Introduction to Decision Making Support Using Statistics

By Warren Beatty

Palatable, quick, easy introduction to basic statistics using the statistical capabilities of Gnumeric, a free spreadsheet that can be downloaded.

• Language: English
• Publisher: Each Voice Publishing
• Release date: Jul 11, 2013
• ISBN: 9780989210508

Warren Beatty

Warren Beatty is a retired University Professor who holds a Ph.D. in Statistics from The Florida State University. He taught Business Statistics, Management Science, Management Information Systems, and Decision Support at the University of South Alabama (where he managed one of the world's first campus-wide interactive computer systems before joining the faculty) and the University of West Florida. He also taught in Germany, France, The Netherlands, and England. He was an early proponent of the Internet and spreadsheets as teaching tools. He was the author or co-author of more than forty referred academic papers. This book is his initial foray into writing fiction. He has been married for almost fifty years to the same woman. He has three children, and (so far) three grandchildren. He served for twenty two years in the U.S. Army, and went to Desert Shield/Desert Storm, where he was a Group NBC officer. He is a HUGE car racing fan, particularly Formula One and NASCAR. He was a very slow short track racer. His personal web site address is: http://ebsfords.6te.net/wb/

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Table of Contents

Preface: Purpose, Intended Audience, Scope

Gnumeric Help: Gnumeric Help and Compatibility with Excel

Introduction: Definition of Statistics and the Two Types of Statistics: Descriptive and Inferential; to Decision Making, Assumptions, Freebie

Chapter 1: Introduction to Variables; Some Basic Variable Characteristics, and Calculations: Mean, Median, Mode; to Variable Variation: Range, Variance, Standard Deviation; and an Introduction to Sampling, Sampling Error, and the Margin of Error

Chapter 2: Introduction to Probability, the Foundation of Statistics, and to the Binomial Probability Distribution, Gauss’ Normal Probability Distribution, and Gosset’s Student’s t Probability Distribution

Chapter 3: Estimation and Confidence Intervals

Chapter 4: One Population Hypotheses and Hypothesis Testing, two tail and one tail testing

Chapter 5: Two Population Hypotheses and Hypothesis Testing, two tail and one tail testing

Chapter 6: ANOVA, Three or More Population Hypotheses and Hypothesis Testing

Chapter 7: Introduction to Linear Regression and Correlation

Chapter 8: Introduction to Forecasting Using Exponential Smoothing, Moving Average, and Regression

Chapter 9: Introduction to Descriptive Statistics

Glossary: A Glossary of Statistics Terms

Statistical Symbols: Symbols and their Definitions

Formulae: Statistics Formulae used in this book

Spreadsheet Use: A Quick & Dirty Spreadsheet Tutorial

Answers to Exercises

Preface

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I always find that statistics are hard to swallow and impossible to digest. The only one I can ever remember is that if all the people who go to sleep in church were laid end to end they would be a lot more comfortable!

—Mrs. Robert A. Taft (Martha Wheaton Bowers), daughter-in-law of W.H. Taft, 27th US President

Like other occult techniques of divination, the statistical method has a private jargon deliberately contrived to obscure its methods from non-practitioners. —G.O. Ashley

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Purpose

This book is designed for students (and managers) who want to know about statistics and some of the tools used by statisticians. To be a knowledgeable consumer of the world’s use of statistics, one must understand how statistics can support critical decisions. One needs very little knowledge of mathematics in order to understand the material in this book. Statistical computer packages, such as the spreadsheet Gnumeric, have almost eliminated the need for computational formulae. Because the computer will perform the calculations for you, all the formulae have been relegated to one section that contains formulae, symbols, and terms.

This book is written to free the statistics instructor from having to tell students HOW to generate statistical output to be discussed. It frees the instructor to concentrate on what he or she does best — convey statistical concepts by using illustrations students can generate for themselves.

There is a quote about statistics attributed to Benjamin Disraeli: Lies, damned lies, and statistics. Disraeli was referring the use of statistics to strengthen weak arguments. Mark Twain expanded upon Disraeli’s remark: There are three kinds of lies: lies, damned lies, and statistics.’ With that introduction to statistics, you had better understand what is going on in order to protect yourself, just like the last instruction the referee gives to boxers: Protect yourself at all times.’

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As Twain DIDN’T say: liars, outliers, and out-and-out liars! (Nor did Disraeli...). —Robert Dawson

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This book will help you:

Understand the statistics presented in your world in particular and in the world in general.

Communicate to others how statistical information supports your decision.

Understand the relationship between statistics and decision support.

Apply this new knowledge of statistics and use these new helpful new tools to improve your decision-making.

Use statistics to support your decision-making.

