the conclusions.
This book is also designed to help those of you who are looking to get a solid foundation in introductory statistics or those taking a statistics class and wanting some backup. You’ll gain a working knowledge of the big ideas of statistics and gather a boatload of tools and tricks of the trade that’ll help you get ahead of the curve, especially for taking exams.
This book is chock-full of real examples from real sources that are relevant to your everyday life — from the latest medical breakthroughs, crime studies, and population trends to the latest U.S. government reports. I even address a survey on the worst cars of the millennium! By reading this book, you’ll understand how to collect, display, and analyze data correctly and effectively, and you’ll be ready to critically examine and make informed decisions about the latest polls, surveys, experiments, and reports that bombard you every day. You will even find out how to use crickets to gauge temperature!
You will also get to climb inside the minds of statisticians to see what’s worth taking seriously and what isn’t to be taken so seriously. After all, with the right skills and knowledge, you don’t have to be a professional statistician to understand introductory statistics. You can be a data guru in your own right.
About This Book
This book departs from traditional statistics texts, references, supplemental books, and study guides in the following ways:
It includes practical and intuitive explanations of statistical concepts, ideas, techniques, formulas, and calculations found in an introductory statistics course.
It shows you clear and concise step-by-step procedures that explain how you can intuitively work through statistics problems.
It features interesting real-world examples relating to your everyday life and workplace.
It contains plenty of excellent practice problems crafted in a straightforward manner to lead you down the path of success.
It offers not only answers, but also clear, complete explanations of the answers. Explanations help you know exactly how to approach a problem, what information you need to solve it, and common problems you need to avoid.
It includes tips, strategies, and warnings based on my vast experience with students of all backgrounds and learning styles.
It gives you upfront and honest answers to your questions like, “What does this really mean?” and “When and how will I ever use this?”
As you work your way through the lessons and problems in this book, you should be aware of four conventions that I’ve used.
Dual use of the word
statistics:
In some situations, I refer to statistics as a subject of study or as a field of research, so the word is a singular noun. For example, “Statistics is really quite an interesting subject.” In other situations, I refer to statistics as the plural of
statistic,
in a numerical sense. For example, “The most commonly used statistics are the mean and the standard deviation.”
Use of the word
data:
You’re probably unaware of the debate raging among statisticians about whether the word
data
should be singular (“data is ”) or plural (“data are ”). It got so bad that one group of statisticians had to develop two versions of a statistics T-shirt: “Messy Data Happens” and “Messy Data Happen.” I go with the plural version of the word
data
in this book.
Use of the term
standard deviation:
When I use the term
standard deviation,
I mean
s,
the sample standard deviation. (When I refer to the population standard deviation, I let you know.)
Use of
italics:
I use
italics
to let you know a new statistical term is appearing on the scene. Look for a definition accompanying its first appearance.
Foolish Assumptions
I don’t assume that you’ve had any previous experience with statistics, other than the fact that you’re a member of the general public who gets bombarded every day with statistics in the form of numbers, percents, charts, graphs, “statistically significant” results, “scientific” studies, polls, surveys, experiments, and so on.
What I do assume is that you can do some of the basic mathematical operations and understand some of the basic notation used in algebra, such as the variables x and y, summation signs (∑), taking the square root, squaring a number, and so on. If you need to brush up on your algebra skills, check out U Can Algebra I For Dummies by Mary Jane Sterling (Wiley).
I don’t want to mislead you: You do encounter formulas in this book, because statistics does involve a bit of number crunching. But don’t let that worry you. I take you slowly and carefully through each step of any calculations you need to do, explaining things both with notation and without. I also provide practice questions for you to work so you can become familiar and comfortable with the calculations and make them your own.
Icons Used in This Book
You’ll see the following five icons throughout the book:
Each example is a stat question based on the discussion and explanation, followed by a solution. Work through these examples, and then refer to them to help you solve the practice problems that follow them as well as the quiz questions at the end of the chapter.
This icon points out important information that you need to focus on. Make sure you understand this information fully before moving on. You can skim through these icons when reading a chapter to make sure you remember the highlights.
Tips are hints that can help speed you along when answering a question. See whether you find them useful when working on practice problems.
This icon flags common mistakes that students make if they’re not careful. Take note and proceed with caution!
When you see this icon, it’s time to put on your thinking cap and work out a few practice problems on your own. The answers and detailed solutions are available so you can feel confident about your progress.
