# Fieller's Theorem Degrees of Freedom

In a previous question I was trying to figure out how to compute the confidence interval of a ratio. Having come to the conclusion that the correct way to do this is Fieller's Theorem, I realize I'm very unsure about my interpretation of the degrees of freedom.

I'm trying to compute confidence intervals for a speedup -- computed as a ratio:

$$\frac{\text{time mean}_{\text{1 thread}}}{\text{time mean}_{n \text{ threads}}}$$

Each thread count has $k$ samples.

I want to say I need 1 degree of freedom here... but I also have been known to be wrong in these things before...

• Online documentation indicates the degrees of freedom will be $a+b-2,$ where $a$ is sample size of numerator and $b$ is sample size of denominator. Why do you think it should be 1 degree of freedom? – soakley Aug 23 '13 at 20:20
• A day later, I now... don't really recall. :S I grabbed my stats book and agree that $a + b - 2$ is reasonable (though, it doesn't have Fieller's Theorem). – Matthew G. Aug 23 '13 at 21:44