We present a comparative analysis of various methods to study the $\rho \rightarrow \pi \pi$ resonance. We use $N_f=2+1$ of clover fermions at a pion mass of approximately $320$ MeV and a lattice size of approximately $3.6$ fm, to investigate two ways of determining the parameters of the elastic $\pi\pi$ scattering; one is by extracting infinite volume phase shifts using the L\"uscher analysis and the other is by directly fitting a model for the $T$-matrix to the energy spectrum. We find that both methods give consistent results, and obtain$m_\rho = 0.7976(28){stat}(24){sys}(54){a}\:\:{\rm GeV}$ and $g{\rho\pi\pi} = 5.69(13){stat}(16){sys}$. The two- and three-point functions required are evaluated by implementing combinations of stochastic and sequential propagators.

Hadron Spectroscopy and Interactions