Beyond the Book
In addition to the material in the print or e-book you’re reading right now, this book also comes with a handy online Cheat Sheet. Use it when you need a quick refresher on a formula or the next step in conducting a hypothesis test. To get this Cheat Sheet, simply go to www.dummies.com and type Statistics All in One For Dummies Cheat Sheet in the Search box.
You’ll also have access to online quizzes related to each chapter, beginning with Unit 2, Chapter 4. These quizzes provide a whole new set of problems for practice and confidence-building. To access the quizzes, follow these simple steps:
Register your book or ebook at Dummies.com to get your PIN. Go to
www.dummies.com/go/getaccess
.
Select your product from the drop-down list on that page.
Follow the prompts to validate your product, and then check your email for a confirmation message that includes your PIN and instructions for logging in.
If you do not receive this email within two hours, please check your spam folder before contacting us through our Technical Support website at http://support.wiley.com or by phone at 877-762-2974.
Now you’re ready to go! You can come back to the practice material as often as you want — simply log on with the username and password you created during your initial login. No need to enter the access code a second time.
Your registration is good for one year from the day you activate your PIN.
Where to Go from Here
This book is written in such a way that you can start anywhere and still be able to understand what’s going on. So you can take a peek at the table of contents or the index, look up the information that interests you, and flip to the page listed. However, if you have a specific topic in mind and are eager to dive into it, here are some directions:
To work on interpreting graphs, charts, means or medians, and the like, head to
Unit 2
.
To find info on the normal,
Z
-,
t
-, or binomial distributions or the Central Limit Theorem, see
Unit 3
.
To focus on confidence intervals and hypothesis tests of all shapes and sizes, flip to
Unit 4
.
To delve into surveys, experiments, regression, and two-way tables, see
Unit 5
.
Or if you aren’t sure where you want to start, start with Chapter 1 for the big picture and then plow your way through the rest of the book. Ready, set, go!
Unit 1
Getting Started with Statistics
In This Unit …
Chapter 1: The Statistics of Everyday Life
Statistics and the Media: More Questions than Answers?
Using Statistics at Work
Chapter 2: Taking Control: So Many Numbers, So Little Time
Detecting Errors, Exaggerations, and Just Plain Lies
Feeling the Impact of Misleading Statistics
Chapter 3: Tools of the Trade
Thriving in a Statistical World
Statistics: More than Just Numbers
Designing Appropriate Studies
Collecting Quality Data
Grabbing Some Basic Statistical Jargon
Drawing Credible Conclusions
Becoming a Sleuth, Not a Skeptic
Chapter 1
The Statistics of Everyday Life
IN THIS CHAPTER
Raising questions about statistics you see in everyday life
Encountering statistics in the workplace
Today’s society is completely taken over by numbers. Numbers are everywhere you look, from billboards showing the on-time statistics for a particular airline, to sports shows discussing the Las Vegas odds for upcoming football games. The evening news is filled with stories focusing on crime rates, the expected life span of junk-food junkies, and the president’s approval rating. On a normal day, you can run into 5, 10, or even 20 different statistics (with many more on election night). Just by reading a Sunday newspaper all the way through, you come across literally hundreds of statistics in reports, advertisements, and articles covering everything from soup (how much does an average person consume per year?) to nuts (almonds are known to have positive health effects — what about other types of nuts?).
In this chapter we discuss the statistics that often appear in your life and work, and talk about how statistics are presented to the general public. After reading this chapter, you’ll realize just how often the media hits you with numbers and how important it is to be able to unravel the meaning of those numbers. Like it or not, statistics are a big part of your life. So, if you can’t beat ’em, join ’em. And if you don’t want to join ’em, at least try to understand ’em.
Statistics and the Media: More Questions than Answers?
Open a newspaper and start looking for examples of articles and stories involving numbers. It doesn’t take long before those numbers begin to pile up. Readers are inundated with results of studies, announcements of breakthroughs, statistical reports, forecasts, projections, charts, graphs, and summaries. The extent to which statistics occur in the media is mind-boggling. You may not even be aware of how many times you’re hit with numbers nowadays.
This section looks at just a few examples from one Sunday paper’s worth of news that I read the other day. When you see how frequently statistics are reported in the news without providing all the information you need, you may find yourself getting nervous, wondering what you can and can’t believe anymore. Relax! That’s what this book is for — to help you sort out the good information from the bad (the chapters in Unit 2 give you a great start on that).
