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.

Since you are only dealing with mean values and their standard errors, you can rephrase the task as comparing the (assumed) norm distribution of the sample mean and the distribution of the theoretical mean (and its variation, given a certain sample size).
Assuming normal distributions, this task can be achieved by the KS-test which allows to compare two distributions.
