Table of Contents

Foreword, David S. Moore.            Preface, Dani Ben-Zvi and Joan Garfield

Extracts:

Ben Zvi and Garfield (p. 7):  "Although no formal agreement has been made regarding the definition and distinctions of statistical literacy, reasoning and thinking, the following list summarizes our current thoughts:  

• Statistical literacy includes basic and important skills that may be used in understanding statistical information or research results.  These skills include being able to organize data, construct and display tables, and work with different representations of data.  Statistical literacy also includes an understanding of the concepts, vocabulary and symbols and includes an understanding of probability as a measure of uncertainty. 

• Statistical reasoning may be defined as the way people reason with statistical ideas and make sense of statistical information.  This involves making interpretations based on sets of data, representations of data, or statistical summaries of data.  Statistical reasoning may involve connecting one concept to another (e.g., center and spread), or it may combine ideas about data and chance.  Reasoning means understanding and being able to explain statistical processes and being able to fully interpret statistical results.

• Statistical thinking involves an understanding of why and how statistical investigations are conducted and the "big ideas" that underlie statistical investigation.  These ideas include the omnipresent nature of variation and when and how to use appropriate methods of data analysis such as numerical summaries and visual displays of data.  Statistical thinking involves an understanding of the nature of sampling, how we make inferences from samples to populations, and why designed experiments are needed in order to establish causation.  It includes an understanding of how models are used to simulate random phenomena, how data are produced to estimate probabilities, and how, when and why existing inferential tools can be used to aid an investigative process.  Statistical thinking also includes being abele to understand and utilize the context of a problem in forming investigations and drawing conclusions and recognizing and understanding the entire process (from question posing to data collection to choosing analyses to testing assumptions, etc.).  Finally, statistical thinkers are able to critique and evaluate results of a problem solved or a statistical study.

Ben Zvi and Garfield (p. 11):  "Gal proposes ... a conceptualization of statistical literacy and its main components.  Statistical literacy is described as a key ability expected of citizens in information-laden societies, an expected outcome of schooling, and a necessary component of adults' numeracy literacy.  Statistical literacy is portrayed as the ability to interpret, critically evaluate and communicate about statistical information and messages.  Gal suggests that statistically literate behavior is predicated on the joint activation of both a knowledge component (comprised of five cognitive elements: literacy skills, statistical knowledge, mathematical knowledge, context knowledge and critical questions) and a dispositional component (comprised of two elements: critical stance, and beliefs and attitudes)."

Pfannkuch and Wild (p. 27):  "Causal Inference:"  Fisher's "insistence on raising other possible causes for lung cancer -- together with Cornfield, Doll and Hill's careful logical analyses of the data -- markedly increased awareness of the importance of statistical thinking in medicine.  Alternative explanations of rhe association between lung cancer and smoking suggested by Fisher and others were systematically refuted by Cornfield, Doll and Hill until there could be no other plausible interpretation of the data.  The debate  on the association between smoking and lung cancer, which began in 1928, culminated in the 1964 publication of the US Surgeon General's report, a landmark in the setting of standards of evidence of inference of a causal relationship from observational studies."  Thus, in epidemiology, it was recognized that purely statistical methods applied to observational data cannot prove a causal relationship.  Causal significance was therefore based on "expert" judgment utilizing a number of causal criteria such as consistency of association in study after study, strength of association, temporal pattern and coherence of the causal hypothesis with a large body of evidence.   It should be noted that whether the study is experimental or observational, the researcher always has the obligation to seek out and evaluate alternative explanations and possible biases before drawing causal inference."

Gal (p. 40): "This paper develops a conception of statistical literacy that pertains to what is expected of adults (as opposed to students actively learning statistics), particularly those living in industrialized societies.  It is proposed here that in this context, the term statistical literacy refers broadly to two interrelated concepts, primarily (a) people's ability to interpret and critically evaluate statistical information, data-related arguments, or stochastic phenomena, which they may encounter in diverse contexts, and when relevant (b) their ability to discuss or communicate their reactions to such statistical information, such as their understanding of the meaning of the information, their opinions about the implications of this information, or their concerns regarding the acceptability of given conclusions." 

Table of Contents

Section 1: Statistics Teachers in Mathematics Departments

2.  Teaching a Data-Oriented, Activity-Based Course,  Alan Rossman

Section 2: Statistics Teachers in Two-Year or Community Colleges

Section 4:  Teaching Statistics to Students in Other Disciplines

Extracts:

Moreno (p. 24): "Overall, I want my students to leave my course with a conceptual understanding of what statistics does and why it is needed, and how statistics does what it does.  Fundamental ideas that they should appreciate as citizens are: the reason for statistics; the understanding of graphs, the purpose of basic summary statistics, the design of an experiment, observational study, survey, poll; that statistics does not prove anything; uncertainty and the concept of probability (including risk analysis); misleading conclusions implied from newspaper articles headlines; and the question of statistical hypothesis testing."

Moreno (p. 30):  "We are not large enough to afford to offer both a statistical literacy course (that focuses on concepts) and a statistical methods, I have to find a way to blend concepts and methods into one course."  "No matter how the course is presented, it must be meaningful in order for a student to become a  statistically literate citizen,  it must be useful for a student's major; it must be interesting and fun as a classroom experience."

Lock (p. 36): "students to find an article in a journal, magazine, book or newspaper that uses statistical reasoning in some way and write a critique of about how statistical issues are handled in that article.  As part of the write up, I ask students to include a couple of statistically-related questions that they would want to ask the author(s) of the article." 

