Statistics II For Dummies®, 2nd Edition

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Statistics II For Dummies®

To view this book's Cheat Sheet, simply go to www.dummies.com and search for “Statistics II For Dummies Cheat Sheet” in the Search box.

Table of Contents

Cover

Title Page

Introduction

About This Book
Foolish Assumptions
Icons Used in This Book
Beyond the Book
Where to Go from Here

Part 1: Tackling Data Analysis and Model-Building Basics

Chapter 1: Beyond Number Crunching: The Art and Science of Data Analysis
1. Data Analysis: Looking before You Crunch
2. Getting the Big Picture: An Overview of Stats II
Chapter 2: Finding the Right Analysis for the Job
1. Categorical versus Quantitative Variables
2. Statistics for Categorical Variables
3. Statistics for Quantitative Variables
4. Avoiding Bias
5. Measuring Precision with Margin of Error
6. Knowing Your Limitations
Chapter 3: Having the Normal and Sampling Distributions in Your Back Pocket
1. Recognizing the VIP Distribution — the Normal
2. Finally Getting Comfortable with Sampling Distributions
3. Heads Up! Building Confidence Intervals and Hypothesis Tests
Chapter 4: Reviewing Confidence Intervals and Hypothesis Tests
1. Estimating Parameters by Using Confidence Intervals
2. What’s the Hype about Hypothesis Tests?

Part 2: Using Different Types of Regression to Make Predictions

Chapter 5: Getting in Line with Simple Linear Regression
1. Exploring Relationships with Scatterplots and Correlations
2. Building a Simple Linear Regression Model
3. No Conclusion Left Behind: Tests and Confidence Intervals for Regression
4. Checking the Model’s Fit (The Data, Not the Clothes!)
5. Knowing the Limitations of Your Regression Analysis
Chapter 6: Multiple Regression with Two X Variables
1. Getting to Know the Multiple Regression Model
2. Looking at x’s and y’s
3. Collecting the Data
4. Pinpointing Possible Relationships
5. Checking for Multicolinearity
6. Finding the Best-Fitting Model for Two x Variables
7. Predicting y by Using the x Variables
8. Checking the Fit of the Multiple Regression Model
Chapter 7: How Can I Miss You If You Won’t Leave? Regression Model Selection
1. Getting a Kick out of Estimating Punt Distance
2. Just Like Buying Shoes: The Model Looks Nice, But Does It Fit?
Chapter 8: Getting Ahead of the Learning Curve with Nonlinear Regression
1. Anticipating Nonlinear Regression
2. Starting Out with Scatterplots
3. Handling Curves in the Road with Polynomials
4. Going Up? Going Down? Go Exponential!
Chapter 9: Yes, No, Maybe So: Making Predictions by Using Logistic Regression
1. Understanding a Logistic Regression Model
2. Carrying Out a Logistic Regression Analysis

Part 3: Analyzing Variance with ANOVA

Chapter 10: Testing Lots of Means? Come On Over to ANOVA!
1. Comparing Two Means with a t-Test
2. Evaluating More Means with ANOVA
3. Checking the Conditions
4. Setting Up the Hypotheses
5. Doing the F-Test
6. Checking the Fit of the ANOVA Model
Chapter 11: Sorting Out the Means with Multiple Comparisons
1. Following Up after ANOVA
2. Pinpointing Differing Means with Fisher and Tukey
3. Examining the Output to Determine the Analysis
4. So Many Other Procedures, So Little Time!
Chapter 12: Finding Your Way through Two-Way ANOVA
1. Setting Up the Two-Way ANOVA Model
2. Understanding Interaction Effects
3. Testing the Terms in Two-Way ANOVA
4. Running the Two-Way ANOVA Table
5. Are Whites Whiter in Hot Water? Two-Way ANOVA Investigates
Chapter 13: Regression and ANOVA: Surprise Relatives!
1. Seeing Regression through the Eyes of Variation
2. Regression and ANOVA: A Meeting of the Models

