Illustrating Degrees of Freedom in Multimedia

Chong Ho Yu, Ph.D., Wenjuo Lo, and Shawn Stockford

Please open the following link to view the multimedia tutorial module.
Degrees of Freedom

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Chong Ho Yu, Ph.D.


  • Please use the latest Flash Player to view the module. The module cannot be properly displayed with older versions of Flash.
  • In addition, audio clips are inserted in this module and thus a sound card is required in the client computer.
  • Last, it is recommended that the optimal resolution for playing this module is 1024*768. If you experience difficulties in viewing the program such as some sentences are obscured, please set your display to the recommended resolution.


"Degree of freedom" (df) is an "intimate stranger" to statistics students. Every quantitative-based research paper requires reporting of degrees of freedom associated with the test results such as "F(df1, df2)," yet very few people understand why it is essential to do so. Although the concept "degree of freedom" is taught in introductory statistics classes, many students learn the literal definition of this term rather than its deeper meaning. Failure to understand "degrees of freedom" has a side effect: Students and inexperienced researchers mis-interpret a "perfect-fitted" model or an "over-fitted" model as a good model. To rectify this situation, two approaches of illustrating df in terms of sample size and dimensionality are recommended. To enhance the pedagogy of this concept, a multimedia program written in Macromedia Flash (Macromedia, 2001) was developed. In the program, different aspects of the above concepts are visualized and interactive features (questions and answers) are added to encourage the learners to think about the deeper meanings of df.


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