Statistics II for Dummies E-Book

Deborah J. Rumsey

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch
• Veröffentlichungsjahr: 2012

Seitenzahl: 636

Beschreibung

The ideal supplement and study guide for students preparing for advanced statistics Packed with fresh and practical examples appropriate for a range of degree-seeking students, Statistics II For Dummies helps any reader succeed in an upper-level statistics course. It picks up with data analysis where Statistics For Dummies left off, featuring new and updated examples, real-world applications, and test-taking strategies for success. This easy-to-understand guide covers such key topics as sorting and testing models, using regression to make predictions, performing variance analysis (ANOVA), drawing test conclusions with chi-squares, and making comparisons with the Rank Sum Test.

Leseprobe

Statistics II For Dummies®

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Table of Contents

Introduction

About This Book

Conventions Used in This Book

What You’re Not to Read

Foolish Assumptions

How This Book Is Organized

Part I: Tackling Data Analysis and Model-Building Basics

Part II: Using Different Types of Regression to Make Predictions

Part III: Analyzing Variance with ANOVA

Part IV: Building Strong Connections with Chi-Square Tests

Part V: Nonparametric Statistics: Rebels without a Distribution

Part VI: The Part of Tens

Icons Used in This Book

Where to Go from Here

Part I: Tackling Data Analysis and Model-Building Basics

Chapter 1: Beyond Number Crunching: The Art and Science of Data Analysis

Data Analysis: Looking before You Crunch

Nothing (not even a straight line) lasts forever

Data snooping isn’t cool

No (data) fishing allowed

Getting the Big Picture: An Overview of Stats II

Population parameter

Sample statistic

Confidence interval

Hypothesis test

Analysis of variance (ANOVA)

Multiple comparisons

Interaction effects

Correlation

Linear regression

Chi-square tests

Nonparametrics

Chapter 2: Finding the Right Analysis for the Job

Categorical versus Quantitative Variables

Statistics for Categorical Variables

Estimating a proportion

Comparing proportions

Looking for relationships between categorical variables

Building models to make predictions

Statistics for Quantitative Variables

Making estimates

Making comparisons

Exploring relationships

Predicting y using x

Avoiding Bias

Measuring Precision with Margin of Error

Knowing Your Limitations

Chapter 3: Reviewing Confidence Intervals and Hypothesis Tests

Estimating Parameters by Using Confidence Intervals

Getting the basics: The general form of a confidence interval

Finding the confidence interval for a population mean

What changes the margin of error?

Interpreting a confidence interval

What’s the Hype about Hypothesis Tests?

What Ho and Ha really represent

Gathering your evidence into a test statistic

Determining strength of evidence with a p-value

False alarms and missed opportunities: Type I and II errors

The power of a hypothesis test

Part II: Using Different Types of Regression to Make Predictions

Chapter 4: Getting in Line with Simple Linear Regression

Exploring Relationships with Scatterplots and Correlations

Using scatterplots to explore relationships

Collating the information by using the correlation coefficient

Building a Simple Linear Regression Model

Finding the best-fitting line to model your data

The y-intercept of the regression line

The slope of the regression line

Making point estimates by using the regression line

No Conclusion Left Behind: Tests and Confidence Intervals for Regression

Scrutinizing the slope

Inspecting the y-intercept

Building confidence intervals for the average response

Making the band with prediction intervals

Checking the Model’s Fit (The Data, Not the Clothes!)

Defining the conditions

Finding and exploring the residuals

Using r2 to measure model fit

Scoping for outliers

Knowing the Limitations of Your Regression Analysis

Avoiding slipping into cause-and-effect mode

Extrapolation: The ultimate no-no

Sometimes you need more than one variable

Chapter 5: Multiple Regression with Two X Variables

Getting to Know the Multiple Regression Model

Discovering the uses of multiple regression

Looking at the general form of the multiple regression model

Stepping through the analysis

Looking at x’s and y’s

Collecting the Data

Pinpointing Possible Relationships

Making scatterplots

Correlations: Examining the bond

Checking for Multicolinearity

Finding the Best-Fitting Model for Two x Variables

Getting the multiple regression coefficients

Interpreting the coefficients

Testing the coefficients

Predicting y by Using the x Variables

Checking the Fit of the Multiple Regression Model

Noting the conditions

Plotting a plan to check the conditions

Checking the three conditions

Chapter 6: How Can I Miss You If You Won’t Leave? Regression Model Selection

Getting a Kick out of Estimating Punt Distance

Brainstorming variables and collecting data

Examining scatterplots and correlations

Just Like Buying Shoes: The Model Looks Nice, But Does It Fit?