Part 4: Building Strong Connections with Chi-Square Tests and Nonparametrics

Chapter 14: Forming Associations with Two-Way Tables
1. Breaking Down a Two-Way Table
2. Breaking Down the Probabilities
3. Trying To Be Independent
4. Demystifying Simpson’s Paradox
Chapter 15: Being Independent Enough for the Chi-Square Test
1. The Chi-Square Test for Independence
2. Comparing Two Tests for Comparing Two Proportions
Chapter 16: Using Chi-Square Tests for Goodness-of-Fit (Your Data, Not Your Jeans)
1. Finding the Goodness-of-Fit Statistic
2. Interpreting the Goodness-of-Fit Statistic Using a Chi-Square
Chapter 17: Rebels Without a Distribution — Nonparametric Procedures
1. Arguing for Nonparametric Statistics
2. Mastering the Basics of Nonparametric Statistics
Chapter 18: All Signs Point to the Sign Test
1. Reading the Signs: The Sign Test

Part 5: Putting it All Together: Multi-Stage Analysis of a Large Data Set

Chapter 19: Conducting a Multi-Stage Analysis of a Large Data Set
1. Steps Involved in Working with a Large Data Set
2. Wrangling Data
3. Visualizing Data
4. Exploring the Data
5. Looking for Relationships
6. Building Models and Making Inferences
7. Sharing the Story
Chapter 20: A Statistician Watches the Movies
1. Examining the Movie Variables and Asking Questions
2. Visualizing the Movie Data
3. Doing Descriptive Dirty Work
4. Looking for Relationships
5. Building a Model for Predicting U.S. Revenue
6. Writing It Up
Chapter 21: Looking Inside the Refrigerator
1. Refrigerator Data — The Variables
2. Exploring the Data
3. Analyzing the Data
4. Writing It Up

Part 6: The Part of Tens

Chapter 22: Ten Common Errors in Statistical Conclusions
1. Claiming These Statistics Prove …
2. It’s Not Technically Statistically Significant, But …
3. Concluding That x Causes y
4. Assuming the Data Was Normal
5. Only Reporting “Important” Results
6. Assuming a Bigger Sample Is Always Better
7. It’s Not Technically Random, But …
8. Assuming That 1,000 Responses Is 1,000 Responses
9. Of Course the Results Apply to the General Population
10. Deciding Just to Leave It Out
Chapter 23: Ten Ways to Get Ahead by Knowing Statistics
1. Asking the Right Questions
2. Being Skeptical
3. Collecting and Analyzing Data Correctly
4. Calling for Help
5. Retracing Someone Else’s Steps
6. Putting the Pieces Together
7. Checking Your Answers
8. Explaining the Output
9. Making Convincing Recommendations
10. Establishing Yourself as the Statistics Go-To Person
Chapter 24: Ten Cool Jobs That Use Statistics
1. Pollster
2. Data Scientist
3. Ornithologist (Bird Watcher)
4. Sportscaster or Sportswriter
5. Journalist
6. Crime Fighter
7. Medical Professional
8. Marketing Executive
9. Lawyer

Appendix A: Reference Tables

t-Table
Binomial Table
Chi-Square Table
F-Table
Z-Table

Index

About the Author

Advertisement Page

Connect with Dummies

End User License Agreement

List of Tables

Chapter 1

TABLE 1-1 Table Setup for the Breakfast and Age Group Question

Chapter 2

TABLE 2-1 Gender and Political Affiliation of 56,735 U.S. Voters

Chapter 4

TABLE 4-1 Comparing the Values of Power for versus (H_o is )

Chapter 5

TABLE 5-1 Average Textbook Weight and Student Weight (Grades 1–12)

Chapter 6

TABLE 6-1 Advertising Dollars and Sales of Plasma TVs

Chapter 7

TABLE 7-1 Data Collected for Punt Distance Study
TABLE 7-2 Correlations between Distance of a Punt and Other Variables

Chapter 8

TABLE 8-1 Number of People Knowing a Secret over a 6-Day Period
TABLE 8-2 Log(y) Values for the Secret-Spreading Data

Chapter 9

TABLE 9-1 Movie Enjoyment (Yes or No Data) Based on Age

Chapter 10

TABLE 10-1 Watermelon Seed-Spitting Distances for Four Age Groups of Children (M...
TABLE 10-2 Comparing Variances of Four Data Sets to Check the Equal Variance Con...

