A Program for Teaching
Statistical Concepts

Contents

Introduction
Exercises Using Models'n'Data
Some Simple Examples
Statistical Models
Graphical Displays of Data
Fitting Models to Data
Analysis of Data
Hardware and System Software Required
Obtaining a Copy
About the Author!

Introduction

Models`n`Data was been designed to help teach statistics. It is a flexible platform on which a wide variety of exercises and demonstrations can be performed, both at introductory level and in more specialised courses. Not only does it display and analyse real data sets, but it can also create, manipulate and display a wide variety of statistical models.

With Models`n`Data you can ...

• Demonstrate most statistical concepts in introductory courses and many from more advanced courses. By repeatedly generating data from models, then examining these repeated random samples, you can build up sampling distributions of many types of summary.
   
• Graphically fit models to data sets.
   
• Graphically display data in a wide range of ways; you can interact with most data displays. The display and analysis features cover everything required in introductory statistics courses and exceed the features in many 'major' statistics programs.

Exercises Using Models'n'Data

Two sets of exercises have been written to help teach statistical concepts using Models'n'Data.

Statistical Exercises Using Models'n'Data

by W. Douglas Stirling, published by John Wiley (1995), Brisbane

This is a 300-page spiral-bound set of exercises that teaches all the statistical concepts that are usually included in an introductory statistics course at university level. A copy of the program is included with the book.

Models'n'Data Exercises for New Zealand High Schools

edited by W. Douglas Stirling, published by the New Zealand Statistical Association (1996), Wellington

This 200-page publication contains 4 sets of exercises covering

• Investigating Data Displays
• Investigating Statistics and Probability
• Investigating Probability Distributions
• Investigating Sampling Distributions and Confidence Intervals

The exercises are aimed at the New Zealand high school Statistics syllabus and introduce basic statistical concepts more gently than the university exercises.

At present, the high school exercises are only available within New Zealand, where they may be freely used by teachers and students.

Some Simple Examples

Confidence intervals

A simple example the program's use for teaching the properties of confidence intervals.
 

Central Limit Theorem

An example demonstrating the Central Limit Theorem.
 

Least Squares Extrapolation

A third example demonstrates the risks when extrapolating with least squares lines.

Statistical Models

Models`n`Data can create and manipulate a wide range of statistical models, ranging from simple univariate distributions and simple random samples from finite populations to

• mixture models,
• regression models with 1 or 2 explanatories,
• 2-way Anova models,
• ARMA(1,1) models,
• Birth-death processes,
• Markov Chain models, and
• Queuing models.

All such models can be displayed graphically. Click here for examples of models and their display.

Graphical Displays of Data

Real data sets (and data generated from models) can be displayed graphically in a variety of ways. These include all the standard displays from introductory statistics courses, plus a few less common ones.

Most of the displays can be interactively modified with tools and controls. Click here for examples of data displays and their manipulation.

Fitting Models to Data

Models`n`Data allows students to fit various standard models to real data sets by graphically matching a display of the model with the corresponding data display. This helps explain the meaning of the model parameters and the range of 'shapes' that the model can take.

Click here for examples of fitting models to data.

Analysis of Data

Models`n`Data can evaluate a wide range of summaries from data. The available summaries depend on the structure of the data set.

• Statistics
• Lines and planes
• Confidence intervals
• Hypothesis tests
• Tabular summaries

All types of summaries can be evaluated either from real data sets or data that has been generated from a statistical model. In the latter case, the sampling distribution of the summary can be built up in a simulation.

Click here for examples of evaluating summaries from data.

Hardware and System Software Required

Models`n`Data only runs on old Apple Macintosh computers -- even on the original Mac Plus! Versions do not exist for Windows or Unix operating systems. The program has not been updated for many years and does not run under MacOS X or later.

Click here for more information about the minimum system requirements to run Models`n`Data.

Obtaining a Copy

Version 2.3 of Models'n'Data is provided with each of the sets of exercises described above. They each provide well-explained introductions to the program and its features, and it is recommended that you use at least the first chapter or two to become familiar with the features of Models'n'Data.

About the author!

The program Models'n'Data was written by Doug Stirling, a Senior Lecturer in the Department of Statistics at Massey University in New Zealand.

Comments and Mail

Copyright © 1997 Doug Stirling