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Home , Descriptive statistics, Inductive reasoning

STATISTICS

Milo Schield Ó Spring Day, 2001

SL2000T1

SL2000T1 TABLE OF CONTENTS

DESCRIPTIVE

Part I: Fundamentals 1. and Statistics 2. Describing Count-Based 3. Comparing Count-Based Data 4. Interpreting Count-Based Data 5. Reading and Interpreting Measurements

Part II: Graphs and Models 6. Graphs 7. Linear Models – Single Factor 8. Linear Models – Multiple Factors 9. Non-linear Models

INFERENTIAL STATISTICS

Part III: and Inferential Statistics 10. Obtaining Statistics: Samples, Surveys and 11. Statistical Expectation, Chance and Error 12. Statistical Confidence in Estimates 13. in Judgements

Part IV: Statistical and Decision making 14. Interpreting Statistical involving Chance

Page a DEDICATION

to

Florence Nightingale, Ayn Rand

and Julian Simon

MISSION

To help students

read and interpret

statistics

as in arguments

Page b

Page c

Introduction

TO STUDENTS

Statistics are different; Statistics is important. 1 Statistics is not just arithmetic. Arithmetic deals with : 2+2 = 4. Statistics deals with : the chance of two heads in flipping a fair coin twice is 25%. 2 Statistics are not just numbers. Numbers just are: 2+2 = 4. Statistics describe : for US teens age 15-17, the birth rate for Asians is half of the birth rate for American Indians. 3 Statistics is essential to understanding the . Both the social sciences (psychology, , economics and political ) and the physical sciences (, , ) rely on statistics for and . 4 Statistics is a language just like accounting, finance or economics. All four disciplines involve measurements and use common words in technical ways. But, in terms of measurements, statistics is the most gen- eral; statistics is the language of data.

Statistical literacy is different from traditional statistics. · Traditional statistics focuses on role of chance in confidence inter- vals and hypothesis tests. In traditional statistics, there is typically an answer is either right or wrong and it can be proved. · Statistical literacy studies the use of statistics as evidence in argu- ments. Statistical literacy focuses on the role of factors or models as ex- planations or as predictors. In statistical literacy, factors or models are either weaker or stronger in their ability to explain or predict.

Science of Statistical literacy is a science of method – as are & statis- Method tics, and . Sciences of method are fundamental to human thought. They can be classified by their content and by their method of reasoning.

Table 1 ------METHOD OF REASONING ------FORMAL/SYMBOLIC INFORMAL/PRACTICAL CONTENT (Deductive) (Inductive) WORDS Logic Critical Thinking NUMBERS Mathematics; Probability & Statistical Literacy Traditional Statistics

Page i Milo Schield Introduction

Methods of · Logic, mathematics and traditional statistics focus on symbolic - reasoning ing using deductive arguments. If a deductive is valid, the answer is certain to be true given the of the . Although lim- ited in scope, this formal is very valuable. · Critical thinking and statistical literacy focus on practical reasoning us- ing inductive arguments. These inductive arguments are on a spectrum from very weak to very strong. Although practical reasoning lacks formal , it is much broader in scope; practical reasoning is the reasoning we do everyday.

Content is more Most students view the between words and numbers (rows) important than as more important than the distinction between the methods of reason- method ing (columns). The row-distinction is easier to recognize (numbers versus words). The row-distinction explains how these four courses are related to academic departments. Critical thinking and logic are part of , statistics and probability are typically part of Mathematics.

Method is This book argues that method is more important than content; the dis- more funda- tinction between symbolic reasoning and practical reasoning (columns) is mental than more fundamental than the distinction between words and numbers content (rows). This book views statistical literacy as being closer to critical thinking than to mathematics. As human beings, is our primary method of thought. We are not omniscient; we need to choose know- ing our choice may be in error. We need to act knowing out actions may have consequences that were unforeseen and perhaps unforeseeable. Thus, our method of thinking is primary; the content of our thinking is secondary.

Challenge This emphasis on statistical literacy may be challenging for those who · prefer the certainty of mathematics or logic, or · have difficulty with the English language. Both will be challenged to read and interpret statistics as evidence.

This book is different -- radically different! This book is dedicated to help- ing you learn to think more effectively by using statistics as evidence. This is not a course where students memorize, regurgitate and forget mathe- matical statistics and then say, "I just didn't get it." This course focuses on the thinking we do every day. The principles learned in this book can help you think with more clarity and certainty. If you can master these principles, you will have an insight that many people lack. And with this insight you can work more effectively toward achieving wisdom in all areas of your life.

