This work examines the accuracy of different many-body methods for the calculations of parity violating electric dipole (E1PV) amplitudes in atomic systems. In the last decade, many different groups claim to achieve its accuracy below 0.5%, for the 6s2S1/2 → 7s2S1/2 transition in the 133Cs atom. One of the major issues in these calculations is the opposite signs among the core correlation contribution from different works. To estimate E1PV of the above transition, various groups have used different many-body methods both in the linear response and sum-over-states approaches. By examining how these methods capture various electron correlation effects, we identify the underlying cause of sign discrepancies in the previously reported results. We also demonstrate how the double-core polarization effects and scaled wave functions influence estimation of the E1PV amplitudes. The comprehensive discussions provided in this work will not only aid in our understanding on the potentials of the employed many-body methods, but it will also serve as a road map for improving the E1PV calculation in the atomic systems further.