Re: Citation for df formula

Bruce Weaver <bweaver@xxxxxxxxxxxx> wrote in
news:fa4c5o02ujb@xxxxxxxxxxxxxxxxx:

Scott Seidman wrote:
Can anyone provide a reference for the fractional degree of freedom
formula at http://www.andrews.edu/~calkins/math/edrm611/edrm10.htm??

Thanks in advance!



Dave Howell's "Statistical Methods for Psychology" (2007, 6th edition)
gives that same formula for df, *except* that the bit in the first
pair of parentheses is squared. I.e.,

Let a = (s1^2/n1 + s2^2/n2)^2
Let b = (s1^2/n1)^2 ÷ (n1-1)
Let c = (s2^2/n2)^2 ÷ (n2-1)

df = a / (b + c)

Howell attributes this formula to Welch (1938) and Satterthwaite
(1946), and says that they apparently developed it independently.
Both papers are available as PDFs if your institution has access to
JSTOR and Biometrika.


Satterthwaite FE. 1946. An approximate distribution of estimates of
variance components. Biometrics Bull 2:110?4.

Welch BL. 1938. The significance of the difference between two means
when the population variances are unequal. Biometrika 29:350?62.



Excellent!! Thanks so much, to both responders.

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Scott
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