  The study of the relative phase between strong and electromagnetic amplitudes
is of great importance for understanding the dynamics of charmonium decays. The
information of the phase can be obtained model-independently by fitting the
scan data of some special decay channels, one of which is $\psi^{\prime} \to
K^{+}K^{-}$. To find out the optimal data taking strategy for a scan experiment
in the measurement of the phase in $\psi^{\prime} \to K^{+} K^{-}$, the
minimization process is analyzed from a theoretical point of view. The result
indicates that for one parameter fit, only one data taking point in the
vicinity of a resonance peak is sufficient to acquire the optimal precision.
Numerical results are obtained by fitting simulated scan data. Besides the
results related to the relative phase between strong and electromagnetic
amplitudes, the method is extended to analyze the fits of other resonant
parameters, such as the mass and the total decay width of $\psi^{\prime}$.
