if the total sample size is 75, what is the degree of freedom for the correlation coefficient?

Question

if the total sample size is 75, what is the degree of freedom for the correlation coefficient?

Answer 1

The term degrees of freedom refers to the number of scores within a data set that are free to vary. In any sample with a fixed mean, the sum of the deviation scores is equal to zero. If your sample has an n equal to 10. The first 9 scores are free to vary but the 10th score must be a specific value that makes the entire distribution equal to zero. Therefore in a single sample the degrees of freedom would be equal to n - 1.

 

The degrees of freedom for a correlation is slightly different because n equals number of pairs not simply sample size. Therefore, the degrees of freedom for a correlation in n - 2. So to calculate the degrees of freedom you simply take the number of pairs and subtract two.

 

Therefore the degrees of freedom is n - 2 => 75 - 2 = 73.