Assessing the fit of multiple regression models

Model selection procedures

Chapter 7: Getting Ahead of the Learning Curve with Nonlinear Regression

Anticipating Nonlinear Regression

Starting Out with Scatterplots

Handling Curves in the Road with Polynomials

Bringing back polynomials

Searching for the best polynomial model

Using a second-degree polynomial to pass the quiz

Assessing the fit of a polynomial model

Making predictions

Going Up? Going Down? Go Exponential!

Recollecting exponential models

Searching for the best exponential model

Spreading secrets at an exponential rate

Chapter 8: Yes, No, Maybe So: Making Predictions by Using Logistic Regression

Understanding a Logistic Regression Model

How is logistic regression different from other regressions?

Using an S-curve to estimate probabilities

Interpreting the coefficients of the logistic regression model

The logistic regression model in action

Carrying Out a Logistic Regression Analysis

Running the analysis in Minitab

Finding the coefficients and making the model

Estimating p

Checking the fit of the model

Fitting the movie model

Part III: Analyzing Variance with ANOVA

Chapter 9: Testing Lots of Means? Come On Over to ANOVA!

Comparing Two Means with a t-Test

Evaluating More Means with ANOVA

Spitting seeds: A situation just waiting for ANOVA

Walking through the steps of ANOVA

Checking the Conditions

Verifying independence

Looking for what’s normal

Taking note of spread

Setting Up the Hypotheses

Doing the F-Test

Running ANOVA in Minitab

Breaking down the variance into sums of squares

Locating those mean sums of squares

Figuring the F-statistic

Making conclusions from ANOVA

What’s next?

Checking the Fit of the ANOVA Model

Chapter 10: Sorting Out the Means with Multiple Comparisons

Following Up after ANOVA

Comparing cellphone minutes: An example

Setting the stage for multiple comparison procedures

Pinpointing Differing Means with Fisher and Tukey

Fishing for differences with Fisher’s LSD

Using Fisher’s new and improved LSD

Separating the turkeys with Tukey’s test

Examining the Output to Determine the Analysis

So Many Other Procedures, So Little Time!

Controlling for baloney with the Bonferroni adjustment

Comparing combinations by using Scheffe’s method

Finding out whodunit with Dunnett’s test

Staying cool with Student Newman-Keuls

Duncan’s multiple range test

Going nonparametric with the Kruskal-Wallis test

Chapter 11: Finding Your Way through Two-Way ANOVA

Setting Up the Two-Way ANOVA Model

Determining the treatments

Stepping through the sums of squares

Understanding Interaction Effects

What is interaction, anyway?

Interacting with interaction plots

Testing the Terms in Two-Way ANOVA

Running the Two-Way ANOVA Table

Interpreting the results: Numbers and graphs

Are Whites Whiter in Hot Water? Two-Way ANOVA Investigates

Chapter 12: Regression and ANOVA: Surprise Relatives!

Seeing Regression through the Eyes of Variation

Spotting variability and finding an “x-planation”

