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-
-
- Statutor
- Version 1.23
- A computer-based teaching tool for statistical concepts
- Copyright 1991
- The Regents of the University of Michigan
- All Rights Reserved
-
- developed by
- Robert A. Wolfe
- Department of Biostatistics
- School of Public Health
- University of Michigan
- Ann Arbor, MI 48109
- 4/18/91
- bobwolfe@umich.edu
-
- 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
- sampling experiments.
-
- 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
- statistical instruction.
-
- 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
- important concepts.
-
- 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.
-
- Specific demonstrations:
-
- 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
- non-linear relationships.
-
- 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 bands.
-
- 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
- prediction bands.
-
- 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
- classroom.
-
- 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.
-
- NOTICE:
-
- 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.
-
- Compatibility:
-
- 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).
-
- Distribution:
-
- Statutor may be freely distributed, so long as it is not changed and this
- document file is distributed with it.
-
- Availability:
-
- Anonymous FTP at oak.oakland.edu in pub/msdos/education/statu123.zip
-
-