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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 material was originally developed through CAUSE
as part of its collaboration with the SERC Pedagogic Service.


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.

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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.

Teaching Materials

Teaching Notes and Tips

A little bit of careful planning will make this demonstration go smoothly.
  • Students should bring a calculator to class to aide in summary statistic calculations. Although it may not be necessary, it streamlines the activity process.
  • The instructor will create stations around the classroom that correspond to the following six college major classifications:
    • Biological Sciences
    • Physical Sciences
    • Humanities
    • Engineering
    • Business
    • Education
    At each station, the instructor will provide a means for students to record their age.
    One possible way to create stations for your students in the classroom
  • The instructor will then ask the students to record their ages at the station that best corresponds to their college major. This process works best with students called upon by rows.
  • Once all students have recorded their ages the instructor will break up the class evenly into groups for all the college majors that have students represented in the class.
  • The groups will then work on the worksheet provided. As the students are calculating the summary statistics, the instructor should prepare the Excel spreadsheet provided. (Excel PRIVATE FILE 19kB Aug14 06) This spreadsheet will carry out the Analysis of Variance (ANOVA) test procedure for four, five and all six major classifications.
  • After a discussion about the Analysis of Variance process and some discussion about the distributions of mean square treatment and mean square error, the instructor will use the online demo to simulate the distributions of mean square treatment and mean square error.

Tips for applet usage are given in the attached document.


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 PRIVATE FILE 22kB Aug14 06) are provided.

References and Resources

  • Sampling Distributions of Analysis of Variance (ANOVA) Method Applet


Mathematics:Statistics:Statistical Inference and Techniques, Mathematics:Statistics, Mathematics, Statistics:Statistical Inference and Techniques:Sampling Distributions, Mathematics:Statistics:Data Collection

Resource Type


Grade Level

College Upper (15-16), College Lower (13-14)

Ready for Use

Ready to Use:Meets Peer Review Standard:Anonymous Peer Review