Getting results with regression

Assessing the fit of the regression model

Regression and ANOVA: A Meeting of the Models

Comparing sums of squares

Dividing up the degrees of freedom

Bringing regression to the ANOVA table

Relating the F- and t-statistics: The final frontier

Part IV: Building Strong Connections with Chi-Square Tests

Chapter 13: Forming Associations with Two-Way Tables

Breaking Down a Two-Way Table

Organizing data into a two-way table

Filling in the cell counts

Making marginal totals

Breaking Down the Probabilities

Marginal probabilities

Joint probabilities

Conditional probabilities

Trying To Be Independent

Checking for independence between two categories

Checking for independence between two variables

Demystifying Simpson’s Paradox

Experiencing Simpson’s Paradox

Figuring out why Simpson’s Paradox occurs

Keeping one eye open for Simpson’s Paradox

Chapter 14: Being Independent Enough for the Chi-Square Test

The Chi-square Test for Independence

Collecting and organizing the data

Determining the hypotheses

Figuring expected cell counts

Checking the conditions for the test

Calculating the Chi-square test statistic

Finding your results on the Chi-square table

Drawing your conclusions

Putting the Chi-square to the test

Comparing Two Tests for Comparing Two Proportions

Getting reacquainted with the Z-test for two population proportions

Equating Chi-square tests and Z-tests for a two-by-two table

Chapter 15: Using Chi-Square Tests for Goodness-of-Fit (Your Data, Not Your Jeans)

Finding the Goodness-of-Fit Statistic

What’s observed versus what’s expected

Calculating the goodness-of-fit statistic

Interpreting the Goodness-of-Fit Statistic Using a Chi-Square

Checking the conditions before you start

The steps of the Chi-square goodness-of-fit test

Part V: Nonparametric Statistics: Rebels without a Distribution

Chapter 16: Going Nonparametric

Arguing for Nonparametric Statistics

No need to fret if conditions aren’t met

The median’s in the spotlight for a change

So, what’s the catch?

Mastering the Basics of Nonparametric Statistics

Sign

Rank

Signed rank

Rank sum

Chapter 17: All Signs Point to the Sign Test and Signed Rank Test

Reading the Signs: The Sign Test

Testing the median

Estimating the median

Testing matched pairs

Going a Step Further with the Signed Rank Test

A limitation of the sign test

Stepping through the signed rank test

Losing weight with signed ranks

Chapter 18: Pulling Rank with the Rank Sum Test

Conducting the Rank Sum Test

Checking the conditions

Stepping through the test

Stepping up the sample size

Performing a Rank Sum Test: Which Real Estate Agent Sells Homes Faster?

Checking the conditions for this test

Testing the hypotheses

Chapter 19: Do the Kruskal-Wallis and Rank the Sums with the Wilcoxon

Doing the Kruskal-Wallis Test to Compare More than Two Populations

Checking the conditions

Setting up the test

Conducting the test step by step

Pinpointing the Differences: The Wilcoxon Rank Sum Test

Pairing off with pairwise comparisons

Carrying out comparison tests to see who’s different

Examining the medians to see how they’re different

Chapter 20: Pointing Out Correlations with Spearman’s Rank

Pickin’ On Pearson and His Precious Conditions

Scoring with Spearman’s Rank Correlation

Figuring Spearman’s rank correlation

Watching Spearman at work: Relating aptitude to performance

Part VI: The Part of Tens

Chapter 21: Ten Common Errors in Statistical Conclusions

Claiming These Statistics Prove . . .

It’s Not Technically Statistically Significant, But . . .

Concluding That x Causes y

Assuming the Data Was Normal

Only Reporting “Important” Results

Assuming a Bigger Sample Is Always Better

It’s Not Technically Random, But . . .

Assuming That 1,000 Responses Is 1,000 Responses

Of Course the Results Apply to the General Population

Deciding Just to Leave It Out

Chapter 22: Ten Ways to Get Ahead by Knowing Statistics

Asking the Right Questions

Being Skeptical

Collecting and Analyzing Data Correctly

Calling for Help

Retracing Someone Else’s Steps

Putting the Pieces Together

Checking Your Answers

Explaining the Output

Making Convincing Recommendations

Establishing Yourself as the Statistics Go-To Guy or Gal

Chapter 23: Ten Cool Jobs That Use Statistics

Pollster

Ornithologist (Bird Watcher)

Sportscaster or Sportswriter

Journalist

Crime Fighter

Medical Professional

Marketing Executive

Lawyer

Stock Broker

Appendix: Reference Tables

Cheat Sheet

End User License Agreement

Statistics II For Dummies®

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Copyright © 2009 by Wiley Publishing, Inc., Indianapolis, Indiana

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Dedication

To my husband Eric: My sun rises and sets with you. To my son Clint: I love you up to the moon and back.