Peterson (p. 40-41): "Chance is a course about how to read a newspaper.  More specifically, it aims to make students more informed consumers of news stories that involve statistical reasoning.  The course therefore focuses on reading and responding to real-world applications of probability and statistics as they are reported in the news media."  "The Chance course is designed to help students read, interpret, and critically evaluate statistical information from these sources."  "All versions of the Chance course share similar goals.  First, we hope that students will develop an appreciation for the importance of random phenomena in the world around them, and learn to use statistical reasoning in everyday life.  Second, we want our graduates to be critical readers of news stories that involve probability and able with expressing statistical insights in oral and written English."   "I have found that several broad themes always seem to run through my courses.  The first is that numbers never "speak for themselves."  "A second major theme is to understand the implication of variation and being able to reason in the face of uncertainty."  "Third is the repeated warning that correlation is not causation."  "Statistics provides a wonderful framework for understanding why causality is so hard to establish.  The pitfalls of lurking variables and the virtues of good experimental design are important lessons for all students to internalize."  "A fourth theme involves learning how to read a graph, and how to recognize graphical abuses in the popular press."  "My last theme .... is that chance is lumpy." 

Peterson (p. 46): "Recent years have seen increasing calls for required courses in quantitative literacy."  "On the whole, I agree with those writers who have argued that quantitative literacy is not identical with statistical literacy.  Nevertheless, as Cobb's (1997) essay shows, statisticians have an enormously important role to play at these discussions.  The practice of statistics is, by its very nature, interdisciplinary, and the lessons we have learned as statisticians can provide important models for quantitative literacy."

delMas (p. 53): "The overarching goal of the course is to have students develop problem solving and decision making skills through the collection, analysis, and interpretation of data.  Students are expected to learn how to analyze and interpret quantitative information, to use statistical thinking, to develop statistical reasoning, and to communicate using the language of statistics.  Students are also expected to develop a level of statistical literacy that enables them to critically assess information encountered in the media and other sources." 

Extracts:

Cobb (p. 3): "We offer two recommendations:  A. More Data and Concepts,  B. Emphasize Statistical Thinking.  An introductory course should take as its main goal helping students to learn the basic elements of statistical thinking.  Many advanced courses would be improved by a more explicit emphasis on those same basic elements, namely: 1) The need for data, 2) The importance of data production, 3) The omnipresence of variability, 4) The quantification and explanation of variability, 5) Effective learning requires feedback. "

Cobb (p. 4): "How Students Learn: What Research Tells Us.  Shorn of all subtlety and led out of the protective fold of the education research literature, there comes a sheepish little fact:  lectures don't work nearly as well as many of us would like to think.  This rather discouraging assertion follows from two clusters or research results  -- the first shows what makes learning hard and lecturing often ineffective, the second shows what does seem to work when lecturing doesn't.   1) Basic concepts are hard and misconceptions persistent.  2) Learning is constructive.  3) Foster active learning. As a rule, teachers of statistics should rely much less on lecturing, much more on the following alternatives:  i. Projects either group or individual.  ii. Lab exercises.  iii. Group problem solving and discussion.  iv. Written and oral presentations.  v. Demonstrations based on class-generated data. 

Table of Contents

 Introduction: Thomas L. Moore (Grinnell)

A Time-Subject Index for Against All Odds: Inside Statistics, by Edward R. Mansfield.

WWW Resources for Teaching Statistics

Section 6: Assessment

Beyond Testing and Grading: New Ways to Use Assessment to Improve Student Learning, Joan B. Garfield

Experiences with Authentic Assessment Techniques in an Introductory Statistics Course, Beth L. Chance

Bibliography on Assessment

Author Contact Information

Extracts:

Moore (p. 3): "Statistics is the science of gaining information from data.  Data are of course numbers, but they are more than that.  Data are numbers with context."  "The questions [involving statistics in the daily news] are strikingly different from the issues we most often address in teaching statistics.  A mathematics student who takes a typical course on probability and statistics is ill-prepared to answer such questions.  Students in traditional statistical methods courses are only a bit better off.  A wide gap separates statistical teaching from statistical practice."

Shafer (p. 93): This paper "reviews Kolmogorov's axiomatization and the three standard interpretations of this axiomatization: the belief interpretation, the frequency interpretation, and the support interpretation.  Each interpretation, as we shall see, has its appeal and its difficulties."  "Probability is a complex idea, one that draws together ideas about fair price, rational belief and knowledge of the long run."

Table of Contents

 Preface: David . Hoaglin and David S. Moore

Chapter 6: What is Probability?  (Glen Shafer).  6.1 Introduction.   6.2 Three Interpretations of Kolmogorov's Axioms.   6.3  Three Interpretations in Practice.  6.4  Three Aspects of Probability.  6.5  Lessons for Teaching. 

Chapter 7: The Reasoning of Statistical inference (Lincoln E. Moses).  7.1 Introduction.  7.2 Some Examples.   7.3 Some Types of Statistical Inference.  7.4 Which Model? Which Analysis?  7.5 Theoretical Statistics.  7.6 Remarks about Teaching Statistical inference.

Chapter 8: Diagnostics (David C. Hoaglin). 8.1 Diagnosis.  8.2 Leverage and Influence in Simple Regression.   8.3 Leverage and Influence in Multiple Regression.  8.4 Departures from Assumptions.   8.5 Robust/Resistant Alternatives.  8.6 Cooperative Diversity.  8.7 Conclusion.

Chapter 9. Resistant and Robust Procedures (Thomas P. Hettmansperger and Simon J. Sheather).  9.1 Introduction.  9.2 Basic Likelihood Theory for the Location-Scale Model.  9.3 Basic Likelihood Theory.  9.4 Robust and Resistant Methods.  9.5 Resistance Properties of Estimates.  9.6 The Simple Regression Model.  9.7 Diagnostics.  9.8 Bounded-Influence Regression Estimates.  9.9 Extensions and Further Developments.

Index.