The sizes of galaxies are known to be closely related with their masses, luminosities, redshifts and morphologies. However, when we fix these quantities and morphology, we still find large dispersions in the galaxy size distribution. We investigate the origin of these dispersions for red early-type galaxies, using two SDSS-based catalogs. We find that the sizes of faint galaxies (${log}(M_{dyn}/M_{odot})$ < 10.3 or $M_r$ >-19.5) are affected more significantly by luminosity, while the sizes of bright galaxies (${log}(M_{dyn}/M_{odot})$ > 11.4 or $M_r$ <-21.4) are by dynamical mass. At fixed mass and luminosity, the sizes of low-mass galaxies (${log}(M_{dyn}/M_{odot})$ ~ 10.45 and $M_r$~-19.8) are relatively less sensitive to their colors, color gradients and axis ratios. On the other hand, the sizes of intermediate-mass (${log}(M_{dyn}/M_{odot})$ ~ 10.85 and $M_r$~-20.4) and high-mass (${log}(M_{dyn}/M_{odot})$ ~ 11.25 and $M_r$~-21.0) galaxies significantly depend on those parameters, in the sense that larger red early-type galaxies have bluer colors, more negative color gradients (bluer outskirts) and smaller axis ratios. These results indicate that the sizes of intermediate- and high-mass red early-type galaxies are significantly affected by their recent minor mergers or rotations. Major dry mergers also may have influenced on the size growth of high-mass red early-type galaxies.