8.2:
Degrees of Freedom
The degree of freedom is the number of independent pieces of information or sample values required to perform any calculation.
The degrees of freedom vary significantly depending on what is already known or what is required to be calculated.
Consider the spots on seven dalmatians with a mean of 100 spots. Here, the first six counts can be freely assigned.
Since the sum of the seven sample values is 700, the seventh sample value must be equal to 700 minus the sum of the first six counts, which is 100.
Since the first six counts are independent, while the seventh count is dependent on other values, there are six degrees of freedom.
Therefore, the number of degrees of freedom is the sample size minus one.
The degrees of freedom are used to calculate standard deviation and statistical estimates such as the Student t-distribution and the Chi-Square distribution tests.
8.2:
Degrees of Freedom
The degree of freedom for a particular statistical calculation is the number of values that are free to vary. Thus, the minimum number of independent numbers can specify a particular statistic. The degrees of freedom differ greatly depending on known and uncalculated statistical components.
For example, suppose there are three unknown numbers whose mean is 10; although we can freely assign values to the first and second numbers, the value of the last number can not be arbitrarily assigned. Since the first two are independent, with the third one dependent, the dataset is said to have two degrees of freedom. In many statistical methods, the number of degrees of freedom is usually calculated as one minus the sample size. The degrees of freedom have broad applications in calculating standard deviation and statistical estimates in methods such as the Student t distribution and the Chi-Square distribution tests.