I'm currently working on a research on photometry of eclipsing binary stars with the goal of deriving new values on their stellar properties. How do I test my hypothesis to determine if there is difference in the values?
I would need to know the hypothesis being tested and the data set against which it is being tested. What are the properties that you wish to re-evaluate. Statistical tools are not "one-size fits all", they must be tailored to the problem under consideration.
I agree completely with Dwight Hoxie. I would add that besides measuring values of the “properties” at various times, you will need error models of the measurements that are as accurate as you can make them. At some point you will need to determine whether any observed changes in the “property” values can be explained by statistical fluctuations in your measurement errors instead of actual changes in the stars. Error models treat measurement errors as random variables, hence they must include the distributions of the random variables (e.g., Gaussian, Uniform, Poisson, etc.).
You should also think about the trade-off you want between the cost of saying the properties have not changed when in fact they have versus the cost of saying the properties have changed when in fact they have not. That trade-off will determine the level of statistical significance to be used as a threshold if you end up using a traditional test of statistical significance, and it plays an even bigger role if you implement a full-blown decision theory.
It is also good to be on the lookout for possible correlations in your measurement errors, although I suppose that is included in “error models of the measurements that are as accurate as you can make them”. Good luck!
The photometric uncertainties (error bars) at each point in your light curve will imply a range of possible fits for eclipse depth and, to a lesser extent, duration. These will then translate into a range of model values for stellar radii etc. So as the other respondents have pointed out, whether your inferred stellar properties are genuinely different to the “accepted” values will depend on what the error bars on them are.