# Number of degrees of freedom in the sigma estimate

1. Mar 12, 2010

### Reid

1. The problem statement, all variables and given/known data
I have estimated the standard deviation of the population of my samples from the standard deviations from each of the samples with the equation found below. And I am to construct a confidence interval for a contrast, thus I will need the number of degrees of freedom for which the estimate of the standard deviation is based on. And I really can't tell!

2. Relevant equations
The estimation of the standard deviation is given by
$$\sigma=\sqrt{\frac{N_{X}(\sigma_{X}^{2}+\mu_{X}^{2})+N_{Y}(\sigma_{Y}^{2}+\mu_{Y}^{2})}{N_{X}+N_{Y}}-\mu^{2}_{XY}},$$
where $$N_{X}, N_{Y}, \mu_{X}, \mu_{Y}, \mu_{XY}$$ are the sample populations of samples X and Y, the means of samples X, Y and the mean of the entire population XY.

3. The attempt at a solution
For every estimate of a population one looses one degree of freedom but then the standard deviation would be based on $$N-1=25-1=24$$ degrees of freedom... is this correct?