Probing popcorn problems
The first article I came across that dealt with numbers was “Popcorn plant faces health probe,” with the subheading: “Sick workers say flavoring chemicals caused lung problems.” The article describes how the Centers for Disease Control (CDC) expressed concern about a possible link between exposure to chemicals in microwave popcorn flavorings and some cases of fixed obstructive lung disease. Eight people from one popcorn factory alone contracted this lung disease, and four of them were awaiting lung transplants.
According to the article, similar cases were reported at other popcorn factories. Now, you may be wondering, what about the folks who eat microwave popcorn? According to the article, the CDC found “no reason to believe that people who eat microwave popcorn have anything to fear.” (Stay tuned.) The next step is to evaluate employees in more depth, including conducting surveys to determine health and possible exposures to the flavoring chemicals, checks of lung capacity, and detailed air samples. The question here is: How many cases of this lung disease constitute a real pattern, compared to mere chance or a statistical anomaly? (You find out more about this in Chapter 15.)
Venturing into viruses
A second article discussed a recent cyber attack: A wormlike virus made its way through the Internet, slowing down web browsing and email delivery around the world. How many computers were affected? The experts quoted in the article said that 39,000 computers were infected, and they in turn affected hundreds of thousands of other systems.
Questions: How did the experts get that number? Did they check each computer out there to see whether it was affected? The fact that the article was written less than 24 hours after the attack suggests the number is a guess. Then why say 39,000 and not 40,000 — to make it seem less like a guess? To find out more on how to guesstimate with confidence (and how to evaluate someone else’s numbers), see Chapter 14.
Comprehending crashes
Next in the paper was an alert about the soaring number of motorcycle fatalities. Experts said that the fatality rate — the number of fatalities per 100,000 registered vehicles — for motorcyclists has been steadily increasing, as reported by the National Highway Traffic Safety Administration (NHTSA). In the article, many possible causes for the increased motorcycle death rate were discussed, including age, gender, size of engine, whether the driver had a license, alcohol use, and state helmet laws (or lack thereof). The report was very comprehensive, showing various tables and graphs with the following titles:
Motorcyclists killed and injured, and fatality and injury rates by year, per number of registered vehicles, and per millions of vehicle miles traveled
Motorcycle rider fatalities by state, helmet use, and blood alcohol content
Occupant fatality rates by vehicle type (motorcycles, passenger cars, light trucks), per 10,000 registered vehicles and per 100 million vehicle miles traveled
Motorcyclist fatalities by age group
Motorcyclist fatalities by engine size (displacement)
Previous driving records of drivers involved in fatal traffic crashes by type of vehicle (including previous crashes, DUI convictions, speeding convictions, and license suspensions and revocations)
This article was very informative and provided a wealth of detailed information regarding motorcycle fatalities and injuries in the U.S. However, the onslaught of so many tables, graphs, rates, numbers, and conclusions can be overwhelming and confusing and lead you to miss the big picture. With a little practice, and help from Unit 2, you’ll be better able to sort out graphs, tables, and charts and all the statistics that go along with them. For example, some important statistical issues come up when you see rates versus counts (such as death rates versus number of deaths). As I address in Chapter 2, counts can give you misleading information if they’re used when rates would be more appropriate.
Mulling malpractice
Further along in the newspaper was a report about a recent medical malpractice insurance study: Malpractice cases affect people in terms of the fees doctors charge and the ability to get the healthcare they need. The article indicates that one in five Georgia doctors have stopped doing risky procedures (such as delivering babies) because of the ever-increasing malpractice insurance rates in the state. This is described as a “national epidemic” and a “health crisis” around the country. Some brief details of the study are included, and the article states that of the 2,200 Georgia doctors surveyed, 2,800 of them — which they say represent about 18 percent of those sampled — were expected to stop providing high-risk procedures.
Wait a minute! That can’t be right. Out of 2,200 doctors, 2,800 don’t perform the procedures, and that is supposed to represent 18 percent? That’s impossible! You can’t have a bigger number on the top of a fraction, and still have the fraction be under 100 percent, right? This is one of many examples of errors in media reporting of statistics. So what’s the real percentage? There’s no way to tell from the article. Chapter 4 nails down the particulars of calculating these kinds of statistics so you can know what to look for and immediately tell when something’s not right.
Belaboring the loss of land
In the same Sunday paper was an article about the extent of land development and speculation across the United States. Knowing how many homes are likely to be built in your neck of the woods is an important issue to get a handle on. Statistics are given regarding the number of acres of farmland being lost to development each year. To further illustrate how much land is being lost, the area is also listed in terms of football fields. In this particular example, experts said that the mid-Ohio area is losing 150,000 acres per year, which is 234 square miles, or 115,385 football fields (including end zones). How do people come up with these numbers, and how accurate are they? And does it help to visualize land loss in terms of the corresponding number of football fields? I discuss the accuracy of data collected in more detail in Chapter 17.
