Seismic magnitude has been an indistinct concept since modern seismology
was established. The author discusses it thoroughly , provides an
general expression of definition that is only relevant to the source
characteristics and explains the magnitude conversion problem
physically. Based on the essential understanding of magnitude estimation
problems, the author introduces a method called two-way fixed effects
regression, which has been applied in seismology since Keiiti Aki
studied the properties of coda waves. A series of check tests are
carefully designed to examine the hypotheses of this method and then the
author applies it to the error analysis of the peak ground acceleration
magnitude. The source, path and site errors are estimated by this
approach and the robustness of separation is checked. The acquired
knowledge about the errors in magnitude estimation may help us to
improve the precision of magnitude estimation during earthquake early
warning.