Winston H. Cherry:   statistics teaching materials

Contents of this page:   Introduction
    Probability Distribution Tables
    Distinctions and Notation
    Statistics Courses
    Newspaper Articles of Statistical Interest
    Statistical Highlights

Introduction

      This web site is a work in progress;   first postings date from early 2012 (although most of these have been replaced by later versions) and substantial completion may take up to 20 years.   One of its goals is to make readily accessible a set of ideas that can benefit society by helping to promote statistical literacy;   another goal is to reduce the need for teachers of introductory statistics to devote resources to preparing teaching materials that are already available and accessible.

      These Course Materials were originally prepared for four introductory courses, and one follow-on course, offered in the Department of Statistics and Actuarial Science at the University of Waterloo, Ontario, Canada.   The Materials refer to the course curricula for the period 1990 to 2004, but they remain useful because they cover topics relevant to all introductory statistics teaching.   The courses were:

Statistics 220 and Statistics 221 (Introduction to Statistical Methods 1 and 2), which were required courses for the 3-year Bachelor of Mathematics degree.

Statistics 230 (Probability) and Statistics 231 (Statistics), required for the 4-year Bachelor of Mathematics.

Statistics 332, a required third-year course for the 4-year Mathematics degree in Honours Statistics;   originally a course on survey sampling, it later became half survey sampling and half experimental design.

      Materials are subdivided into numbered `Figures', to provide easier access to discussion of individual topics;   Figure titles are listed in the Table of Contents on the overleaf side of the relevant Title Page.   Blocks of the same (or similar) material in different Figures and, particularly, in the later Statistical Highlights, make the set of ideas more self-contained within a Figure or Highlight.   The set of 106 Statistical Highlights can be thought of as `Statistics 101' but with the caveat that the Highlights are grouped in fifteen broad topics and arranged alphabatically so that, for instance, the introductory What is Statistics About? is Highlight #87.

      Experience indicates that introductory statistics cannot be presented in a strictly sequential manner;   in this, statistics differs from (deductive) mathematics, which can proceed from (simple) axioms to progressively more complex `theorems'.   By contrast, statistical investigative processes (for instance, sampling, measuring, modelling, estimating and comparing) involve such long sequences of ideas that it is seldom feasible to develop them systematically before the mention of these ideas in other contexts becomes unavoidable.   Particularly for expository Materials, most obviously among the alphabetized Statistical Highlights, it may be necessary to read earlier sections or later Appendices for definitions or explanations of terms used in the title matter of a Highlight (or Figure);   this may reflect, in part, the inductive component of investigative processes in statistics.

      The nature of the subject matter in these Materials requires serious intellectual engagement from the user;   clarity of presentation can go only so far in reducing the mental effort involved.   Users may find the Materials easier to study from printed pages than from a computer screen;   their format is set for two-sided printing.   Many files are given in both pdf and ps format so that loss of image quality in fine detail (like closely-spaced parallel lines) in pdf files can (hopefully) be avoided by using the postcript versions.   A minimum screen size of 20+ inches is recommended for viewing the Materials.

      The files for these Materials originate as postscript output from Groff;   a small proportion involve more than one concatenated postscript file -- for example, to generate output with a mixture of portrait and landscape orientations or to combine text and a jpeg graphic.   As of late 2014, such files may not be correctly displayed by the viewer in some browsers.   For these files, additional pdf and ps files are provided for the components, which are then viewed (or printed) individually.   For instance, for the normal (and other) distribution tables which follow immediately below, the .pdf1 and .ps1 files give the first side, the .pdf2 and .ps2 files give the second side, etc.;   the correct orientations for successive sides of these tables (in printed copies) are indicated in their titles as portrait (P) or landscape (L). [Alternatively, the multi- or single-sided .ps files can be downloaded and printed on a postscript printer.]   For files dating from 2012 and 2013, which were (unfortunately) posted in only pdf format, it is an on-going task to add their postscript versions.

      These Materials contain numerous statistical ideas from the public domain;   they also contain insights the writer has obtained over several decades from discussions with many colleagues, most notably the innovative framework for introductory statistics teaching, based on the FDEAC cycle, proposed around 1990 by Professors R.J. Mackay and R.W. Oldford.

      Articles (for example, from newspapers) illustrative of statistical ideas involve the work of many authors;   this provides a broader perspective than one author is likely to achieve.   However, the non-statistical content or context of such articles often involves matters only incidental to statistical issues that are the primary concern of these Materials.   Achieving the broader perspective may occasionally involve including in these Materials an article which presents a divergent (or even `wrong') view of some statistical issue.

Probability Distribution Tables [39 sides]

Termoniolgy, Notation and Distinctions [8 sides]

Understanding of statistical methods is enhanced by consistently maintaining distinctions between:

- the population and the sample,

- the real world and the model, (and related to this distinction)

- the individual case and behaviour under repetition.

Terminology and notation used throughout these Materials to maintain these distinctions is:

- upper-case bold letters to represent population quantities,

- lower-case roman letters to represent data values (and specified values like a sample size),

- upper-case italic letters to represent random variables (mainly in probability and statistical models),

- lower-case italic letters to represent values of random variables,

- Greek letters for model parameters.

One of the statistician's tasks in data-based investigating is to try to ensure that data values (in the second notation category) can reasonably be treated as though they are values of random variables (the fourth category).  This can usually be accomplished by developing and executing a Plan for the investigation that adequately manages all relevant categories of error.

Statistics Courses

As of late 2025, only the Statistics 231 Materials and the Statistical Highlights are substantially complete;   the aim of on-going work is to achieve this state of affairs for Statistics 220, Statistics 221 and Statistics 332 (1995 Curriculum), as well as the newspaper articles of statistical interest (see immediately below) as time allows.

Newspaper Articles of Statistical Interest (grouped by year of publication)

Statistical Highlights (listed alphabetically)