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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.
$$V_{\text{exp}} \pm \sigma_{V_{\text{exp}}}$$ 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.
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