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Number of degrees of freedom in the sigma estimate

  1. Mar 12, 2010 #1
    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
    [tex]\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}},[/tex]
    where [tex]N_{X}, N_{Y}, \mu_{X}, \mu_{Y}, \mu_{XY} [/tex] 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 [tex]N-1=25-1=24[/tex] degrees of freedom... is this correct?
     
  2. jcsd
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