A number one less than the number of frequencies being tested with a chi-square test.

A term for potential or kinetic energy which appears as the square of some coordinate or velocity. Thus there are three degrees of translational freedom for a molecule, corresponding to the three direction , y and in which it may travel. (The kinetic energy term in each of these directions contains a v2 term.)

(statistics) an unrestricted variable in a frequency distribution

one of the minimum number of parameters needed to describe the state of a physical system

an independent motion (rotation or translation) of a mechanism

displacement quantity which defines the shape and location of an object. In the two dimensional plane, a rigid object has three degrees of freedom: two translations and one rotation. In three dimensional space, a rigid object has six degrees of freedom (three translations and three rotations).

(DF) A mathematical concept that indicates the number of observations or values in a distribution that are independent of each other or are free to vary. They are used with various measures such as t-tests to refine the results of treatments of probability or chance in determining statistical significance. For example, if you have a distribution of three numbers that could vary but the sum of those numbers has to equal 100, then although you could select three numbers, in reality you only have to select two because the third number is determined by the first two numbers selected. In this case, there are two independent values, or two degrees of freedom.

the number of independent pieces of information contained in a statistic. If observations are independent, it is computed as the number of observations minus the number of estimated parameters. [6

A parameter in some commonly used probability distributions; e.g., the t distribution and the chi-square distribution.

A degree of freedom accounts for an independent variable in a system. Independent variables allow for changes within a system. For instance, the movement of two atoms in a gas is independent of each other assigning the distance between two atoms one degree of freedom. Two atoms covalently linked together within a molecule (a chemical bond) are also described by the same degree of freedom, also their movements are usually coupled. While this is true for the movement of the entire molecule, the length of the chemical bond is not static, but vibrates at very short time ranges measured in femto seconds to pico seconds (one trillionth to one billionth of a second). How many degrees of freedom a system has depends on the number of components and their interactions.