Degrees of freedom (DOF) is a concept that has different meanings depending on the context. In statistics, degrees of freedom represent the number of independent values that can vary in an analysis without breaking any constraints
. In mechanics, degrees of freedom refer to the number of independent variables that define the possible positions or motions of a mechanical system in space
. In statistics, the number of degrees of freedom is the number of independent pieces of information that go into the estimate of a parameter, minus the number of parameters used as intermediate steps in the estimation of the parameter itself
. For example, if the variance is to be estimated from a random sample of independent scores, the degrees of freedom is equal to the number of independent scores (N) minus the number of parameters estimated as intermediate steps (one, namely, the sample mean)
. In mechanics, degrees of freedom (DOF) measurements assume that the mechanism is both rigid and unconstrained, whether it operates in two- dimensional or three-dimensional space
. The number of degrees of freedom is equal to the total number of independent displacements or aspects of motion
. Degrees of freedom apply to two types of motion: translational and rotational
. In summary, degrees of freedom can be understood as:
- In statistics: The number of independent values that can vary in an analysis without breaking any constraints
- In mechanics: The number of independent variables that define the possible positions or motions of a mechanical system in space
