Degrees of freedom
- Thread starter ron
- Start date
It's the number of independent data points or observations, or the number that are free to vary.
If you have a sample of 4 numbers, and you tell me three of them along with the sample mean, I can "determine" what the 4th number is - in other words, it's determined by the other 3 items and the sample mean - it's not free to vary. That's why degrees of freedom is often n-1.
If you have a sample of 4 numbers, and you tell me three of them along with the sample mean, I can "determine" what the 4th number is - in other words, it's determined by the other 3 items and the sample mean - it's not free to vary. That's why degrees of freedom is often n-1.
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Degrees of Freedom
Used in slightly different senses throughout the study of statistics, Degrees of Freedom were first introduced by Fisher based on the idea of degrees of freedom in a dynamical system (e.g., the number of independent co-ordinate values which are necessary to determine it). The degrees of freedom of a set of observations are the number of values which could be assigned arbitrarily within the specification of the system. For example, in a sample of size n grouped into k intervals, there are k-1 degrees of freedom, because k-1 frequencies are specified while the other one is specified by the total size n. Thus in a p by q contingency table with fixed marginal totals, there are (p-1)(q-1) degrees of freedom. In some circumstances the term degrees of freedom is used to denote the number of independent comparisons which can be made between the members of a sample.
Degrees of Freedom
Used in slightly different senses throughout the study of statistics, Degrees of Freedom were first introduced by Fisher based on the idea of degrees of freedom in a dynamical system (e.g., the number of independent co-ordinate values which are necessary to determine it). The degrees of freedom of a set of observations are the number of values which could be assigned arbitrarily within the specification of the system. For example, in a sample of size n grouped into k intervals, there are k-1 degrees of freedom, because k-1 frequencies are specified while the other one is specified by the total size n. Thus in a p by q contingency table with fixed marginal totals, there are (p-1)(q-1) degrees of freedom. In some circumstances the term degrees of freedom is used to denote the number of independent comparisons which can be made between the members of a sample.