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«ta t i s t i c s S e nt ia l s Ess Learn: • Exactly what you need to know about statistical ideas and techniques • The “must-know” formulas ...»

-- [ Page 1 ] --

sier!™

ing Everything Ea

Mak

ta t i s t i c s

S

e nt ia l s

Ess

Learn:

• Exactly what you need to know

about statistical ideas and

techniques

• The “must-know” formulas and

calculations

• Core topics in quick, focused

lessons

Deborah Rumsey, PhD

Auxiliary Professor and

Statistics Education Specialist,

The Ohio State University

Statistics

Essentials

FOR

DUMmIES

by Deborah Rumsey, PhD

Statistics Essentials For Dummies® Published by Wiley Publishing, Inc.

111 River St.

Hoboken, NJ 07030-5774 www.wiley.com Copyright © 2010 by Wiley Publishing, Inc., Indianapolis, Indiana 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 either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600. 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, the Wiley Publishing logo, For Dummies, the Dummies Man logo, A Reference for the Rest of Us!, The Dummies Way, Dummies Daily, The Fun and Easy Way, Dummies.com, Making Everything Easier, and related trade dress are trademarks or registered trademarks of John Wiley & Sons, Inc. and/or its affiliates in the United States and other countries, and may not be used without written permission. All other trademarks are the property of their respective owners. Wiley Publishing, Inc., is not associated with any product or vendor mentioned in this book.

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Library of Congress Control Number: 2010925241 ISBN: 978-0-470-61839-4 Manufactured in the United States of America 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.

Publisher’s Acknowledgments We’re proud of this book; please send us your comments 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 317-572-4002.





Some of the people who helped bring this book to market include the following:

–  –  –

Publishing and Editorial for Consumer Dummies Diane Graves Steele, Vice President and Publisher, Consumer Dummies Kristin Ferguson-Wagstaffe, Product Development Director, Consumer Dummies Ensley Eikenburg, Associate Publisher, Travel Kelly Regan, Editorial Director, Travel Publishing for Technology Dummies Andy Cummings, Vice President and Publisher, Dummies Technology/ General User Composition Services Debbie Stailey, Director of Composition Services

Contents at a Glance

Introduction

Chapter 1: Statistics in a Nutshell

Chapter 2: Descriptive Statistics

Chapter 3: Charts and Graphs

Chapter 4: The Binomial Distribution

Chapter 5: The Normal Distribution

Chapter 6: Sampling Distributions and the Central Limit Theorem

Chapter 7: Confidence Intervals

Chapter 8: Hypothesis Tests

Chapter 9: The t-distribution

Chapter 10: Correlation and Regression

Chapter 11: Two-Way Tables

Chapter 12: A Checklist for Samples and Surveys

Chapter 13: A Checklist for Judging Experiments

Chapter 14: Ten Common Statistical Mistakes

Appendix: Tables for Reference

Index

Table of Contents

Introduction......................................1 About This Book

Conventions Used in This Book

Foolish Assumptions

Icons Used in This Book

Where to Go from Here

Chapter 1: Statistics in a Nutshell...................5 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...................13 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......................23 Pie Charts

Bar Graphs

Time Charts

viii Statistics Essentials For Dummies

–  –  –

Chapter 5: The Normal Distribution.................45

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

–  –  –

Sample size and standard error

Population standard deviation and standard error.....60 The shape

Case 1: Distribution of X is normal

Case 2: Distribution of X is unknown or not normal

Finding Probabilities for

The Sampling Distribution of the Sample Proportion......... 63 What proportion of students need math help?.......... 64 Finding Probabilities for

Chapter 7: Confidence Intervals....................69 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................ 77 Confidence Interval for the Difference of Two Means......... 78 Confidence Interval for the Difference of Two Proportions

Interpreting Confidence Intervals

Spotting Misleading Confidence Intervals

Chapter 8: Hypothesis Tests.......................87 Doing a Hypothesis Test

Identifying what you’re testing

Setting up the hypotheses

What’s the alternative?

Knowing which hypothesis is which................ 89 Finding sample statistics

Standardizing the evidence: the test statistic............ 90

Weighing the evidence and making decisions:

p-values

Finding the p-value

Interpreting a p-value

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

x Statistics Essentials For Dummies You Could Be Wrong: Errors in Hypothesis Testing......... 104 A false alarm: Type-1 error

A missed detection: Type-2 error

Chapter 9: The t-distribution......................107

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............113 Picturing the Relationship with a Scatterplot

Making a scatterplot

Interpreting a scatterplot

Measuring Relationships Using the Correlation................ 115 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

Interpreting the slope

Interpreting the y-intercept

The best-fitting line for the crickets................ 123 Making Predictions

Avoid Extrapolation!

Correlation Doesn’t Necessarily Mean Cause-and-Effect.....125

–  –  –

Chapter 12: A Checklist for Samples and Surveys...137 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....147 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......155 Misleading Graphs

Pie charts

Bar graphs

Time charts

Histograms

Biased Data

No Margin of Error

Nonrandom Samples

Missing Sample Sizes

Misinterpreted Correlations

Confounding Variables

xii Statistics Essentials For Dummies Botched Numbers

Selectively Reporting Results

The Almighty Anecdote

–  –  –

Index..........................................171

Introduction

T his 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, twoway 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 explanations empower you to know you’re doing things right and whether others do it wrong.

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



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