Intended Audience

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What is the difference between an extroverted and an introverted statistician? The extroverted statistician looks at your shoes while talking to you. —Jim Box

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Let’s be honest: Statistics can intimidate, confuse, and mislead people into believing things that are not true. Percentages and large volumes of numbers may frighten some people. Have you ever heard the phrase caveat emptor — let the buyer beware? This book, by arming you with decision-making knowledge, will remove some of the confusion, as well as help you recognize misleading information.

Perhaps you are not reading this book by choice, but by necessity. A statistics course is required of almost all majors. If you are the student who just wants to get through the required statistics course, this book is written with you in mind.

Along the way you will see that a knowledge of statistics is quite easy to obtain, useful to have, and can assist you when you have to make everyday decisions. You may even get hooked on statistics and want to take other, more advanced statistics courses. You may consider statisticians weird for their desire to incorporate historical data that may be used to forecast the relative probability of several potential outcomes, but that’s okay — we’re here to help you overcome this perceived character flaw (considering statisticians weird) so that you can love (or at least like) using statistics to improve your decisions just as much as we do.

This book is for you if you are wary of statistics, mathematics, or of computers and spreadsheets. This book will help anyone who wants to learn how to apply and interpret Gnumeric’s statistical tools in order to generate decision-making information, and how to interpret the information generated. This book illustrates how to conduct statistical tests and how to interpret the results.

Anyone majoring in business, psychology, education, sociology, engineering, or computer science who wants to learn how to use Gnumeric to solve and interpret statistics problems can benefit. This book is appropriate for use in ANY statistics course, whether undergraduate of graduate.

While this book is aimed primarily at college students, it can be useful to managers who want to use a spreadsheet to generate information in support of decision-making. Managers, after all, are students themselves, and the learning process never ends!

Don’t like the order of presentation? Chapters 1 and 2 introduce some fundamental statistics concepts. All other chapters are stand alone so the topics they cover can be addressed in the order that best suits the instructor’s needs.

Scope and Topic Coverage

It is simply not possible to acquire a complete understanding of statistics via a single introductory course. Therefore, what this book does is introduce statistics topics that you are most likely to see and use from a decision support perspective.

Some Basic Statistics Concepts

Introduction to Variables and Simple Calculations Using Gnumeric

Introduction to Probability and Some Very Useful Probability Distributions

Confidence Intervals

One Population Hypothesis Testing

Two Population Hypothesis Testing

ANOVA: Three (or more) Population Hypothesis Testing

Regression

Forecasting

Descriptive Statistics

Glossary of Statistics Terms

Statistics Symbols

Statistics Calculation Formulae

A Gnumeric Spreadsheet Tutorial

Why You Need This Book

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It is proven that the celebration of birthdays is healthy. Statistics show that those people who celebrate the most birthdays become the oldest. —S. den Hartog

Meaningless statistics are up 6.5 percent from last year.

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This book is a palatable introduction to basic statistics. It focuses upon applications using a spreadsheet with statistics capabilities to generate information, and upon interpretation of results in support of decision making, rather than upon statistical calculations. It introduces the most used statistical tools or procedures that can be useful with any discipline. It prepares you to be a consumer of statistics in the world.

Gnumeric is a computer spreadsheet program that is a Microsoft Excel look-alike and work-alike, and can be downloaded for FREE, at no cost to you. Excel costs quite a bit of money. Therefore, buying this book can save you a lot of money, both initially by not having to buy Excel, and by making you a better decision maker. Additionally, all the functions and tools in this book are also applicable to Excel users. Do not worry if you have already bought Excel; everything in this book is applicable.

This is the first book to use the capability of Gnumeric to teach statistics. You will learn how to use Gnumeric to perform statistical procedures without getting swamped or overpowered by statistical theory or formulae. The best part is that the Gnumeric spreadsheet is used to generate statistics examples, applications, and illustrations throughout the entire book. In addition, this book, in the Gnumeric Tutorial, includes instructions for downloading and installing your own copy of Gnumeric.

You get what you pay for, period. However Gnumeric may be an exception to that rule. Excel is the most popular and widely sold spreadsheet and statistics software in the world today. Learning to use Gnumeric can get you ready if you ever are asked if you know how to use Excel (like at a job interview), or if you need to know how to use statistics.

There are literally thousands of statistics resources available on the Internet, but those resources are inconsistent and make use of many available statistics programs. There is a lot to be said for a consistent presentation that uses only one statistics program.

Most chapters have supporting Gnumeric spreadsheets available for download at rwno.limewebs.com/stat. You will find separate download for Chapter Examples, Chapter Exercise Data, and Chapter Exercise Answers.

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Humor Alert: There are, throughout this book, inclusions of Statistics Humor, denoted by centered italics.

