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

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