Chapter 11

TABLE 11-1 Cellphone Minutes Used in One Month

Chapter 12

TABLE 12-1 Six Treatment Combinations for the Drug Study Example
TABLE 12-2 Data and Its Respective Levels from Two Factors

Chapter 13

TABLE 13-1 First Ten Observations from the Education and Internet Use Example

Chapter 14

TABLE 14-1 Two-Way Table for the Cellphone Data
TABLE 14-2 Completed Two-Way Table for the Cellphone Data
TABLE 14-3 Marginal and Grand Totals for the Cellphone Data
TABLE 14-4 Confirmation Calls Related to Showing Up for the Appointment
TABLE 14-5 Video Games Won and Lost for Males Versus Females
TABLE 14-6 Three-Way Table for Gender, Game Level, and Game Outcome

Chapter 15

TABLE 15-1 Gender and House Paint Color Preference: Observed Cell Counts
TABLE 15-2 Gender and House Paint Color Preference: Expected Cell Counts
TABLE 15-3 Age Group and Opinion on Cellphone Ban: Observed Cell Counts
TABLE 15-4 Age Group and Opinion on Cellphone Ban: Expected Cell Counts

Chapter 16

TABLE 16-1 Expected Percentage of Each Color of M&M’S Milk Chocolate Candies
TABLE 16-2 Percentage of M&M’S Observed in One Bag (1.69 oz.) versus Percentage ...
TABLE 16-3 Goodness-of-Fit Statistic for M&M’S Example

Chapter 18

TABLE 18-1 Sample of House Prices in a Neighborhood
TABLE 18-2 Binomial Probabilities to Help Calculate a Confidence Interval for th...
TABLE 18-3 Testing the Effectiveness of Chewing Gum in Lowering Test Anxiety

Chapter 20

TABLE 20-1 The Top Eight Movies of 2018 in Terms of U.S. Box Office Revenue
TABLE 20-2 Some Descriptive Statistics for Runtime through Audience Ratings

Chapter 21

TABLE 21-1 Descriptive Statistics for 41 Refrigerators

Appendix 1

TABLE A-1 The t-Table
TABLE A-2 The Binomial Table
TABLE A-3 The Chi-Square Table
TABLE A-4 The F-Table
TABLE A-5 The Z-Table

List of Illustrations

Chapter 1

FIGURE 1-1: Coffees sold at various air temperatures on football game day.

Chapter 2

FIGURE 2-1: The two-dimensional scatterplot helps you look for relationships in...

Chapter 3

FIGURE 3-1: Three normal distributions, with means and standard deviations of a...

Chapter 4

FIGURE 4-1: Power curve for H_o: versus H_a: , for and .
FIGURE 4-2: Power curve for H_o: versus H_a: , for and .

Chapter 5

FIGURE 5-1: Scatterplot of average student weight versus average textbook weigh...
FIGURE 5-2: Simple linear regression analysis for the textbook-weight example.
FIGURE 5-3: Regression analysis for study time and quiz score data.
FIGURE 5-4: Prediction interval of textbook weight for a 100-pound child.
FIGURE 5-5: Conditions of a simple linear regression model.
FIGURE 5-6: Standardized residual plots for textbook-weight data.
FIGURE 5-7: Scatterplot of textbook-weight data minus the outlier.
FIGURE 5-8: Residual plots for textbook-weight data minus the outlier.

Chapter 6

FIGURE 6-1: Scatterplots of a) TV ad spending and b) Internet ad spending versu...
FIGURE 6-2: Correlation values and p-values for the TV sales example.
FIGURE 6-3: (Selected) Regression output for the ads and plasma TV sales exampl...
FIGURE 6-4: Residual plots for the ads and plasma TV sales example.
FIGURE 6-5: Standardized residual plots for the ads and plasma TV example.

