Astronomy

Is threre a relation between relative or absolute error and standard deviation for ratio of power spectra?

Is threre a relation between relative or absolute error and standard deviation for ratio of power spectra?

I have to compute the variance on this ratio, that is to say on the observable $O$ :

$$O=left(frac{C_{ell, mathrm{gal}, mathrm{sp}}^{prime}}{C_{ell, mathrm{gal}, mathrm{ph}}^{prime}} ight)=left(frac{b_{s p}}{b_{p h}} ight)^{2}quad(1)$$

where $C'_{ell}$ are angular power spectra (or matter power spectra).

Can I apply for this the computation of relative or absolute error like in electricity, we have $U=RI$ and the error on the quantity $R$ :

$$dfrac{Delta R}{R}= dfrac{Delta U}{U}+dfrac{Delta I}{I}$$

Is there a relation between absolute or relative error with the standard deviation of theses ratio ?

I would like to apply it to equation($1$) to compute this error or variance : is the right method ? If not, which solution would be possible ?

I have difficulties to grasp the subtilities between uncertainty and standard deviation : I just need to compute $sigma_{o}^{2}$.