For more on the author, see his web site at www.augsburg.edu/ppages/~schield or contact him at [email protected].

Page ii Milo Schield Introduction

THE BOOK

This book has features not found in any other statistics book to date: · an over-arching focus on statistical literacy · a focus on arguing about causality and the effects of control. · Ch. 3: Reading in tables · Ch. 6 and 9: Reading and interpreting graphs. · Ch. 16: Interpreting confidence and significance for decisions. Since this book has a very non-standard approach, it will be liked by some and disliked by others

This book is divided into two sections: and Inferential Statistics. Inferential statistics focuses entirely on the variability due to chance. Descriptive statistics ignores this topic.

Descriptive statistics - Part 1 deals with fundamentals of practical reasoning (1) and with reading and interpreting the data found in newspapers, essays and books (2, 3, 4 and 5). In each case, the focus is on communication: de- scribing the data so others can understand it.

Descriptive statistics - Part 2 deals with graphs (6) and models (7, 8 and 9). The focus is using the graph or model to explain or predict.

Inferential statistics – Part 3 deals with statistical studies (10), and probability (11), confidence intervals (11) and hypothesis tests (12). This part is the main topic in most statistics texts.

Inferential statistics – Part 4 deals with interpreting confidence intervals and hypothesis tests in terms of decision-making (14).

Other books Other books having a similar focus on practical reasoning include: · Critical thinking: "The Art of Reasoning" by David Kelley "Logical : A New Approach" by Richard Connell · Language: "Twice As Less" by Eleanor Orr · Economics: "Hidden Order" by David Friedman · : "Prove It With Figures" by Hans Zeisel and David Kaye · Journalism: "News and Numbers" by Victor Cohn

Benefit The primary benefit of study this book is to help readers improve their think- ing – their ability to reason about arguments – and thus to make better deci- sions in pursuit of their own happiness and well being.

Page iii Milo Schield Introduction

THE AUTHOR

Author Milo Schield, Associate Professor at Augsburg College, 2211 Riverside Avenue, Minneapolis, MN 55454 since 1985. He can be contacted at [email protected].

Author’s Dr. Schield has a Bachelors degree in physics from Iowa State University, a academic and Masters degree in physics from the University of Illinois, and a Ph.D. in space intellectual physics from Rice University. He has done post-graduate work at the Uni- credentials versity of Iowa in Economics and at the University of Minnesota in Insurance and in Business, Government and Society. He has studied philosophy on an on-going basis.

Author’s Dr. Schield has been a Senior Consultant with a national CPA firm for 2 professional years, a Senior Operations Analyst for a large property-casualty credentials insurance company for 8 years, and a co-founder and President of a small computer business for 5 years. He earned a certificate in Managerial Ac- counting (CMA).

Author’s Dr. Schield has taught for over 15 years. He has taught at the University of teaching Iowa, National College, the University of St. Thomas and Augsburg College. credentials He has taught traditional undergraduates, adult undergraduates and graduate students. He has taught a variety of subjects including accounting, finance, microeconomics, critical thinking, and statistics.

Author’s Doctor Schield has been a visiting scholar at the Royal Statistical Societies’ statistical Centre for Statistical Education at the University of Nottingham in Nottingham credentials England. Dr. Schield has given papers on statistical education and statistical literacy at numerous conferences including ICOTS-5 (Singapore), ICME-6 (Tokyo), ASA, MSMESB, AMATYC and APDU. He has given talks at various colleges in England, Scotland and Wales, China and Australia. He has given talks on reading tables at the US Bureau of the and the US Bureau of Labor Statistics.

Publications See www.augsburg.edu/ppages/schield for a list of publications.

Page iv Milo Schield Introduction

ACKNOWLEDGMENTS

I want to thank my colleagues at St. Thomas and Augsburg for their role in bringing this book into being: Dr. Bernie Folz, Earl Alton, Bruce Reichen- bach, Amin Kader and, most of all, John Cerrito who never ceased saying, "students need to read and interpret data."

I am indebted to the following authors for their role in my intellectual devel- opment through their publications of novels, texts and audio tapes: Ayn Rand, Nathaniel Branden, Dr. , Dr. Richard Connell, Dr. David Kelly and Dr. Harry Biswanger.