About the Author

Deborah Rumsey has a PhD in Statistics from The Ohio State University (1993), where she’s a Statistics Education Specialist/Auxiliary Faculty Member for the Department of Statistics. Dr. Rumsey has been given the distinction of being named a Fellow of the American Statistical Association. She has also won the Presidential Teaching Award from Kansas State University. She’s the author of Statistics For Dummies, Statistics Workbook For Dummies, and Probability For Dummies and has published numerous papers and given many professional presentations on the subject of statistics education. Her passions include being with her family, bird watching, getting more seat time on her Kubota tractor, and cheering the Ohio State Buckeyes on to another National Championship.

Author’s Acknowledgments

Thanks again to Lindsay Lefevere and Kathy Cox for giving me the opportunity to write this book; to Natalie Harris and Chrissy Guthrie for their unwavering support and perfect chiseling and molding of my words and ideas; to Kim Gilbert, University of Georgia, for a thorough technical view; and to Elizabeth Rea and Sarah Westfall for great copy-editing. Special thanks to Elizabeth Stasny for guidance and support from day one; and to Joan Garfield for constant inspiration and encouragement.

Publisher’s Acknowledgments

We’re proud of this book; please send us your comments through our Dummies online registration form located at http://dummies.custhelp.com. For other comments, please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993, or fax [phone].

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Introduction

So you’ve gone through some of the basics of statistics. Means, medians, and standard deviations all ring a bell. You know about surveys and experiments and the basic ideas of correlation and simple regression. You’ve studied probability, margin of error, and a few hypothesis tests and confidence intervals. Are you ready to load your statistical toolbox with a new level of tools? Statistics II For Dummies picks up right where Statistics For Dummies (Wiley) leaves off and keeps you moving along the road of statistical ideas and techniques in a positive, step-by-step way.

The focus of Statistics II For Dummies is on finding more ways of analyzing data. I provide step-by-step instructions for using techniques such as multiple regression, nonlinear regression, one-way and two-way analysis of variance (ANOVA), Chi-square tests, and nonparametric statistics. Using these new techniques, you estimate, investigate, correlate, and congregate even more variables based on the information at hand.

About This Book

This book is designed for those who have completed the basic concepts of statistics through confidence intervals and hypothesis testing (found in Statistics For Dummies) and are ready to plow ahead to get through the final part of Stats I, or to tackle Stats II. However, I do pepper in some brief overviews of Stats I as needed, just to remind you of what was covered and make sure you’re up to speed. For each new technique, you get an overview of when and why it’s used, how to know when you need it, step-by-step directions on how to do it, and tips and tricks from a seasoned data analyst (yours truly). Because it’s very important to be able to know which method to use when, I emphasize what makes each technique distinct and what the results say. You also see many applications of the techniques used in real life.

I also include interpretation of computer output for data analysis purposes. I show you how to use the software to get the results, but I focus more on how to interpret the results found in the output, because you’re more likely to be interpreting this kind of information rather than doing the programming specifically. And because the equations and calculations can get too involved by hand, you often use a computer to get your results. I include instructions for using Minitab to conduct many of the calculations in this book. Most statistics teachers who cover these topics hold this philosophy as well. (What a relief!)

This book is different from the other Stats II books in many ways. Notably, this book features

Full explanations of Stats II concepts. Many statistics textbooks squeeze all the Stats II topics at the very end of Stats I coverage; as a result, these topics tend to get condensed and presented as if they’re optional. But no worries; I take the time to clearly and fully explain all the information you need to survive and thrive.

Dissection of computer output. Throughout the book, I present many examples that use statistical software to analyze the data. In each case, I present the computer output and explain how I got it and what it means.

An extensive number ofexamples. I include plenty of examples to cover the many different types of problems you’ll face.

Lots of tips, strategies, and warnings. I share with you some trade secrets, based on my experience teaching and supporting students and grading their papers.

