# How to express the agreement between experiment and theoretical observation?

Let us suppose I have a value measured from experiment and given by $$V_{\text{exp}} \pm \sigma_{V_{\text{exp}}}$$ and a theoretical value given as $$V_{\text{the}} \pm \sigma_{V_{\text{the}}}$$

Is there a statistical way to measure how well $$V_{\text{the}}$$ matches with the $$V_{\text{exp}}$$.

In other words, what is the right way to tell that $$V_{\text{the}}$$ is a valid theory (or not) for the given experimental result?

It seems to be that we should take the difference,

$$(V_{\text{exp}} \pm \sigma_{V_{\text{exp}}})- (V_{\text{the}} \pm \sigma_{V_{\text{the}}})$$

and that is $$(V_{\text{exp}} - V_{\text{the}}) \pm \sqrt{\sigma_{V_{\text{exp}}}^2 + \sigma_{V_{\text{the}}}^2} \equiv \Delta V \pm \sigma_{\Delta V}$$

If $$\Delta V - \sigma_{\Delta V} < 0 < \Delta V + \sigma_{\Delta V}$$ we say that the theory is valid I guess. But is a there a measure of how valid...like at which $$\sigma$$ ?

I guess it is $$\frac{\sigma_{\Delta V}}{\Delta V}$$, but I am not sure. Any help would be appreciated.