Scrutinizing schools
The next topic in the paper was school proficiency — specifically, whether extra school sessions help students perform better. The article stated that 81.3 percent of students in this particular district who attended extra sessions passed the writing proficiency test, whereas only 71.7 percent of those who didn’t participate in the extra school sessions passed it. But is this enough of a difference to account for the $386,000 price tag per year? And what’s happening in these sessions to cause an improvement? Are students in these sessions spending more time just preparing for those exams rather than learning more about writing in general? And here’s the big question: Were the participants in the extra sessions student volunteers who may be more motivated than the average student to try to improve their test scores? The article didn’t say.
Studies like this appear all the time, and the only way to know what to believe is to understand what questions to ask and to be able to critique the quality of the study. That’s all part of statistics! The good news is, with a few clarifying questions, you can quickly critique statistical studies and their results. Chapter 18 helps you do just that.
Scanning sports
The sports section is probably the most numerically jam-packed section of the newspaper. Beginning with game scores, the win/loss percentages for each team, and the relative standing for each team, the specialized statistics reported in the sports world are so deep that they require wading boots to get through. For example, basketball statistics are broken down by team, by quarter, and by player. For each player, you get minutes played, field goals, free throws, rebounds, assists, personal fouls, turnovers, blocks, steals, and total points.
Who needs to know this stuff, besides the players’ mothers? Apparently, many fans do. Statistics are something that sports fans can never get enough of and players often can’t stand to hear about. Stats are the substance of water-cooler debates and the fuel for armchair quarterbacks around the world.
STUDYING SURVEYS OF ALL SHAPES AND SIZES
Surveys and polls are among the most visible mechanisms used by today’s media to grab your attention. It seems that everyone, including market managers, insurance companies, TV stations, community groups, and even students in high school classes, wants to do a survey. Here are just a few examples of survey results that are part of today’s news:
With the aging of the American workforce, companies are planning for their future leadership. (How do they know that the American workforce is aging, and if it is, by how much is it aging?) A recent survey shows that nearly 67 percent of human resource managers polled said that planning for succession had become more important in the past five years than it had been in the past. The survey also says that 88 percent of the 210 respondents said they usually or often fill senior positions with internal candidates. But how many managers did not respond, and is 210 respondents really enough people to warrant a story on the front page of the business section? Believe it or not, when you start looking for them, you’ll find numerous examples in the news of surveys based on far fewer participants than 210. (To be fair, however, 210 can actually be a good number of subjects in some situations. The issues of what sample size is large enough and what percentage of respondents is big enough are addressed in full detail in Chapter 17.)
Some surveys are based on current interests and trends. For example, a Harris-Interactive survey found that nearly half (47 percent) of U.S. teens say their social lives would end or be worsened without their cellphones, and 57 percent go as far as to say that their cellphones are the key to their social life. The study also found that 42 percent of teens say that they can text while blindfolded (how do you really test this?). Keep in perspective, though, that the study did not tell you what percentage of teens actually have cellphones or what demographic characteristics those teens have compared to teens who do not have cellphones. And remember that data collected on topics like this aren’t always accurate, because the individuals who are surveyed may tend to give biased answers (who wouldn’t want to say they can text blindfolded?). For more information on how to interpret and evaluate the results of surveys, see Chapter 17.
Fantasy sports have also made a huge impact on the sports money-making machine. Fantasy sports are games where participants act as owners to build their own teams from existing players in a professional league. The fantasy team owners then compete against each other. What is the competition based on? Statistical performance of the players and teams involved, as measured by rules set up by a “league commissioner” and an established point system. According to the Fantasy Sports Trade Association, the number of people age 12 and up who are involved in fantasy sports is more than 30 million, and the amount of money spent is $3 to 4 billion per year. (And even here, you can ask how the numbers were calculated — the questions never end, do they?)
Banking on business news
The business section of the newspaper provides statistics about the stock market. In one week, the market went down 455 points; is that decrease a lot or a little? You need to calculate a percentage to really get a handle on that.
The business section of my paper contained reports on the highest yields nationwide on every kind of certificate of deposit (CD) imaginable. (By the way, how do they know those yields are the highest?) I also found reports about rates on 30-year fixed loans, 15-year fixed loans, 1-year adjustable rate loans, new car loans, used car loans, home equity loans, and loans from your grandmother (well, actually no, but if grandma read these statistics, she might increase her cushy rates).
