The results of the FCRAO Extragalactic CO Survey are used to examine the trends in the global star formation efficiency among galaxies as a function of galaxy size and environment. For isolated spiral galaxies, Virgo cluster spiral galaxies, pairs, and field spiral galaxies, an intriguing new result indicates that the global star formation efficiency decreases as the galaxy size increases. The galaxies in these diverse environments all exhibit the same trend in that the mean global star formation efficiency is 4 times smaller in galaxies 100 kpc in diameter compared to those only 10 kpc across. This trend may result from a greater shear in the disks of large galaxies, in which flat rotation curves are found, in contrast to the disks of smaller galaxies, in which rotation curves are rising over most of the disk. This shear would be expected to increase the turbulent energy in molecular clouds and to possibly reduce the efficiency of star formation. In sharp contrast to this trend of decreasing star formation efficiency with increasing galaxy size, the galaxies that are independently recognized to be merger remnants all display a completely different behavior in the star formation efficiency variation with galaxy size. At every galaxy size, the merger remnants display the largest star formation efficiencies observed. Furthermore, there appears to be a maximum star formation efficiency that merger remnants can maintain.