I have the following problem:
I want to compare two different quantification processes and I use the coefficient of variation as quality metric. So in principle my data look like:
experiment method1 method2
1 a11 a12
2 a21 a22
3 a31 a32
and so on
method 2 gives a lower CoV (standard deviation / mean). However the question is: is it statistically significant?
If the coefficient of variation is defined by $$\text{CV}=\dfrac{\sqrt{\text{Var}[X]}}{\mathbb{E}[X]}.$$
If you estimate the coefficient of variation by $\hat{\text{CV}}=s/\bar{x}$. You can use the following confidence intervals $\text{CI}$ to see if all coefficients lie inside the same confidence interval (hence, no change).
$$\text{CI}:\hat{\text{CV}}\pm z_{1-\alpha/2}\sqrt{\dfrac{\hat{\text{CV}}^4+0.5\hat{\text{CV}}^2}{N}}.$$
In which $N$ is the sample size.