Finally, I saw numerous ads for those beloved credit cards — ads listing the interest rates, the annual fees, and the number of days in the billing cycle. How do you compare all the information about investments, loans, and credit cards in order to make a good decision? What statistics are most important? The real question is: Are the numbers reported in the paper giving the whole story, or do you need to do more detective work to get at the truth? Chapters 17 and 18 help you start tearing apart these numbers and making decisions about them.
Touring the travel news
You can’t even escape the barrage of numbers by heading to the travel section. For example, there I found that the most frequently asked question coming in to the Transportation Security Administration’s response center (which receives about 2,000 telephone calls, 2,500 email messages, and 200 letters per week on average — would you want to be the one counting all of those?) is, “Can I carry this on a plane?” This can refer to anything from an animal to a wedding dress to a giant tin of popcorn. (I wouldn’t recommend the tin of popcorn. You have to put it in the overhead compartment horizontally, and because things shift during a flight, the cover will likely open; and when you go to claim your tin at the end of the flight, you and your seatmates will be showered. Yes, I saw it happen once.)
The number of reported responses in this case leads to an interesting statistical question: How many operators are needed at various times of the day to field those calls, emails, and letters coming in? Estimating the number of anticipated calls is your first step, and being wrong can cost you money (if you overestimate it) or a lot of bad PR (if you underestimate it). These kinds of statistical challenges are tackled in Chapter 14.
Surveying sexual stats
In today’s age of info-overkill, it’s very easy to find out what the latest buzz is, including the latest research on people’s sex lives. An article in my paper reported that married people have 6.9 more sexual encounters per year than people who have never been married. That’s nice to know, I guess, but how did someone come up with this number? The article I’m looking at doesn’t say (maybe some statistics are better left unsaid?).
If someone conducts a survey by calling people on the phone asking for a few minutes of their time to discuss their sex lives, who will be the most likely to want to talk about it? And what are they going to say in response to the question, “How many times a week do you have sex?” Are they going to report the honest truth, tell you to mind your own business, or exaggerate a little? Self-reported surveys can be a real source of bias and can lead to misleading statistics. But how would you recommend people go about finding out more about this very personal subject? Sometimes, research is more difficult than it seems. (Chapter 17 discusses biases that come up when collecting certain types of survey data.)
Breaking down weather reports
Weather reports provide another mass of statistics, with forecasts of the next day’s high and low temperatures (how do they decide it’ll be 16 degrees and not 15 degrees?) along with reports of the day’s UV factor, pollen count, pollution standard index, and water quality and quantity. (How do they get these numbers — by taking samples? How many samples do they take, and where do they take them?) You can find out what the weather is right now anywhere in the world. You can get a forecast looking ahead three days, a week, a month, or even a year! Meteorologists collect and record tons and tons of data on the weather each day. Not only do these numbers help you decide whether to take your umbrella to work, but they also help weather researchers to better predict longer-term forecasts and even global climate changes over time.
Even with all the information and technologies available to weather researchers, how accurate are weather reports these days? Given the number of times you get rained on when you were told it was going to be sunny, it seems they still have work to do on those forecasts. What the abundance of data really shows, though, is that the number of variables affecting weather is almost overwhelming, not just to you, but for meteorologists, too.
Statistical computer models play an important role in making predictions about major weather-related events, such as hurricanes, earthquakes, and volcano eruptions. Scientists still have some work to do before they can predict tornados before they begin to form, or tell you exactly where and when a hurricane is going to hit land, but that’s certainly their goal, and they continue to get better at it. For more on modeling and statistics, see Chapter 19.
Using Statistics at Work
Now let’s put down the Sunday newspaper and move on to the daily grind of the workplace. If you’re working for an accounting firm, of course numbers are part of your daily life. But what about people like nurses, portrait studio photographers, store managers, newspaper reporters, office staff, or construction workers? Do numbers play a role in those jobs? You bet. This section gives you a few examples of how statistics creep into every workplace.
You don’t have to go far to see how statistics weaves its way in and out of your life and work. The secret is being able to determine what it all means and what you can believe, and to be able to make sound decisions based on the real story behind numbers so you can handle and become used to the statistics of everyday life.
