A computer-based teaching tool for statistical concepts
The Regents of the University of Michigan
All Rights Reserved
Robert A. Wolfe
Department of Biostatistics
School of Public Health
University of Michigan
Ann Arbor, MI 48109
Objectives of the program:
Statutor is designed to simplify the learning and teaching of statistical
concepts, especially those related to sampling distributions based on
sampling from a population. The program integrates the display of explanatory
text with graphic displays to show the essential components of several
Specific topics that are included in the demonstrations include:
1. Sampling variability of the sample mean
2. Central Limit Theorem
3. Confidence intervals for the mean
4. Correlation coefficients
5. Explained sum of squares and residual variation in regression
6. Variability of the sample regression line
7. Confidence and prediction bands for the regression line
With an understanding of these sampling experiments, the student will be
better prepared to move on to the details of statistical computation and
inference that comprise the bulk of the curriculum in many statistics courses.
These demonstrations are not designed to replace the content of a traditional
statistics course and some of the concepts presented in these demonstrations
may be difficult for a student who is not concurrently studying statistics.
Statutor is designed to complement a more complete presentation of
Traditionally, there have been two common approaches used in statistics
courses to show the concepts of sampling variability. One approach is to have
the students carry out a physical experiment, such as coin tossing, and to
examine the results from several such experiments. Another approach with more
sophisticated students is to have the student use a computer language or
statistical package to generate samples and summarize the results from a
series of samples. Both of these methods are relatively demanding of student
and teacher time.
Statutor can let the student actively carry out directed
sampling experiments without requiring the time or sophistication needed for
more traditional methods.
Overview of the program:
Statutor is menu driven. The main menu allows choices of demonstrations
related to the sample mean, confidence intervals for the mean, linear
correlation measures, linear regression statistics, confidence bands for
regression, prediction bands for regression.
Each of the demonstrations has options to control sample sizes and
population distributions and other characteristics of the sampling
experiment. The program will use default values for these choices if
the user just presses the enter key whenever such a choice is to be
made. Univariate populations include the logistic, binomial,
uniform, exponential, and Gaussian. Sample sizes can range up to 500.
Each of the demonstrations includes a sampling experiment which shows
statistical results after each sample is drawn. By default, the program
pauses and waits (for up to 2 minutes) for the ``enter'' key or the ``space
bar'' to be pressed before the next sample is selected. Optionally, a
demonstration can be speeded up so that samples are drawn with only a short
pause between them. The user can toggle between these two display modes by
pressing the ``P'' key on the keyboard.
Several of the sampling experiments move slowly and show extra detail
while the first several samples are being selected and then speed up
for subsequent samples. This assures that the student understands the
steps involved in the experiment while preventing boredom from
slow-moving displays at the end of the experiment. Each
demonstration stops automatically after 500 samples have been
drawn, or when the user directs the program to stop sampling by pressing the
``Q'' (Quit) key on the keyboard.
Although the specific details of each demonstration are organized
to best meet the learning objectives of that demonstration, all
of the demonstrations follow the same general format. Each
demonstration starts with a written introduction that introduces
important concepts. Next, the sampling experiment is carried out
with graphical displays. Finally, there is a review of the
The demonstrations allow some deviations from the linear format
discussed above. For example, the introductory material can be
skipped by teachers and students who do not need to review it so
that the sampling experiment can be begun immediately. It is
also possible to move back to prior steps in each demonstration.
The first choice on the main menu leads to a secondary menu of
details about Statutor. The options available on this secondary menu are
discussed in another section later in this documentation. Among other
choices, this secondary menu includes options to change the color and
resolution of the display if the computer hardware can support it. The
secondary menu also includes a short tutorial on use of the keyboard.
The first demonstration shows the sampling distribution of the
sample mean. First, the concept of a population is introduced.
Next, successive samples are selected from the population and
each sample histogram is shown on the same screen as the
population distribution. After the third sample has been drawn,
another histogram is added to the screen showing, cumulatively,
the histogram of the sample means from all of the samples
selected during the experiment. The scaling of the third
histogram can be based on either the original scale of the data
or on a scale related to the standard error of the mean. After
the sampling experiment is finished, the implications of the
central limit theorem are mentioned.
Confidence intervals for a population mean are presented in the second
demonstration. The proper interpretation of the confidence probability is
shown through repeated sampling.
Several measures related to linear correlation are presented in
the third demonstration, which shows a variety of linear and
non-linear scatterplots. The concepts presented include the
correlation coefficient (r), r-squared, residual variance, and
The regression demonstration focuses on inferences for the slope
parameter. The sampling distribution of the t-statistic for the
slope parameter is presented during the sampling experiment. The
utility of the t-distribution for hypothesis testing is discussed
after the sampling experiment.
The confidence band demonstration reinforces the meaning of a
parameter, an estimator, and a confidence interval. The
demonstration makes it clear that the population regression line
is a population characteristic about which inference is made.
For many students, the concept of a parameter becomes more
meaningful when the ``parameter'' is represented graphically as a whole line
instead of as a numerical value. The graphic image of a confidence band
capturing the population regression line clarifies the purpose of a confidence
interval for the student.
The prediction band demonstration emphasizes that statistical
tools can also be used to make probabilistic statements about
the subjects in a population. The meaning of the probability
associated with a prediction band is shown by graphically
demonstrating the fraction of the population values captured by
The regression review demonstration encompasses the ideas
presented in the basic regression demonstration, the confidence
band demonstration, and the prediction band demonstration. This
demonstration allows simultaneous displays of both confidence and
Options for hardware control:
The first main menu choice, called ``Look Here First'', leads to a secondary
menu of items that are related to the overall operation of the program. This
secondary menu offers a short tutorial on use of the keyboard, choice of the
colors and resolution of the display screen, and some other technical details
and information about hardware and licensing.
The short introduction to the use of the keyboard clarifies how
to use the keyboard to control the sampling experiments. The keyboard
tutorial also shows some of the options that are available in the
demonstrations. Many users of the program skip this tutorial, but it is
better to review it. This tutorial takes only a few minutes to review.
Statutor allows use of color displays. Color highlighting is used to
emphasize important words or concepts, so it is useful to have the
colors displayed on the screen. Colors may also be useful if you have
a monochrome screen that can display shades of gray.
With certain graphics boards it is possible to switch between high and
low resolution displays. The low resolution displays use a larger
font for the text, which may be useful for projecting images in a
The program uses symbols that are built in to the computer for certain
special symbols such as the square root and summation notation. On
most computers the program can detect if these symbols are available
and can emulate them if they are not.
The author makes no claims as to the fitness or correctness of this software
for any use whatsoever, and it is provided ``as is''. Any use of this
software is at the user's own risk. Accordingly, the author assumes no
responsibility for the use of this software by the recipient. In no event
shall the Regents of the University of Michigan be liable for any special,
indirect, or consequential damages or any damages whatsoever arising out of or
in connection with the use or performance of this software. The Regents of
the University of Michigan disclaim all warranties with regard to this
software, including all implied warranties of merchantibility and fitness.
Further, the author assumes no obligation to furnish any assistance of any
kind whatsoever, or to furnish any additional information or documentation.
The software is designed to run on an IBM PC or compatible with 320K RAM
minimum, DOS 2.0, and a graphics display adapter (CGA, Hercules, EGA, or VGA).
Statutor may be freely distributed, so long as it is not changed and this
document file is distributed with it.
Anonymous FTP at oak.oakland.edu in pub/msdos/education/statu123.zip