Chapter 7

FIGURE 7-1: A matrix of all scatterplots between pairs of variables in the punt...
FIGURE 7-2: Best subsets procedure results for the punt distance example.

Chapter 8

FIGURE 8-1: Learning curve for time performing a new task.
FIGURE 8-2: A scatterplot showing the spread of a secret over a six-day period.
FIGURE 8-3: Example of a second-degree polynomial.
FIGURE 8-4: Example of a third-degree polynomial.
FIGURE 8-5: Example of a fourth-degree polynomial.
FIGURE 8-6: Scatterplot showing study time and quiz scores.
FIGURE 8-7: Trying to fit a straight line to quadratic data.
FIGURE 8-8: Minitab output for fitting a parabola to the quiz-score data.
FIGURE 8-9: The parabola appears to fit the quiz-score data nicely.
FIGURE 8-10: Standardized residual plots for the quiz-score data, using the qua...
FIGURE 8-11: The exponential regression model for different values of β.
FIGURE 8-12: Minitab fits a line to the log(y) for the secret-spreading data.
FIGURE 8-13: A scatterplot showing the fit of a straight line to log(y) data.
FIGURE 8-14: Residual plots showing the fit of a straight line to log(y) data.

Chapter 9

FIGURE 9-1: Two basic types of S-curves.
FIGURE 9-2: The model-building part of the movie and age data’s logistic regres...
FIGURE 9-3: The best-fitting S-curve for the movie and age data.
FIGURE 9-4: The model-fitting part of the movie and age data’s logistic regress...
FIGURE 9-5: Actual observed values (0 and 1) compared to the model.

Chapter 10

FIGURE 10-1: A t-test comparing mean watermelon seed-spitting distances for fem...
FIGURE 10-2: Checking ANOVA conditions by using histograms and descriptive stat...
FIGURE 10-3: Examining side-by-side boxplots to check the equal variance condit...
FIGURE 10-4: ANOVA Minitab output for the watermelon seed-spitting example.
FIGURE 10-5: F-distribution with (3, 16) degrees of freedom.

Chapter 11

FIGURE 11-1: Basic statistics and confidence intervals for the cellphone data.
FIGURE 11-2: ANOVA results for comparing cellphone use for four age groups.
FIGURE 11-3: Output showing Fisher’s LSD applied to the cellphone data.
FIGURE 11-4: Output for Tukey’s test used to compare cellphone usage.
FIGURE 11-5: Multiple comparison results for the cereal example.

Chapter 12

FIGURE 12-1: Five examples of the results from a two-way ANOVA with interaction...
FIGURE 12-2: ANOVA tables for the interaction plots from Figure 12-1.
FIGURE 12-3: ANOVA table for the clothing example.
FIGURE 12-4: Boxplots showing how brand of detergent and water temperature inte...

Chapter 13

FIGURE 13-1: Output for simple linear regression applied to education and Inter...
FIGURE 13-2: Connecting means of populations to the slope of a line.

Chapter 14

FIGURE 14-1: Pie charts comparing teen versus adult personal cellphone use.

Chapter 15

FIGURE 15-1: Minitab output for the house paint color preference versus gender ...
FIGURE 15-2: Chi-square distributions with 1, 2, 4, 6, 8, and 10 degrees of fre...
FIGURE 15-3: Minitab output comparing the proportion of adult and teenage owner...
FIGURE 15-4: Minitab output testing independence of age group and latest cellph...

Chapter 16

FIGURE 16-1: Chi-square distribution with 5 degrees of freedom.
FIGURE 16-2: Graph of observed versus expected counts for the M&M’S colors data...
FIGURE 16-3: Minitab output of Chi-square goodness-of-fit test on M&M’S colors ...

Chapter 17

FIGURE 17-1: Symmetric and skewed histograms.

Chapter 18

FIGURE 18-1: Histogram of the selling prices of ten houses.
FIGURE 18-2: Sign test for house prices conducted by Minitab.

