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The number of independent measurements available for estimating a population parameter
This crops up everywhere in statistical tests, and is used to calculate the p value. It is a fairly deep mathematical topic and we need not go fully into it here. Broadly speaking, the larger the sample size, the larger the df: the smaller the sample, the smaller the df. However, this is modified by the number of groups you have and the parameters being estimated. A small df makes it more difficult to detect significance.
In statistics, degrees of freedom (df) are generally calculated as the sample size minus the number of estimated parameters. So as an example, the distribution has -1 df since we estimate the sample's standard deviation. Furthermore, since we define and since Thus knowledge of only the first -1 of their values also specifies so there really are only -1 differences that are free to vary. Thus dividing by -1 gives the average of the freely varying squared differences between the 's and . Of course, when becomes very large, there is very little difference between dividing by -1 versus . Another compelling reason for dividing by -1 is that when we observe the elements of a random sample, from a population, it is not true that 2 is equal to the population variance . If we were repeatedly to take random samples of the same size and compute 2 for each of them, the long-term average of these 2 values would be , which is the basis for using 2 as a reasonable estimate of . Dividing by -1 for small samples especially, gives a more conservative estimate of the population variance.
The number of values/amounts that are free to vary in one calculation. Degrees of freedom are used in the formulas that test hypotheses statistically..
This term is used by Fuller to mean the number of independent forces necessary to completely restrain a body in space, or by others in reference to the overall stability of systems.
( df): A structural aspect of the experimental design, determined by the number of scores and not their values.  The general rule is that each observation generates one df.  The number of elements in each subdivision of the design determines the allocation of df s to structural units.  Some statistical tests, among them F and t, require df specification to determine critical values.
1). The number of independent comparisons that can be made in a set of data. 2). The maximum number of quantities whose values are free to vary before the remainder of the quantities are determined.
( Stat.) The number of independent comparisons; the number of deviations, or items, minus the number of constants, computed from the sample for fixing the points from which the deviations are measured. ( USFT).
Each joint having 1 degree of freedom implies that a simple robotic arm with 3 degrees of freedom may move in three ways: left and right, forward and backward, and up and down
The number of ways in which the results in a table can vary, given the column and row totals. The above table has 6 data cells (excluding the totals and the labels, and shown in blue above): 2 columns and 3 rows of data. If a figure in one row or column is changed, another has to change in the opposite direction to maintain the total. Thus degrees of freedom ( df for short) is columns-minus-1 times rows-minus-1, or in this case 2.
In an unconstrained dynamic or other system, the number of independent variables required to specify completely the state of the system at a given moment. If the system has constraints, that is, kinematic or geometric relations between the variables, each such relation reduces by one the number of degrees of freedom of the system. In a continuous medium with given boundary conditions, the number of degrees of freedom is the number of normal modes of oscillation. Thus, a particle moving in space has three degrees of freedom; an incompressible fluid with a free surface has an infinite number of degrees of freedom.
An estimate of the number of independent categories in a particular statistical test or experiment.
Robots are typically capable of movement along a number of axes; these movements can be rotational or translational. The number of axes of movement (degrees of freedom), their arrangement and their sequence of operation, permits movement of the robot to any point within its envelope. Robots have three arm movements (up-down, in-out, side-to-side). In addition, they can have as many as three additional wrist movements on the end of the robot's arm: yaw (side to side), pitch (up and down), and rotational (clockwise).
Probability distributions for test statistics (t, F, Ï‡ 2) are families of curves that have lightly different shapes, depending on sample size. In order to locate the correct distribution among these families, the degrees of freedom are determined from the research sample size.
For chi-square tests, the number of cells in the table whose expected number of subjects does not depend on the expected number of subjects in other cells.
The number of distinct quantities required to represent a set of numbers. When discussing variability or comparison, the degrees of freedom are one fewer than the number of distinct quantities being compared.
The number of independent variables that must be specified to determine the state of a system. For example, to specify the position of a molecule, the x, y, and z coordinates are required, so it has 3 degrees of freedom. A collection of N molecules has 3N degrees of freedom. However in some cases, such as a diatomic molecule, certain degrees of freedom are restricted, reducing the number. See the short discussion elsewhere
of Independent Forces Needed to Restrain a Body in Space
The number of statistically independent features in biometric data.
A phrase used in mechanical vibration to describe the complexity of the system. The number of degrees of freedom is the number of independent variables describing the state of a vibrating system.
The number of degrees of freedom explains how many values are free to vary in the final calculation of a statistic.
The degrees of freedom is the number of values in the calculation of a statistic that are free to vary - the total number of observations in the sample minus the number of samples.
Statistics: Tables of t-distribution involve the idea of degrees of freedom. Expressed simply, the number of degrees of freedom is the size of the sample N, minus the number k of the population parameters (constraints), that must be estimated from the sample observations.
A statistical term indicating the number of variables or data points used for testing a relationship. The greater the degrees of freedom, the greater the confidence that can be placed on the statistical significance of the results.
The number of independent variables in the system. Each joint in a serial robot represents a degree of freedom.