I am attempting to investigate to what quantitative degree a physical theory agrees with observations of the phenomena it predicts (specifically, Fraunhofer theory). I want to use the chi-squared test to produce some confidence levels in the measurements made in different sections of the experiment. The chi-squared test, as far as I'm aware, is just like any other statistical test in that it requires both a null and an alternative hypothesis. I believe that these need to be quite specific in order to make valid conclusions. What I would like is a some advice as to how to proceed with wording these hypotheses. Currently I have: H0: No difference exists between the results expected from Fraunhofer theory and observations made of diffraction phenomena in the Fraunhofer regime. H1: The results expected from Fraunhofer theory and observations made of diffraction phenomena in the Fraunhofer regime disagree at a particular level of precision. I'm a little unsure on the alternative hypothesis in particular. I'm not quite sure how to word it; essentially what we are expecting is that to some quantitative degree, such as 1 in 50, 1 in 100 etc. the measured results will not line up with the expected results. Any and all help will be much appreciated.