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I got two samples, let's say X1 = [1,2,3,4] and X2 = [3,4,5,6]. Now I calculated the speedup as $\frac{\bar{X_1}-\bar{X_2}}{\bar{X_2}}$.

Can someone help me how I calculate the combined standard deviation of this speedup? Is it correct that I have to apply Fieller's Theorem? https://en.wikipedia.org/wiki/Fieller%27s_theorem How does this work out in that case, since it's not a simple fraction?

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Notice that $(\bar{X}_1-\bar{X}_2)/\bar{X}_2 = (\bar{X}_1/\bar{X}_2)-1$.

Now further notice that subtracting a constant doesn't change the standard deviation, so $\text{sd}(\frac{\bar{X}_1}{\bar{X}_2}-1) = \text{sd}(\frac{\bar{X}_1}{\bar{X}_2})$.

And therefore the calculation is for that of a simple ratio of averages.

So the theorem in question should apply directly (as long as otherwise the conditions for it to work still hold).

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