The concept of degree of freedom is originated from classical mechanics to know the position of a point, or, precisely, the minimum number of observations in their respective dimension to know the positional vector. The statisticians harness this concept to test the significance level of the test statistic. Look at any theoretical distribution, they all are having certain degree of freedom and with increasing degree of freedom the shape of the theoretical curve flattens. We all use this statistical norm, however, I want to know the mathematical logic behind using this norm. kindly help.
Dear dr. Prasenjit Acharya,
the concept of degree of freedom was introduced in classical mechanics by Lagrange, who developed analytical mechanics. Apparently, he preferred to develop the equations of dynamics by leaning on algebra rather than on geometry (as Newton did). In fact, the degrees of freedom are independent on spatial dimensions.
Contrarily to classical mechanics, statistical mechanics uses probability theory, which is a mathematical theory independent on mechanics. This is possibly less evident when reading Boltzmann, and is more clearly expressed by Gibbs.
Apparently statistical mechanics was started by Laplace, as he was pondering on the problem of attributing initial conditions (positions and velocities) to a physical system including very many particles. Now, a many-particle system can be dealt with using either descriptive statistics, or inferential statistics. If it is decided to use descriptive statistics, there is no need of statistical significance tests. Otherwise, if the differential equations of dynamics are solved without bothering with initial conditions, probability theory is implied.
Probability theory calls degrees of freedom the independent parameters
(http://math.stackexchange.com/questions/237790/what-is-degree-of-freedom-in-statistics).
I hope that this partially answers your question.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Mechanics
- Classical Mechanics