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The effect of correlations between model parameters and nuisance parametersis discussed, in the context of fitting model parameters to data. Modificationsto the usual $\chi^2$ method are required. Fake data studies, as used atpresent, will not be optimum. Problems will occur for applications of theMaltoni-Schwetz \cite{ms} theorem. Neutrino oscillations are used as examples,but the problems discussed here are general ones, which are often notaddressed.

Effect of Correlations Between Model Parameters and Nuisance Parameters When Model Parameters are Fit to Data