Statistics Essentials For Dummies E-Book

Deborah J. Rumsey

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch
• Veröffentlichungsjahr: 2010

Seitenzahl: 239

Beschreibung

Statistics Essentials For Dummies not only provides studentsenrolled in Statistics I with an excellent high-level overview ofkey concepts, but it also serves as a reference or refresher forstudents in upper-level statistics courses. Free of review andramp-up material, Statistics Essentials For Dummies sticksto the point, with content focused on key course topics only. Itprovides discrete explanations of essential concepts taught in atypical first semester college-level statistics course, from oddsand error margins to confidence intervals and conclusions. Thisguide is also a perfect reference for parents who need to reviewcritical statistics concepts as they help high school students withhomework assignments, as well as for adult learners headed backinto the classroom who just need a refresher of the core concepts. The Essentials For Dummies Series Dummies is proud to present our new series, The Essentials ForDummies. Now students who are prepping for exams, preparing tostudy new material, or who just need a refresher can have aconcise, easy-to-understand review guide that covers an entirecourse by concentrating solely on the most important concepts. Fromalgebra and chemistry to grammar and Spanish, our expert authorsfocus on the skills students most need to succeed in a subject.

Leseprobe

Statistics Essentials For Dummies®

Table of Contents

Introduction

About This Book

Conventions Used in This Book

Foolish Assumptions

Icons Used in This Book

Chapter 1: Statistics in a Nutshell

Designing Studies

Surveys

Experiments

Collecting Data

Selecting a good sample

Avoiding bias in your data

Describing Data

Descriptive statistics

Charts and graphs

Analyzing Data

Making Conclusions

Chapter 2: Descriptive Statistics

Types of Data

Counts and Percents

Measures of Center

Measures of Variability

Percentiles

Finding a percentile

Interpreting percentiles

The Five-Number Summary

Chapter 3: Charts and Graphs

Pie Charts

Bar Graphs

Time Charts

Histograms

Making a histogram

Interpreting a histogram

Evaluating a histogram

Boxplots

Making a boxplot

Interpreting a boxplot

Chapter 4: The Binomial Distribution

Characteristics of a Binomial

Checking the binomial conditions step by step

Non-binomial examples

Finding Binomial Probabilities Using the Formula

Finding Probabilities Using the Binomial Table

Finding probabilities when p ≤ 0.50

Finding probabilities when p > 0.50

Finding probabilities for X greater-than, less-than, or between two values

The Expected Value and Variance of the Binomial

Chapter 5: The Normal Distribution

Basics of the Normal Distribution

The Standard Normal (Z) Distribution

Finding Probabilities for X

Finding X for a Given Probability

Normal Approximation to the Binomial

Chapter 6: Sampling Distributions and the Central Limit Theorem

Sampling Distributions

The mean of a sampling distribution

Standard error of a sampling distribution

Sample size and standard error

Population standard deviation and standard error

The shape

Finding Probabilities for

The Sampling Distribution of the Sample Proportion

What proportion of students need math help?

Finding Probabilities for

Chapter 7: Confidence Intervals

Making Your Best Guesstimate

The Goal: Small Margin of Error

Choosing a Confidence Level

Factoring In the Sample Size

Counting On Population Variability

Confidence Interval for a Population Mean

Confidence Interval for a Population Proportion

Confidence Interval for the Difference of Two Means

Confidence Interval for the Difference of Two Proportions

Interpreting Confidence Intervals

Spotting Misleading Confidence Intervals

Chapter 8: Hypothesis Tests

Doing a Hypothesis Test

Identifying what you’re testing

Setting up the hypotheses

Finding sample statistics

Standardizing the evidence: the test statistic

Weighing the evidence and making decisions: p-values

General steps for a hypothesis test

Testing One Population Mean

Testing One Population Proportion

Comparing Two Population Means

Testing the Mean Difference: Paired Data

Testing Two Population Proportions

You Could Be Wrong: Errors in Hypothesis Testing

A false alarm: Type-1 error

A missed detection: Type-2 error

Chapter 9: The t-distribution

Basics of the t-Distribution

Understanding the t-Table

t-distributions and Hypothesis Tests

Finding critical values

Finding p-values

t-distributions and Confidence Intervals

Chapter 10: Correlation and Regression

Picturing the Relationship with a Scatterplot

Making a scatterplot

Interpreting a scatterplot

Measuring Relationships Using the Correlation

Calculating the correlation

Interpreting the correlation

Properties of the correlation

Finding the Regression Line

Which is X and which is Y?

Checking the conditions

Understanding the equation

Finding the slope

Finding the y-intercept

Interpreting the slope and y-intercept

Making Predictions

Avoid Extrapolation!

