Chapter 10 - Hypothesis Testing and Effect Size, and Confidence Intervals: Two-Sample Designs - Problems - Page 205: 10.6

There are 2 approaches to determining the number of degrees of freedom .

1. We use the sample size N and subtract from it the number of necessary relationships for the data. For example, for a group of values for which the sample standard deviation is to be calculated, a necessary condition is that the sum of the deviations from the mean must be equal to zero. This single necessary relationship means that the number of degrees of freedom is one less that the sample size, or N-1. 2. A second approach to the number of degrees is to consider the number of parameters that are estimated by the sample statistic. For the standard deviation, the calculation has N-1 degrees of freedom because the value X is used as an estimate of (mu). For the liner regression correlation coefficient, the number of degrees of freedom is N-2 because the value of r, the correlation coefficient, is used in the calculation of the liner regression model Y=a+bX, which has 2 parameters, a and b.