Chapter 20

FIGURE 20-1: Pie charts and bar graphs of a) release date (month), b) rating, c...
FIGURE 20-2: Histograms and boxplots of a) runtime through h) audience (ratings...
FIGURE 20-3: Matrix of scatterplots of runtime through audience ratings.
FIGURE 20-4: Matrix of correlations for runtime through audience ratings.
FIGURE 20-5: Stacked bar graph to explore content rating and genre.
FIGURE 20-6: Side-by-side boxplots to look for relationships.
FIGURE 20-7: Linear regression analysis using opening weekend revenue to predic...
FIGURE 20-8: Final regression line on the scatterplot using opening weekend rev...
FIGURE 20-9: Results of best subsets regression model selection for predicting ...

Chapter 21

FIGURE 21-1: Histogram of refrigerator prices.
FIGURE 21-2: Boxplots of refrigerator price by brand.
FIGURE 21-3: ANOVA for testing equality of mean prices across the refrigerator ...
FIGURE 21-4: Tukey’s multiple comparisons using confidence intervals and by bra...
FIGURE 21-5: Cubic-foot capacity being used to predict refrigerator price.
FIGURE 21-6: Matrix of scatterplots for refrigerator data and matrix of correla...
FIGURE 21-7: Scatterplot and regression line for predicting yearly electric use...
FIGURE 21-8: a) Analysis of Variance (ANOVA) for comparing yearly electric use ...
FIGURE 21-9: Two-factor ANOVA with brand and icemaker as the factors and yearly...
FIGURE 21-10: Interaction plot showing mean yearly electric use for each brand,...

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, 2nd Edition, picks up right where Statistics For Dummies, 2nd Edition, (John Wiley & Sons) 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, 2nd Edition, 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), and Chi-square tests, and I give you some practice with big data sets, which are all the rage right now. Using these new techniques, you estimate, investigate, correlate, and congregate even more variables based on the information at hand, and you see how to put the tools together to create a great story about your data (nonfiction, I hope!).

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, 2nd Edition) 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 to 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 apply 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 tell you. You will 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 than doing the programming specifically. Because the equations and calculations can get too involved if you are solving them 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 use this approach as well. (What a relief!)

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

Full explanations of Stats II concepts. Many statistics textbooks squeeze all the Stats II topics at the very end of their 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 of examples. I include plenty of examples to cover the many different types of problems you’ll face. Some examples are short, and some are quite extensive and include multiple variables.
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.

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 H_o (for the null hypothesis) and H_a (for the alternative hypothesis).
The statistical software package I use and display throughout the book is Minitab 18, but I simply refer to it as Minitab.
Whenever I introduce a new term, I italicize it.
Keywords and numbered steps appear in boldface.

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 along with the essential text, usually in the form of a real-life statistics example or some bonus information 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, 2nd Edition), 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 4). Prior experience with simple linear regression isn’t necessary. Only college algebra is needed for the math details. Some experience using statistical software is also 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.

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 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.

Beyond the Book

In addition to all the great content included in the book itself, you can find even more content online. Check out this book’s online Cheat Sheet on dummies.com. It covers the major formulas needed for Statistics II. You can access it by going to www.dummies.com and then typing “Statistics II For Dummies Cheat Sheet” into the search bar.

I’ve also included two major data sets that are analyzed in Chapters 20 and 21, so you can follow along with me or do your own analysis (not required!). Go to www.dummies.com/go/statisticsIIfd2e to access these files.

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 10, the basics of analysis of variance (ANOVA).

Chapter 15 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 in Chapter 17. Start there if you want the full details on the most common nonparametric procedures, used when you do not necessarily have an assumed distribution (for example, a normal).

If you want to see a bunch of Stats II ideas put into practice right off the bat, head to Chapter 19 where I discuss a multi-stage approach to analyzing a big data set, or Chapter 21, where you look into a big data set on refrigerators and see how it’s analyzed in a multi-stage approach.

Part 1

Tackling Data Analysis and Model-Building Basics

IN THIS PART …

Understand why data analysis is both a science and an art.

Make sure you use the right type of analysis for the job.

Work with the normal and binomial distribtions.

Reaquaint yourself with confidence intervals and hypothesis tests.