Data Desk Templates: Teaching/Illustration Templates

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Teaching/Illustration Templates

Confidence Intervals

Creator: Chris Noble

Posting date: 04/05/96

This template demonstrates the random nature of confidence intervals. It generates random samples from a variable and plots confidence intervals for the variable mean generated by those samples.

Comments:

Fri Jul 12 12:36:35 EDT 1996
Name: Bruce Torrence
E-mail: btorrenc@rmc.edu

Comments: Interesting idea, and fun once you get the hang of it. There is one bug: The "Start over" button needs to be pushed twice.

The sampling is done without replacement from a user-provided variable. Unless the number of cases in this variable is very large, the liklihood of a confidence interval containing the true mean will be significantly greater than the specified level of confidence. This undermines the purpose of the lab; The proportion of "Hits" should converge to the level of confidence. With samples of size 20 (on average), at least 1000 cases are needed in the variable from which the sampling occurs. As long as this is kept in mind, the concept is sound. In any event, it is highly realistic; this is exactly how samples are taken in the real world. Just don't let students drag any old variable in for sampling.

Lastly, the graphics are great. It may seem a bit akward at first, but there is no better way to get such a display that I can fathom with the tools at hand. I only wish there were a horizontal line indicating the true mean.

Fractal Generator

Creator: Chris Noble

Posting date: 04/05/96

This template generates pictures of certain kinds of fractal sets. Technically, it runs iterated affine function systems. Pictures include the Sierpinski gasket, ferns, and trees. Includes a file with some sample parameter settings. Note: Users with monitors smaller than 800x600 may have difficulties using this template.

Mandlebrot

Creator: Linde-Zwirble

Posting date: 04/05/96

A fun and interesting build of the famous Mandelbrot Set fractal.

Regression CI Visualization

Creator: Matthew C. Hutcheson

Posting date: 12/18/95

This template demonstrates regression confidence intervals. One somewhat difficult topic in teaching regression is explaining to students why confidence intervals for regression lines are hyperbolic in shape. This template allows one to visualize the process.

The user has control over the sample size, the number of samples, the amount of error variance and heteroskedasticity (non-constant variance). Adjusting the error heteroskedasticity reveals hyperbolic shapes with narrow cones on one end and fat cones on the other end. Increase the sample size to get tighter intervals.

Comments:

Fri Jul 12 12:48:17 EDT 1996
Name: Bruce Torrence
E-mail: btorrenc@rmc.edu

Comments: Very cool. I can't imagine a better way to illustrate this idea. Template keeps it simple, and works like a charm.

Sampling Distribution

Creator: Chris Noble

Posting date: 04/05/96

This template demonstrates the empirical sampling distribution of a sample mean. This can be used to demonstrate the Central Limit Theorem without the restriction of sampling from a uniform population. This template also demonstrates the empirical sampling distribution of the difference between means. It can be used to test the hypothesis of equality of means through resampling rather than parametric methods.

Simple Regression Intervals

Creator: John H. Walker

Posting date: 8/21/00

This template draws prediction and confidence interval bands for a simple regression of Y vs. X on a scatterplot of the data. It also calculates the exact endpoints of these intervals for a user-defined X-value. The user has control over the confidence level, the X-value for the calculated interval, and the color of the lines on the interval plot.

Simulation Sample

Creator: Paul Pratt

Posting date: 12/18/95

This program illustrates the Central Limit Theorem. A random uniform variable with a given number of cases is generated. Its mean is computed and appended to the end of a variable which is plotted in a histogram and probability plot.

Comments:

Fri Jan 12 12:58:47 EST 1996
Name: Geoff Selig
E-mail: gls@alcor.concordia.ca

Comments: The Simulation Sample Template is (erroneously) based on a NORMAL distribution rather than a UNIFORM distribution.

I am looking into modifying the template to a) allow skewed base distributions, and b) to simultaneously show the under- lying distribution of scores as they are generated.

Tweak B0 and B1

Creator: Matthew C. Hutcheson

Posting date: 12/18/95

This template draws a scatterplot and the user has control over the best-fitting line. If the user changes the intercept and slope, then the line automatically moves and summary statistics are automatically computed and updated. This gives insight into minimizing SSE and R2. The user also controls the error structure to see its effect on the regression and the scatterplot.

Finally, the user can hit a button to automatically minimize the best-fitting line using least squares (sum of squares) or sum of absolute error.

Comments:

Fri Jul 12 11:26:28 EDT 1996
Name: Bruce Torrence
E-mail: btorrenc@rmc.edu

Comments: Excellent tool. As informative as it is fun. I only wish there were variable sockets so that I could approach the topic in class with a concrete example, then employ the template.

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Templates that perform specialized computations.

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Templates that perform whole analyses, usually involving both statistics and plots.

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Templates and simulations whose primary purpose is educational in nature.

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