STATISTICS Milo Schield Ó Spring Day, 2001 SL2000T1 SL2000T1 TABLE OF CONTENTS DESCRIPTIVE STATISTICS Part I: Fundamentals 1. Causality and Statistics 2. Describing Count-Based Data 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: Probability and Inferential Statistics 10. Obtaining Statistics: Samples, Surveys and Experiments 11. Statistical Expectation, Chance and Error 12. Statistical Confidence in Estimates 13. Statistical Significance in Judgements Part IV: Statistical Inference and Decision making 14. Interpreting Statistical Arguments involving Chance Page a DEDICATION to Florence Nightingale, Ayn Rand and Julian Simon MISSION To help students read and interpret statistics as evidence in arguments Page b Page c Introduction TO STUDENTS Statistics are different; Statistics is important. 1 Statistics is not just arithmetic. Arithmetic deals with certainties: 2+2 = 4. Statistics deals with uncertainties: 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 reality: 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 sciences. Both the social sciences (psychology, sociology, economics and political science) and the physical sciences (physics, chemistry, biology) rely on statistics for explanations and predictions. 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 mathematics & statis- Method tics, logic and critical thinking. 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 reason- reasoning ing using deductive arguments. If a deductive argument is valid, the answer is certain to be true given the truth of the premises. Although lim- ited in scope, this formal certainty 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 validity, it is much broader in scope; practical reasoning is the common sense reasoning we do everyday. Content is more Most students view the distinction 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 Philosophy, 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, inductive reasoning 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 count data 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: Descriptive Statistics 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), sampling 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 Analysis: A New Approach" by Richard Connell · Language: "Twice As Less" by Eleanor Orr · Economics: "Hidden Order" by David Friedman · Law: "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 Research 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.