Understandable language. I try to keep things conversational to help you understand, remember, and put into practice statistical definitions, techniques, and processes.

Clear and concise step-by-step procedures. In most chapters, you can find steps that intuitively explain how to work through Stats II problems — and remember how to do it on your own later on.

Conventions Used in This Book

Throughout this book, I’ve used several conventions that I want you to be aware of:

I indicate multiplication by using a times sign, indicated by a lowered asterisk, *.

I indicate the null and alternative hypotheses as Ho (for the null hypothesis) and Ha (for the alternative hypothesis).

The statistical software package I use and display throughout the book is Minitab 14, but I simply refer to it as Minitab.

Whenever I introduce a new term, I italicize it.

Keywords and numbered steps appear in boldface.

Web sites and e-mail addresses appear in monofont.

What You’re Not to Read

At times I get into some of the more technical details of formulas and procedures for those individuals who may need to know about them — or just really want to get the full story. These minutiae are marked with a Technical Stuff icon. I also include sidebars as an aside to the essential text, usually in the form of a real-life statistics example or some bonus info you may find interesting. You can feel free to skip those icons and sidebars because you won’t miss any of the main information you need (but by reading them, you may just be able to impress your stats professor with your above-and-beyond knowledge of Stats II!).

Foolish Assumptions

Because this book deals with Stats II, I assume you have one previous course in introductory statistics under your belt (or at least have read Statistics For Dummies), with topics taking you up through the Central Limit Theorem and perhaps an introduction to confidence intervals and hypothesis tests (although I review these concepts briefly in Chapter 3). Prior experience with simple linear regression isn’t necessary. Only college algebra is needed for the mathematics details. And, some experience using statistical software is a plus but not required.

As a student, you may be covering these topics in one of two ways: either at the tail end of your Stats I course (perhaps in a hurried way, but in some way nonetheless); or through a two-course sequence in statistics in which the topics in this book are the focus of the second course. If so, this book provides you the information you need to do well in those courses.

You may simply be interested in Stats II from an everyday point of view, or perhaps you want to add to your understanding of studies and statistical results presented in the media. If this sounds like you, you can find plenty of real-world examples and applications of these statistical techniques in action as well as cautions for interpreting them.

How This Book Is Organized

This book is organized into five major parts that explore the main topic areas in Stats II, along with one bonus part that offers a series of quick top-ten references for you to use. Each part contains chapters that break down the part’s major objective into understandable pieces. The nonlinear setup of this book allows you to skip around and still have easy access to and understanding of any given topic.

Part I: Tackling Data Analysis and Model-Building Basics

This part goes over the big ideas of descriptive and inferential statistics and simple linear regression in the context of model-building and decision-making. Some material from Stats I receives a quick review. I also present you with the typical jargon of Stats II.

Part II: Using Different Types of Regression to Make Predictions

In this part, you can review and extend the ideas of simple linear regression to the process of using more than one predictor variable. This part presents techniques for dealing with data that follows a curve (nonlinear models) and models for yes or no data used to make predictions about whether or not an event will happen (logistic regression). It includes all you need to know about conditions, diagnostics, model-building, data-analysis techniques, and interpreting results.

Part III: Analyzing Variance with ANOVA

You may want to compare the means of more than two populations, and that requires that you use analysis of variance (ANOVA). This part discusses the basic conditions required, the F-test, one-way and two-way ANOVA, and multiple comparisons. The final goal of these analyses is to show whether the means of the given populations are different and if so, which ones are higher or lower than the rest.

Part IV: Building Strong Connections with Chi-Square Tests

This part deals with the Chi-square distribution and how you can use it to model and test categorical (qualitative) data. You find out how to test for independence of two categorical variables using a Chi-square test. (No more making speculations just by looking at the data in a two-way table!) You also see how to use a Chi-square to test how well a model for categorical data fits.

Part V: Nonparametric Statistics: Rebels without a Distribution

This part helps you with techniques used in situations where you can’t (or don’t want to) assume your data comes from a population with a certain distribution, such as when your population isn’t normal (the condition required by most other methods in Stats II).