Delivering babies — and information
Sue works as a nurse during the night shift in the labor and delivery unit at a university hospital. She takes care of several patients in a given evening, and she does her best to accommodate everyone. Her nursing manager has told her that each time she comes on shift she should identify herself to the patient, write her name on the whiteboard in the patient’s room, and ask whether the patient has any questions. Why? Because a few days after each mother leaves with her baby, the hospital gives her a phone call asking about the quality of care, what was missed, what it could do to improve its service and quality of care, and what the staff could do to ensure that the hospital is chosen over other hospitals in town. For example, surveys show that patients who know the names of their nurses feel more comfortable, ask more questions, and have a more positive experience in the hospital than those who don’t know the names of their nurses. Sue’s salary raises depend on her ability to follow through with the needs of new mothers. No doubt the hospital has also done a lot of research to determine the factors involved in quality of patient care well beyond nurse-patient interactions. (See Chapter 18 for in-depth info concerning medical studies.)
Posing for pictures
Carol works as a photographer for a department store portrait studio; one of her strengths is working with babies. Based on the number of photos purchased by customers over the years, this store has found that people buy more posed pictures than natural-looking ones. As a result, store managers encourage their photographers to take posed shots.
A mother comes in with her baby and has a special request: “Could you please not pose my baby too deliberately? I just like his pictures to look natural.” If Carol says, “Can’t do that, sorry. My raises are based on my ability to pose a child well,” you can bet that the mother is going to fill out that survey on quality service after this session — and not just to get $2.00 off her next sitting (if she ever comes back). Instead, Carol should show her boss the information in Chapter 17 about collecting data on customer satisfaction.
Poking through pizza data
Terry is a store manager at a local pizzeria that sells pizza by the slice. He is in charge of determining how many workers to have on staff at a given time, how many pizzas to make ahead of time to accommodate the demand, and how much cheese to order and grate, all with minimal waste of wages and ingredients. Friday night at midnight, the place is dead. Terry has five workers left and has five large pans of pizza he could throw in the oven, making about 40 slices of pizza each. Should he send two of his workers home? Should he put more pizza in the oven or hold off?
The store owner has been tracking the demand for weeks now, so Terry knows that every Friday night things slow down between 10 p.m. and 12 a.m., but then the bar crowd starts pouring in around midnight and doesn’t let up until the doors close at 2:30 a.m. So Terry keeps the workers on, puts in the pizzas in 30-minute intervals from midnight on, and is rewarded with a profitable night, with satisfied customers and a happy boss. For more information on how to make good estimates using statistics, see Chapter 14.
Statistics in the office
D.J. is an administrative assistant for a computer company. How can statistics creep into her office workplace? Easy. Every office is filled with people who want to know answers to questions, and they want someone to “Crunch the numbers,” to “Tell me what this means,” to “Find out if anyone has any hard data on this,” or to simply say, “Does this number make any sense?” They need to know everything from customer satisfaction figures to changes in inventory during the year; from the percentage of time employees spend on email to the cost of supplies for the last three years. Every workplace is filled with statistics, and D.J.’s marketability and value as an employee could go up if she’s the one the head honchos turn to for help. Every office needs a resident statistician — why not let it be you?
Chapter 2
Taking Control: So Many Numbers, So Little Time
IN THIS CHAPTER
Examining the extent of statistics abuse
Feeling the impact of statistics gone wrong
The sheer amount of statistics in daily life can leave you feeling overwhelmed and confused. This chapter gives you a tool to help you deal with statistics: skepticism! Not radical skepticism like “I can’t believe anything anymore,” but healthy skepticism like “Hmm, I wonder where that number came from?” and “I need to find out more information before I believe these results.” To develop healthy skepticism, you need to understand how the chain of statistical information works.
Statistics end up on your TV and in your newspaper as a result of a process. First, the researchers who study an issue generate results; this group is composed of pollsters, doctors, marketing researchers, government researchers, and other scientists. They are considered the original sources of the statistical information.
After they get their results, these researchers naturally want to tell people about them, so they typically either put out a press release or publish a journal article. Enter the journalists or reporters, who are considered the media sources of the information. Journalists hunt for interesting press releases and sort through journals, basically searching for the next headline. When reporters complete their stories, statistics are immediately sent out to the public through all forms of media. Now the information is ready to be taken in by the third group — the consumers of the information (you). You and other consumers of information are faced with the task of listening to and reading the information, sorting through it, and making decisions about it.
At any stage in the process of doing research, communicating results, or consuming information, errors can take place, either unintentionally or by design. The tools and strategies you find in this chapter give you the skills to be a good detective.