I want to thank the following for their role in my intellectual development through their personal involvement: Eileen Schield (my mother), Dr. Ken At- kinson, Dr. Douglas Rasmussen and Dr. Joel Myklebust.

I want to thank the following for their role in my professional development in statistics: the American Statistical Association, the RSS Centre for Statistical Education, Dr. Anne Hawkins, Peter Holmes, Dr. Colin Howson and Donald McNaughton.

I want to thank those who helped me most personally in this project: Bruce Reichenbach, Gerald Kaminski, Tom VV. Burnham, and my wife and 'editor': Linda Schield.

I learned most of my statistics by reading books on statistics. I want to thank the many authors of statistics texts. I am heavily indebted to Mosteller, Smith, Rosenbaum, and Klein but most of all to Freedman, Pisani, Purves, and Adhikari.

I want to thank my many students who gave me feedback – both and bad – about the many drafts of this book. Their feedback enabled me to im- prove this text in ways that will benefit future students.

I invite comments, criticisms and ideas on how to improve this book.

Page v Milo Schield Introduction

TO TEACHERS OF EVIDENTIAL STATISTICS

This book is different because it has a different goal. The goal is not to help students appreciate the truth and power of inferential statistics. The goal is to help students think critically about the support that statistics give to non- statistical conclusions. This book can be used as a supplement -- or as a text -- in a college-level course.

Teaching this material requires different skills. It took me many years to be- come half as good at teaching evidential statistics as I was at teaching tradi- tional descriptive and inferential statistics. But, being able to help students evaluate statistics as evidence is a most worthy and satisfying goal.

I am tired of hearing students say, "Statistics -- the worst course I ever had." I understood that statistics was hard, but to hear students say it wasn't very relevant was most disheartening. Now I understand why my students were right. In teaching traditional statistics, I focused on the glass being half full; my students saw the glass as being half empty.

Not everyone who teaches traditional descriptive and inferential statistics will be good at teaching evidential statistics. Fortunately, our discipline needs both kinds of teachers. Your job is to see how well you can teach this mate- rial and then decide whether that is something you want to do.

Best wishes and a satisfying journey of personal and professional discovery.

I recall one good student saying, "This course wasn't at all what I expected." At the time, I presumed the student thought it was just about descriptive sta- tistics (baseball, sports, or perhaps gambling and lotteries). Now I think the student was saying something more: "This course was just about (the effects due just to chance or non-systematic error) involved in simple generalization. What about the effects of systematic error, of con- founding factors and the use of statistics to identify causality and the conse- quences of a causal intervention? The role of chance seems so artificial, so forced, and so limited in dealing with the sources of variability. Whereas the role of systematic factors in identifying causality seems much more relevant and practical. It seems that have chosen the easy road, the road of mathematical certainty, and are unwilling to take the more difficult road: the road of using statistics as evidence in practical reasoning."

Page vi Milo Schield Introduction

This text was designed to support the of certain principles. Al- though these principles are not complex, learning them requires repetition in different contexts. 1. The primary function of numerical statistics is to support : gen- eralizations, predictions, and explanations. 2. The goal of practical inference is . There are two kinds of pre- diction: prediction based on observational association and prediction based on experimental causation. 3. The primary of statistical inference is . There are two kinds of explanation: explanation based on association (formal) and ex- planation based on causation (material). 4. A most common task in Statistics is generalization: inferring the properties of a population based on the statistics of a . 5. Numerically, statistics are values of properties of entities. What a thing is determines what is can do. 6. There is always an alternate explanation for an inductive inference. 7. Controlling for potentially confounding factors decreases the likelihood of an alternate explanation and thereby increases the likelihood the pro- posed inference is true. 8. Experiments are better able to control for potentially confounding factors than are observational studies. 9. Correlation is typically necessary for causation, but is seldom sufficient. 10. In a cross-sectional study, correlation is typically weak evidence for di- rect causation. In a longitudinal study, correlation is stronger evidence of direct causation. 11. Expected value says nothing about our expected utility. 12. Confidence measures our strength of . Confidence is our reason for action. In some cases, our confidence can be normatively specified. 13. Statistical significance says something about the likelihood of a determi- nate cause, but by itself it says nothing about direct causation.

Order and study the teachers’ manual before you decide to use this text. Without proper training, your use of this text could be a disaster.

Page vii Milo Schield