<p>Testing the rigidity-dependent modulation of cosmic rays (CRs) through superposed epoch or quantitative regression analysis requires precise FD event timing and accurate FD magnitude of real Forbush events. However, superposition tendencies in raw CR data make analysis of CR data a non-trivial exercise. The current work demonstrates that analytical transformation of observational data, such as harmonic analysis, is required to separate the smoothed signal frequency components and other superposed spurious signals from the high-frequency component, which contains the real FD events. Given the comparative detailed and rigorous analyses performed, we speculate that some existing articles in the field, which selected FDs from raw CR data, may contain FD catalogs whose magnitude, number, and timing might possibly be biased by unwanted or spurious signals, such as 11-year solar cycle variations and CR anisotropies. For the first time, rigidity dependence modulation of CRs is tested using FD lists selected through detailed and rigorous analyses. The magnitude and timing of the FDs are not biased by spurious signals. Rather than the commonly employed two-variable regression model, we used multivariate regression analysis, taking into account contributions from other NM characteristics. We find that rigidity, altitude, latitude, and longitude make significant contributions to CR intensity variations.</p>