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Most are rather weak attempts at humor, but the author found them humorous. Anyway, below are some Internet links to statistics humor in case further investigation is warranted.

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If we couldn’t laugh at ourselves, that would be the end of everything.

—Niels Bohr

Rob J. Hyndman’s Statistical Jokes

Gary Ramseyer’s World of Statistical Humor!

Statistics Movies that Never Made it to the Big Screen

Joachim Verhagen’s Science Humor. For some reason, I like 9.5, The Nerd Test

GNUMERIC and EXCEL

You can find many references on the Internet about how the Gnumeric and Excel statistics are inferior to SPSS, SAS, Minitab, and others. For serious statistics, they are correct. However, as an introductory teaching tool, Gnumeric is fine.

Gnumeric statistics functions and Microsoft Excel statistics functions are very similar. They are exactly alike in most cases. So, any Microsoft Excel links that are helpful can also apply to Gnumeric.

Here are some Excel specific links that you may find helpful with Gnumeric.

Link 1: Excel for Statistical Data Analysis

Link 2: Use for Analysis of Economics Data

Link 3: List of Excel Statistical Functions

Link 4: EXCEL Tutorial for Statistical Data Analysis

Introduction

Information is a source of learning. But unless it is organized, processed, and available to the right people in a format for decision making, it is a burden, not a benefit.

—William Pollard (1911 - 1989) Physicist

Information

This book is about generating information using statistical analysis to support decision-making. This book is about using statistics to organize, process, and make available information to support decision making. Raw data does not become information until it has been processed, and then it may become understandable and useable.

The statistics introduced here will work for ANY discipline in which decisions must be made — which pretty much covers any subject that might come to mind where quantitative historical data is available.

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Statistical Analysis: Mysterious, sometimes bizarre, manipulations performed upon the collected data of an experiment in order to obscure the fact that the results have no generalizable meaning for humanity. Commonly, computers are used, lending an additional aura of unreality to the proceedings.

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Definition of Statistics

What is this body of knowledge called Statistics? It is the science that addresses the collection, classification, analysis, and interpretation of numerical facts or data in order to support decision making. Statistics identifies the values, uncertainties, and other issues for a given decision situation. It provides information in order to help you make the best possible decision. It formally orders the analysis and decision making processes so you can make objective decisions. Statistics can save money and/or time. It can be much cheaper and less time consuming to study a subset or sample of the group, or population, that interests you than to study the entire population. And, if study is destructive, you literally cannot study every member of your population. If, for example, you want to advertise the length of a specific type of light bulb’s life, you burn light bulbs until they burn out and record the number of hours they produce light. Studying them is destructive. In this instance, you must test a sample of light bulbs. Trying to sell burnt out light bulbs will prove difficult!

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If I had only one day left to live, I would live it in my statistics class: it would seem so much longer.

—Urban Myth(?)

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Statistics relies upon historical data (that you gather) and analyzes that data to provide information.

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Remember, if you torture historical data enough, it WILL confess.

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You may not realize that you use statistics every day to support decisions you make.

Imagine you are on a jury in a murder trial. The prosecutor calls expert witnesses who testify that the defendant’s DNA was found at the scene of the crime, under the fingernails of the victim. You hear the expert say that the DNA was an exact match, meaning the odds were 540 million to one against the possibility that someone else committed the murder. It is your rudimentary knowledge of statistics that tells you that the odds are so unlikely that another person could have committed the crime that it’s inconceivable to think otherwise. You vote with the other jurors to convict. Statistical analysis played a key role in your decision making.

Consider how you evaluate expected value. Do you play the lottery or gamble? Do you know that the payouts are computed with statistics? And that what you expect to win (or lose) can also be calculated with statistics?

Which route to take? As you drive to and from work, church, or the mall, you decide which route to take. You choose your routes based upon probability, upon what you think traffic situations you might encounter are on alternative routes.

You choose when to start cooking based upon your experience (data collection) of how long it usually takes (interpretation) to cook the selected menu items.

Assessing risk brings statistics into play. You have (or will have) insurance on your car, your house, and your life. Insurance companies use statistics to calculate actuarial tables in order to determine premium rates.

If you play any fantasy sports games, you choose your athletes based upon averages, based upon how you expect them to perform.

Playing a piano invokes one of the central tenants of statistics. All piano keyboards are the same: there is no variation from keyboard to keyboard. So, if you decide to play a piano, think about statistics!

All this book does is provide terminology and structure to the statistical analysis processes that you are already using in the course of a normal life.

Facts about Statistics

There are four very important facts about statistics that you should know:

Statistics in this book have ABSOLUTELY nothing to do with advanced mathematics. It is unfortunate that