Using an Applet to Demonstrate the Sampling Distribution of an F-statistic

This page authored by Roger Woodard, Steve Stanislav, Jennifer Gratton, Pam Arroway, NC State University, based on an applet by Stefan Michiels, Bert Raeymaekers, University Center for Statistics, Katholieke Universiteit Leuven.
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This activity has been undergone anonymous peer review.

This activity was anonymously reviewed by educators with appropriate statistics background according to the CAUSE review criteria for its pedagogic collection.


This page first made public: Feb 6, 2008

This material is replicated on a number of sites as part of the SERC Pedagogic Service Project

Summary

This visualization activity combines student data collection with the use of an applet to enhance the understanding of the distributions of mean square treatment (MST), mean square error (MSE) as well as their ratio, an F-distribution. The applet samples from six treatment populations based on user defined parameters and records by means of histogram: mean square treatment, mean square error and their ratio. Students will see theoretical distributions of the mean square treatment, mean square error and their ratio and how they compare to the histograms generated by the simulated data.



Learning Goals

Identify the distributions of the mean square treatment (MST), mean square error (MSE) and their ratio.

Context for Use

This activity is appropriate for all class sizes and is best used as an interactive activity for an intermediate statistics to upper level course or in a course of experimental design (ANOVA). Prior to use, students should have learned about the Analysis of Variance method. However, you may find it useful to use the activity as an introduction to the material. This demonstration can be completed within a 50 minute class period.

Prior to this activity students should have some understanding of the concept of the Analysis of Variance (ANOVA) method. That is, testing the equality of the expected responses for some number of treatments.

Description and Teaching Materials



Teaching Notes and Tips

A little bit of careful planning will make this demonstration go smoothly.

Tips for applet usage are given in the attached document.

Assessment

Students are assessed by a quiz or exam question concerning the distributions of mean square treatment, mean square error and their ratio.

Also some follow up questions (Microsoft Word 22kB Aug14 06) are provided.

References and Resources



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