Correlation Doesn’t Necessarily Mean Cause-and-Effect

Chapter 11: Two-Way Tables

Organizing and Interpreting a Two-way Table

Defining the outcomes

Setting up the rows and columns

Inserting the numbers

Finding the row, column, and grand totals

Finding Probabilities within a Two-Way Table

Figuring joint probabilities

Calculating marginal probabilities

Finding conditional probabilities

Checking for Independence

Chapter 12: A Checklist for Samples and Surveys

The Target Population Is Well Defined

The Sample Matches the Target Population

The Sample Is Randomly Selected

The Sample Size Is Large Enough

Nonresponse Is Minimized

The importance of following up

Anonymity versus confidentiality

The Survey Is of the Right Type

Questions Are Well Worded

The Timing Is Appropriate

Personnel Are Well Trained

Proper Conclusions Are Made

Chapter 13: A Checklist for Judging Experiments

Experiments versus Observational Studies

Criteria for a Good Experiment

Inspect the Sample Size

Small samples — small conclusions

Original versus final sample size

Examine the Subjects

Check for Random Assignments

Gauge the Placebo Effect

Identify Confounding Variables

Assess Data Quality

Check Out the Analysis

Scrutinize the Conclusions

Overstated results

Ad-hoc explanations

Generalizing beyond the scope

Chapter 14: Ten Common Statistical Mistakes

Misleading Graphs

Pie charts

Bar graphs

Time charts

Histograms

Biased Data

No Margin of Error

Nonrandom Samples

Missing Sample Sizes

Misinterpreted Correlations

Confounding Variables

Botched Numbers

Selectively Reporting Results

The Almighty Anecdote

Appendix: Tables for Reference

Statistics Essentials For Dummies®

by Deborah Rumsey, PhD

Statistics Essentials For Dummies®

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Library of Congress Control Number: 2010925241

ISBN: 978-0-470-61839-4

Manufactured in the United States of America

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About the Author

Deborah Rumsey is a Statistics Education Specialist and Auxiliary Professor at The Ohio State University. Dr. Rumsey is a Fellow of the American Statistical Association and has won a Presidential Teaching Award from Kansas State University. She has served on the American Statistical Association’s Statistics Education Executive Committee and the Advisory Committee on Teacher Enhancement, and is the editor of the Teaching Bits section of the Journal of Statistics Education. She is the author of the books Statistics For Dummies, Statistics II For Dummies, Probability For Dummies, and Statistics Workbook For Dummies. Her passions, besides teaching, include her family, fishing, bird watching, getting “seat time” on her Kubota tractor, and cheering the Ohio State Buckeyes to another national championship.

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Introduction

This book is designed to give you the essential, nitty-gritty information typically covered in a first semester statistics course. It’s bottom-line information for you to use as a refresher, a resource, a quick reference, and/or a study guide. It helps you decipher and make important decisions about statistical polls, experiments, reports and headlines with confidence, being ever aware of the ways people can mislead you with statistics, and how to handle it.

Topics I work you through include graphs and charts, descriptive statistics, the binomial, normal, and t-distributions, two-way tables, simple linear regression, confidence intervals, hypothesis tests, surveys, experiments, and of course the most frustrating yet critical of all statistical topics: sampling distributions and the Central Limit Theorem.

About This Book

This book departs from traditional statistics texts and reference/supplement books and study guides in these ways:

Clear and concise step-by-step procedures that intuitively explain how to work through statistics problems and remember the process.

Focused, intuitive explanationsempower you to know you’re doing things right and whether others do it wrong.

Nonlinear approachso you can quickly zoom in on that concept or technique you need, without having to read other material first.

Easy-to-follow examplesreinforce your understanding and help you immediately see how to apply the concepts in practical settings.

Understandable language helps you remember and put into practice essential statistical concepts and techniques.

Conventions Used in This Book

I refer to statistics in two different ways: as numerical results (such as means and medians); or as a field of study (for example, “Statistics is all about data.”).

The second convention refers to the word data. I’m going to go with the plural version of the word data in this book. For example “data are collected during the experiment” — not “data is collected during the experiment.”

Foolish Assumptions

I assume you’ve had some (not necessarily a lot of) previous experience with statistics somewhere in your past. For example, you can recognize some of the basic statistics such as the mean, median, standard deviation, and perhaps correlation; you can handle some graphs; and you can remember having seen the normal distribution. If it’s been a while and you are a bit rusty, that’s okay; this book is just the thing to jog your memory.

If you have very limited or no prior experience with statistics, allow me to suggest my full-version book, Statistics for Dummies, to build up your foundational knowledge base. But if you are someone who has not seen these ideas before and either doesn’t have time for the full version, or you like to plunge into details right away, this book can work for you.

I assume you’ve had a basic algebra background and can do some of the basic mathematical operations and understand some of the basic notation used in algebra like x, y, summation signs, taking the square root, squaring a number, and so on. (If you’d like some backup on the algebra part, I suggest you consider Algebra I For Dummies and Algebra II For Dummies (Wiley)).

Icons Used in This Book

Here are the road signs you’ll encounter on your journey through this book:

Tips refer to helpful hints or shortcuts you can use to save time.

Read these to get the inside track on why a certain concept is important, what its impact will be on the results, and highlights to keep on your radar.

These alert you to common errors that can cause problems, so you can steer around them.

This book is written in a nonlinear way, so you can start anywhere and still be able to understand what’s happening. However, I can make some recommendations for those who are interested in knowing where to start.

For a quick overview of the topics to refresh your memory, check out Chapter 1. For basic number crunching and graphs, see Chapters 2 and 3. If you’re most interested in common distributions, see Chapters 4 (binomial); 5 (normal); and 9 (t-distribution). Confidence intervals and hypothesis testing are found in Chapters 7 and 8. Correlation and regression are found in Ch 10, and two-way tables and independence are tackled in Ch 11. If you are interested in evaluating and making sense of the results of medical studies, polls, surveys, and experiments, you’ll find all the info in Chapters 12 and 13. Common mistakes to avoid or watch for are seen in Chapter 14.

Chapter 1

Statistics in a Nutshell

In This Chapter

Getting the big picture of the field of statistics

Overviewing the steps of the scientific method

Seeing the role of statistics at each step

The most common description of statistics is that it’s the process of analyzing data — number crunching, in a sense. But statistics is not just about analyzing the data. It’s about the whole process of using the scientific method to answer questions and make decisions. That process involves designing studies, collecting good data, describing the data with numbers and graphs, analyzing the data, and then making conclusions. In this chapter I review each of these steps and show where statistics plays the all-important role.