Degrees+of+Freedom

Degrees of Freedom (GWU EMSE-271)
Index | Topics (Logical Lectures) | Lectures | Problems | Readings | Nomenclature | Concepts

[ Degrees of Freedom of Error | Degrees of Freedom Check Sheet | ANOVA Table Formats ]

"In statistics, the number of **degrees of freedom** is the number of values in the final calculation of a statistic that are free to vary." - [|Wikipedia]

**Degrees of Freedom, as applied, mean slightly different things depending on where it is used**. - PSisson "In general, each item being estimated costs one degree of freedom. The remaining degrees of freedom are used to estimate variability. All we have to do is count properly." - Gerard E. Dallal, Ph.D.

"Estimates of statistical parameters can be based upon different amounts of information or data. The number of independent pieces of information that go into the estimate of a parameter is called the degrees of freedom (df). In general, the degrees of freedom of an estimate is equal to the number of independent scores that go into the estimate minus the number of parameters estimated as intermediate steps in the estimation of the parameter itself." - [|Wikipedia]

"The degrees-of-freedom are also commonly associated with the squared lengths (or “Sum of Squares”) of such vectors, and the parameters of chi-squared and other distributions that arise in associated statistical testing problems." - [|Wikipedia]

"One of the questions an instrutor dreads most from a mathematically unsophisticated audience is, "What exactly is degrees of freedom?" It's not that there's no answer. The mathematical answer is a single phrase, "The rank of a quadratic form." The problem is translating that to an audience whose knowledge of mathematics does not extend beyond high school mathematics. It is one thing to say that degrees of freedom is an index and to describe how to calculate it for certain situations, but none of these pieces of information tells what degrees of freedom means.

... "At the moment, I'm inclined to define **degrees of freedom as a way of keeping score."** - Gerard E. Dallal, Ph.D. [** Worth Reading Once **]
 * Degrees of Freedom Values
 * x - TBD
 * y - TBD
 * Degrees of Freedom for Error
 * One-Way ANOVA Degrees of Freedom (ANOVA Table Formats)

"While introductory texts may introduce degrees of freedom as distribution parameters or through hypothesis testing, it is the underlying geometry that defines degrees of freedom, and is critical to a proper understanding of the concept. Walker (1940) has stated this succinctly:"

"'For the person who is unfamiliar with //N//-dimensional geometry or who knows the contributions to modern sampling theory only from secondhand sources such as textbooks, this concept often seems almost mystical, with no practical meaning.'" - [|Wikipedia]


 * Sources:**
 * Degrees of freedom (statistics). (2009, December 19). In //Wikipedia, The Free Encyclopedia//. Retrieved 14:41, January 5, 2010, from []
 * Degrees of Freedom. (2008), from The Little Handbook of Statistical Practice, Gerard E.Dallal. [|**http://www.StatisticalPractice.com**], Retriefed 10:30 January 5, 2009, from [] [Note: Work in progress check for updates.]
 * EMSE 271, Fall 2009