Degrees Of Freedom

Degrees Of Freedom

 In statistics,the number of values in the final calculation of a statistic that are free to vary

Any of the unrestricted, independent random variables that constitute a statistic. 

The number of degrees of freedom is a measure of how certain we are that our sample population is representative of the entire population - 

the more degrees of freedom, usually the more certain we can be that we have accurately sampled the entire population 

For example, if you have to take ten different courses to graduate, and only ten different courses are offered, then you have nine degrees of freedom. Nine semesters you will be able to choose which class to take; the tenth semester, there will only be one class left to take - there is no choice, if you want to graduate. 

In many statistical problems we are required to determine the degrees of freedom. This refers to a positive whole number that indicates the lack of restrictions in our calculations. The degree of freedom is the number of values in a calculation that we can vary.

we suppose that we know the mean of a data set is 25, with values 20, 10, and two unknown values. These unknowns could be different, so we use two different variables, x and y to denote this. The resulting formula is (20 + 10 + x + y)/4 = 25. With some algebra we obtain y = 70 - x. The formula is written in this form to show that once we choose a value for x, the value for y is determined. This shows that there is one degree of freedom.

Student t Distribution

  When the population standard deviation () is unknown and the sample size is less than 30 (n < 30), the distribution of the test statistic can not be guaranteed to be normal. In fact, the test statistic can be said to conform to what is called a t distribution.

Web  (purpose of df)

Chi-Square Distribution