Part VI: The Part of Tens

Reading this part can give you an edge in a major area beyond the formulas and techniques of Stats II: ending the problem right (knowing what kinds of conclusions you can and can’t make). You also get to know Stats II in the real world, namely how it can help you stand out in a crowd.

You also can find an appendix at the back of this book that contains all the tables you need to understand and complete the calculations in this book.

Icons Used in This Book

I use icons in this book to draw your attention to certain text features that occur on a regular basis. Think of the icons as road signs that you encounter on a trip. Some signs tell you about shortcuts, and others offer more information that you may need; some signs alert you to possible warnings, while others leave you with something to remember.

When you see this icon, it means I’m explaining how to carry out that particular data analysis using Minitab. I also explain the information you get in the computer output so you can interpret your results.

I use this icon to reinforce certain ideas that are critical for success in Stats II, such as things I think are important to review as you prepare for an exam.

When you see this icon, you can skip over the information if you don’t want to get into the nitty-gritty details. They exist mainly for people who have a special interest or obligation to know more about the more technical aspects of certain statistical issues.

This icon points to helpful hints, ideas, or shortcuts that you can use to save time; it also includes alternative ways to think about a particular concept.

I use warning icons to help you stay away from common misconceptions and pitfalls you may face when dealing with ideas and techniques related to Stats II.

Where to Go from Here

This book is written in a nonlinear way, so you can start anywhere and still understand what’s happening. However, I can make some recommendations if you want some direction on where to start.

If you’re thoroughly familiar with the ideas of hypothesis testing and simple linear regression, start with Chapter 5 (multiple regression). Use Chapter 1 if you need a reference for the jargon that statisticians use in Stats II.

If you’ve covered all topics up through the various types of regression (simple, multiple, nonlinear, and logistic) or a subset of those as your professor deemed important, proceed to Chapter 9, the basics of analysis of variance (ANOVA).

Chapter 14 is the place to begin if you want to tackle categorical (qualitative) variables before hitting the quantitative stuff. You can work with the Chi-square test there.

Nonparametric statistics are presented starting with Chapter 16. This area is a hot topic in today’s statistics courses, yet it’s also one that doesn’t seem to get as much space in textbooks as it should. Start here if you want the full details on the most common nonparametric procedures.

Part I

Tackling Data Analysis and Model-Building Basics

In this part . . .

To get you up and moving from the foundational concepts of statistics (covered in your Stats I textbook as well as Statistics For Dummies) to the new and exciting methods presented in this book, I first go over the basics of data analysis, important terminology, main goals and concepts of model-building, and tips for choosing appropriate statistics to fit the job. I refresh your memory of the most heavily referred to items from Stats I, and you also get a head start on making and looking at some basic computer output.

Chapter 1

Beyond Number Crunching: The Art and Science of Data Analysis

In This Chapter

Realizing your role as a data analyst

Avoiding statistical faux pas

Delving into the jargon of Stats II

Because you’re reading this book, you’re likely familiar with the basics of statistics and you’re ready to take it up a notch. That next level involves using what you know, picking up a few more tools and techniques, and finally putting it all to use to help you answer more realistic questions by using real data. In statistical terms, you’re ready to enter the world of the data analyst.

In this chapter, you review the terms involved in statistics as they pertain to data analysis at the Stats II level. You get a glimpse of the impact that your results can have by seeing what these analysis techniques can do. You also gain insight into some of the common misuses of data analysis and their effects.

Data Analysis: Looking before You Crunch

It used to be that statisticians were the only ones who really analyzed data because the only computer programs available were very complicated to use, requiring a great deal of knowledge about statistics to set up and carry out analyses. The calculations were tedious and at times unpredictable, and they required a thorough understanding of the theories and methods behind the calculations to get correct and reliable answers.

Today, anyone who wants to analyze data can do it easily. Many user-friendly statistical software packages are made expressly for that purpose — Microsoft Excel, Minitab, SAS, and SPSS are just a few. Free online programs are available, too, such as Stat Crunch, to help you do just what it says — crunch your numbers and get an answer.